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Laboratory Studies of the Entrainment Zone of a Convectively Mixed Layer
Abstract
In laboratory experiments of simulated atmospheric mixed layers the entrainment zone is investigated from measurements of horizontally averaged temperature and buoyancy flux, and from visual observations of penetrating thermals using a spread laser beam. The region of negative buoyancy flux of entrainment is found to be confined between the outermost height reached by the few most vigorous penetrating parcels, and by the lesser height where mixed-layer fluid occupies, usually, some 90 to 95% of the total area. The height of most negative buoyancy flux of entrainment is found to agree roughly with the level at which mixed-layer fluid occupies half the area.
... air from the free atmosphere. Deardorff et al. (1980) found in laboratory experiments that the ratio of the entrainment zone thickness to the depth of the mixing layer decreases asymptotically with increasing Richardson number as follows (ℎ 2 − ℎ 1 )/ℎ 1 = 0.21 + 1.31/ (see figure 1 for the definitions of ℎ 1 and ℎ 2 ). This ratio is essential for developing entrainment models and has been studied extensively (Lilly 1968;Sullivan et al. 1998;Zilitinkevich et al. 2012;Haghshenas and Mellado 2019). ...
... The potential temperature flux profile provides a precise and convenient demarcation between the mixed layer and the entrainment zone of the CBL (Deardorff 1979;Deardorff et al. 1980). Figure 1 shows a definition of the various length scales in the CBL. ...
... Figure 1 shows a definition of the various length scales in the CBL. Previous studies (Kaimal et al. 1976;Deardorff et al. 1980;Moeng and Sullivan 1994;Noh et al. 2003;Garcia and Mellado 2014;Haghshenas and Mellado 2019) showed that the potential temperature flux (including both the turbulent part and the diffusive part) in CBLs decreases linearly from its maximum value at the surface to a minimum value at = , and then increases steeply to zero in a narrow region ≤ ≤ ℎ 2 at the top of the boundary layer (figure 1). For typical CBLs the condition |d /d | ≪ * holds, which implies that the boundary layer is quasi-stationary (Nieuwstadt et al. 2016, Section 7.6). ...
We develop innovative analytical expressions for the mean wind and potential temperature flux profiles in convective boundary layers (CBLs). CBLs are frequently observed during daytime as the Earth's surface is warmed by solar radiation. Therefore, their modeling is relevant for weather forecasting, climate modeling, and wind energy applications. For CBLs in the convective-roll dominated regime, the mean velocity and potential temperature in the bulk region of the mixed layer are approximately uniform. We propose an analytical expression for the normalized potential temperature flux profile as a function of height, using a perturbation method approach in which we employ the horizontally homogeneous and quasi-stationary characteristics of the surface and inversion layers. The velocity profile in the mixed layer and the entrainment zone is constructed based on insights obtained from the proposed potential temperature flux profile and the convective logarithmic friction law. Combining this with the well-known Monin-Obukhov similarity theory allows us to capture the velocity profile over the entire boundary layer height. The proposed profiles agree excellently with large-eddy simulation results over the range of $-L/z_0 \in [3.6\times10^2, 0.7 \times 10^5]$, where $L$ is the Obukhov length and $z_0$ is the roughness length.
... In all such systems, the two major areas of interest are: 1) the convectively driven 'mixed layer' and 2) dynamics and fluxes through interfacial region sandwiched between turbulent mixed layer and the non-turbulent stably stratified region, often referred to as the 'entrainment zone' 11 . In order to better understand the formation and subsequent deepening of the convectively driven mixed layer, experimental studies 12,13 on the structure of turbulence have successfully established the integral length scale and the horizontal velocity scale in the bulk. ...
... In order to better understand the formation and subsequent deepening of the convectively driven mixed layer, experimental studies 12,13 on the structure of turbulence have successfully established the integral length scale and the horizontal velocity scale in the bulk. The length scale is nothing but the depth of the mixed layer (h) and the convection velocity (U * ) is defined as 11 , ...
... where, g is the gravitational constant, β is the coefficient of thermal expansion, ρ is the reference density, C p is the specific heat for fluid at constant pressure and Q b is the bottom heat flux. Experimental studies indicate that the thickness of the entrainment zone (Z p ) could typically reach upto 25 percent of that of the mixed layer 11 . These studies 11,14,15 emphasize on the importance of entrainment zone physics in understanding phenomena related to the growth/depletion of the mixed layer. ...
After the sunset, under calm and clear sky conditions, aerosol laden surface air-layer, cools radiatively to the upper atmosphere. Predominant effect of the radiative cooling on the vertical temperature profile extends to several hundred meters from the surface. This results in the development of a stable, nocturnal inversion layer. However, ground surface, owing to its higher thermal inertia, lags in the cooling process. Due to this about a meter thick air layer just above the ground can be (2-6)deg Celsius cooler than the ground. Thus, at the surface an unstable convective layer is present, which is capped by a stable inversion layer that extends up to several hundred meters. This configuration involving a convective mixed layer topped by a stably stratified inversion layer is a classic case of penetrative convection. Micrometeorological phenomenon at the surface, such as occurrence of fog, is determined by temperature profile, heat and moisture transport from the ground. Here, we present a computational study of the model penetrative convection, formed due to radiative cooling, in the nocturnal atmospheric boundary layer.
... Entrainment rate is an important parameter for understanding the fundamental physical entrainment processes; however, this parameter cannot be directly measured and instead needs to be inferred from other measurement results (Lenschow et al., 1999). The entrainment zone thickness (EZT) provides a possibility for parameterizing the entrainment rate (Deardorff et al., 1980). The top of the EZ can be regarded as the highest height that the thermal reaches within a region (Stull, 1988), while the bottom of the EZ is difficult to define and is usually taken subjectively as the height where about 5 %-10 % of the air on a horizontal plane has the FA characteristics (e.g., Deardorff et al., 1980;Wilde et al., 1985). ...
... The entrainment zone thickness (EZT) provides a possibility for parameterizing the entrainment rate (Deardorff et al., 1980). The top of the EZ can be regarded as the highest height that the thermal reaches within a region (Stull, 1988), while the bottom of the EZ is difficult to define and is usually taken subjectively as the height where about 5 %-10 % of the air on a horizontal plane has the FA characteristics (e.g., Deardorff et al., 1980;Wilde et al., 1985). The EZT is hence determined by the top and bottom heights of the EZ and reflects the recent mixing history driven mainly by the small-scale turbulent processes responsible for entrainment (Davis et al., 1997). ...
... Based on high-resolution time series of the instantaneous ABL depth retrieved by lidar or wind profiling radar, the standard deviation technique (e.g., Davis et al., 1997) and the cumulative frequency distribution method (e.g., Wilde et al., 1985;Flamant et al., 1997;Pal et al., 2010;Cohn and Angevine, 2000) have been employed to investigate the EZT. However, the above two methods yield EZT values with large differences (e.g., Pal et al., 2010); the choice of specific percentages of air having the FA characteristics for the definition of EZ bottom height varies (between 5 % and 15 %) among researchers (e.g., Deardorff et al., 1980;Wilde et al., 1985;Flamant et al., 1997;Cohn and Angevine, 2000;Pal et al., 2010). Moreover, considering F. Liu et al.: Characteristics of clear-day convective boundary layer 2983 that variations of ABL depths can result not only from entrainment but also non-turbulent processes (e.g., atmospheric gravity waves and mesoscale variations in the ABL structure), the methods depending on variations of ABL depth might not really characterize the true EZ (Davis et al., 1997). ...
Knowledge of the convective boundary layer (CBL) and associated entrainment
zone (EZ) is important for understanding
land–atmosphere interactions and assessing the living conditions in the biosphere. A
tilted 532 nm polarization lidar (30∘ off zenith) has been used for
the routine atmospheric measurements with 10 s time and 6.5 m height
resolution over Wuhan (30.5∘ N, 114.4∘ E). From
lidar-retrieved aerosol backscatter, instantaneous atmospheric boundary layer (ABL) depths are obtained
using the logarithm gradient method and Harr wavelet transform method, while
hourly mean ABL depths are obtained using the variance method. A new approach utilizing the full
width at half maximum of the variance profile of aerosol backscatter ratio
fluctuations is proposed to determine the entrainment zone thickness (EZT).
Four typical clear-day observational cases in different seasons are
presented. The CBL evolution is described and studied in four developing stages (formation,
growth, quasi-stationary and decay); the instantaneous CBL
depths exhibited different fluctuation magnitudes in the four stages and
fluctuations at the growth stage were generally larger. The EZT is
investigated for the same statistical time interval of 09:00–19:00 LT. It is
found that the winter and late autumn cases had an overall smaller mean (mean) and
standard deviation (SD) of EZT data compared to those of the late spring and early
autumn cases. This statistical conclusion was also true for each of the four
developing stages. In addition, compared to those of the late spring and early
autumn cases, the winter and late autumn cases had larger percentages of
EZT falling into the subranges of 0–50 m but smaller percentages of EZT
falling into the subranges of > 150 m. It seems that both the EZT
statistics (mean and SD) and percentage of larger EZT values provide measures of
entrainment intensity. Common statistical characteristics also existed. All
four cases showed moderate variations of the mean of the EZT from stage to stage. The
growth stage always had the largest mean and SD of the EZT and the quasi-stationary
stage usually the smallest SD of the EZT. For all four stages, most EZT values
fell into the 50–150 m subrange; the overall percentage of the EZT falling into
the 50–150 m subrange between 09:00 and 19:00 LT was > 67 % for
all four cases. We believe that the lidar-derived characteristics of the
clear-day CBL and associated EZ can contribute to improving our
understanding of the structures and variations of the CBL as well as providing a
quantitatively observational basis for EZ parameterization in numerical
models.
... The traditional approach to the formulation of parameterizations of subgrid-scale processes is to derive scaling laws that relate the net effect of such processes to variables resolved by the ESMs. These scaling laws are then tested with either field observations (e.g., Large et al., 1994;Price et al., 1986), laboratory experiments (e.g., Cenedese et al., 2004;Deardorff et al., 1980), or results from a high resolution simulations (e.g., Harcourt, 2015;Li & Fox-Kemper, 2017;Reichl et al., 2016;Wang et al., 1996). Rarely are parameterizations tested over a wide range of possible scenarios due to the logistical difficulty and high cost of running many field experiments, the time necessary to change laboratory setups, and computational demand. ...
... The LES simulation described in section 2.1, and many previous studies of penetrative convection, for example, Deardorff et al. (1980) and Van Roekel et al. (2018), show that the boundary layer depth grows as √ t . To be consistent, N h would have to scale as h 2/3 , but this is not observed in the LES simulations nor supported by theory. ...
... Here we summarize the derivation of the KPP boundary layer depth criterion for penetrative convection, because we could not find a succinct description in the published literature. Following Deardorff et al. (1980) we consider the vertical momentum equation for a parcel punching through the entrainment layer, ...
Plain Language Summary
Climate projections are often compromised by significant uncertainties which stem from the representation of physical processes that cannot be resolved—such as clouds in the atmosphere and turbulent swirls in the ocean—but which have to be parameterized. We propose a methodology for improving parameterizations in which they are tested against, and tuned to, high‐resolution numerical simulations of subdomains that represent them more completely. A Bayesian methodology is used to calibrate the parameterizations against the highly resolved model, to assess their fidelity and identify shortcomings. Most importantly, the approach provides estimates of parameter uncertainty. While the method is illustrated for a particular parameterization of boundary layer mixing, it can be applied to any parameterization.
... Entrainment-zone thickness (EZT), entrainment velocity w e (typically defined as the temporal rate of the ABL growth), and entrainment flux ratio A i (the negative ratio of entrainment to surface heat fluxes) are the three commonly-used parameters to describe entrainment processes in the atmospheric models (e.g., Fedorovich et al., 2004). In the past, most of the relevant entrainment studies were limited to laboratory experiments (e.g., Deardorff et al., 1980;Jonker and Jiménez, 2014), field measurements by using sodar (Beyrich and Gryning, 1998), radar profilers (Angevine et al., 1994;Cohn and Angevine, 2000), LiDAR (Flamant et al., 1997;Steyn et al., 1999;Hägeli et al., 2000;He et al., 2006;Träumner et al., 2011), and in-situ aircraft (Lenschow et al., 1999;de Arellano et al., 2004;Canut et al., 2010;Berkes et al., 2016), as well as numerical simulations with ABL bulk models (Conzemius and Fedorovich, 2006;Liu et al., 2016;Haghshenas et al., 2019) and large-eddy simulations (LESs) (e.g., Sullivan et al., 1998;Huang et al., 2011;Brooks and Fowler, 2012;Liu et al., 2018aLiu et al., , 2018bLiu et al., , 2019. Deardorff et al. (1980) found that the EZT normalized with the ABL height (ABLH) showed a strong relationship with w e normalized with the convective velocity scale (w * = [(g/θ 0 )z i Q s ] 1/3 ) from their laboratory experiments, and both showed a linear dependence on the Richardson number (Ri = (g/θ 0 ) ( Δθz i /w * 2 ) ), where g, θ 0 , Δθ, z i and Q s are gravitational acceleration constant, reference potential temperature value, potential temperature increment across the entrainment zone, the ABLH, and surface heat flux, respectively. ...
... In the past, most of the relevant entrainment studies were limited to laboratory experiments (e.g., Deardorff et al., 1980;Jonker and Jiménez, 2014), field measurements by using sodar (Beyrich and Gryning, 1998), radar profilers (Angevine et al., 1994;Cohn and Angevine, 2000), LiDAR (Flamant et al., 1997;Steyn et al., 1999;Hägeli et al., 2000;He et al., 2006;Träumner et al., 2011), and in-situ aircraft (Lenschow et al., 1999;de Arellano et al., 2004;Canut et al., 2010;Berkes et al., 2016), as well as numerical simulations with ABL bulk models (Conzemius and Fedorovich, 2006;Liu et al., 2016;Haghshenas et al., 2019) and large-eddy simulations (LESs) (e.g., Sullivan et al., 1998;Huang et al., 2011;Brooks and Fowler, 2012;Liu et al., 2018aLiu et al., , 2018bLiu et al., , 2019. Deardorff et al. (1980) found that the EZT normalized with the ABL height (ABLH) showed a strong relationship with w e normalized with the convective velocity scale (w * = [(g/θ 0 )z i Q s ] 1/3 ) from their laboratory experiments, and both showed a linear dependence on the Richardson number (Ri = (g/θ 0 ) ( Δθz i /w * 2 ) ), where g, θ 0 , Δθ, z i and Q s are gravitational acceleration constant, reference potential temperature value, potential temperature increment across the entrainment zone, the ABLH, and surface heat flux, respectively. Later, Fedorovich et al. (2004) further found that the normalized entrainment rate (i.e., w e /w * ) followed a − 1 power law with Ri when Ri< 10 and a − 1.5 power law when Ri > 10. ...
... For a convenience of discussion, w e is usually normalized with w * to investigate relationship with different ABL conditions such as stability. The normalized w e /w * can be expressed as a power function of Ri, which is given as follows (Deardorff et al., 1980) ...
Aerosols exert a profound impact on the atmospheric boundary layer (ABL) structures and entrainment processes. However, observational analysis of entrainment under heavily polluted condition is rarely documented due to insufficient measurements. In this study, vertical profiles of potential temperature, water vapor, and particulate matter with aerodynamic diameter smaller than 2.5 μm (PM2.5) measured by unmanned aerial vehicle (UAV), LiDAR-measured extinction coefficients, as well as surface observations are presented to investigate the impact of aerosol radiative effect on entrainment processes under heavy aerosol pollution conditions. Results show that aerosol radiative effect reduces surface heat fluxes and influences entrainment substantially. Observations indicate that the column-like plume rise structure is the instigator accounting for the entrainment processes observed during daytime. A well-established entrainment zone identified in the nighttime (e.g., 02:00 local standard time, LST) is mainly due to strong wind shear generating turbulence. The parameters describing entrainment processes are largely modified by aerosol radiative effect. Specifically, the jumps of scalars on the heavy pollution day are much larger than that on the clean day. Entrainment zone thickness enlarges substantially as PM2.5 concentrations increase. The bin-averaged ratios of entrainment to surface heat fluxes are close to a constant (about 0.21) but show a large standard deviation with aerosol pollution conditions. The dimensionless entrainment velocity does not follow the −1 power-law relationship with Richardson number for the heavily polluted conditions, which is consistent with the previous large-eddy simulation (LES) results. This observational study provides valuable evidence in support of high-resolution modeling studies of entrainment with heavily-polluted aerosol conditions.
... Due to the large-scale turbulent eddies in the entrainment zone, it is difficult to accurately locate the height of zero buoyancy flux in the upper layer, and Fedorovich et al. [7] and Conzemius and Fedorovich [3,4] adopted the height at which the The modified Ri * , using w m in place of w * as the velocity scale, takes full account of the buoyancy and shear effects on entrainment. With such a modified convective Richardson number, Kim et al. [17] gave the following three bulk scaling models: ∆z/z i = 0.075Ri −1 * + 0.0925, with w 2 m = w 2 * + 180.21u 2 * + 0.15 ∆U 2 + ∆V 2 ; (10) ∆z/z i = 2.68Ri −1 * , with w 2 m = w 2 * + 2.99u 2 * + 0.03 ∆U 2 + ∆V 2 ; (11) ∆z/z i = 1.12Ri −1 * + 0.08, with w 2 m = w 2 * + 4u 2 * + 0.1 ∆U 2 + ∆V 2 , (12) which are denoted in this study as Model 3, Model 4, and Model 5, respectively. Heng et al. [18] validated above models with their large-eddy simulation (LES) numerical results, and showed that the entrainment zone thickness predicted by Model 4 is consistent with the data of the barotropic and baroclinic atmosphere; however, the values of the proportional coefficients lead to deviations between the predicted results by the models and the numerical results. ...
... where C 1 , C 2 , and C 3 are constants, and Ri N is defined as (16) in which N is the Brunt-Väisälä frequency, and N 2 = (g/θ 0 )Γ θ . Extensive field observations and lab water tank experiments have shown that the fluctuations of the buoyancy flux near zero in the upper entrainment zone cause large deviations in the determination of the upper limit of z 2 [7,12,19,21], which makes the determination of ∆θ very difficult, and weakens the linearity of the fitted results of ∆z/z i . Hence, Jianning et al. [20] took Γ θ instead of ∆θ as the atmospheric stability parameter, in order to improve the accuracy of the fitted relationship, and obtained another form of the bulk scaling model (denoted here as Model 9) based on the energy relationship of thermals in the entrainment zone: ...
... The authors obtained C 4 = 1.44 with the data of Deardorff et al. [12] and Boers and Eloranta [16], but it was found that Model 9 failed to reflect the effect of the shear on the entrainment process. ...
Studying the thickness of the convective boundary layer (CBL) is helpful for understanding atmospheric structure and the diffusion of air pollutants. When there is velocity shear in CBL, the flow field structure is very different from that of shear-free CBL, which makes the thickness model of the entrainment zone deviate. A large-eddy simulation (LES) approach is carried out for a horizontally homogeneous, atmospheric CBL, with a shear effect promoted by velocity difference to explore the bulk scaling model of the entrainment zone thickness. The post-processed data indicate that the existing bulk scaling models cannot synthetically represent the effects of shear and buoyancy on entrainment, resulting in reduced accuracy or limited applicability. Based on the fraction of turbulent kinetic energy (TKE) used for entrainment, a different form of the characteristic velocity scale, which includes the shear effect, is proposed, and a modified bulk scaling model that uses a potential temperature gradient to replace the potential temperature jump across the entrainment zone is constructed with the numerical results. The new model is found to provide an improved prediction of the entrainment zone thickness in a sheared CBL.
... Continuous heat-flux profiles can be estimated from the evolution of mean temperature profiles based on a range of techniques (e.g. Deardorff et al. 1980;Bange et al. 2007) by utilizing the integrating and averaging capacity of the ABL, and thus linking ground-based flux measurements from masts and towers (2 m to below 100 m) with airborne observations, which are typically taken up to, or slightly above, the mixed-layer depth h. A quasi-Lagrangian integral method has been applied to temperature profiles taken at different distances from the coast by the remotely-piloted aircraft system (RPAS) Aerosonde (Holland et al. 2001) in strong katabatic outflows from the Antarctic continent (Knuth and Cassano 2014). ...
... The heat flux is calculated with the profile-integration method based on an algorithm developed for the SMARTSonde aircraft and used for the first time on RPAS data by Bonin et al. (2013). The general technique, which originates from Deardorff et al. (1980), is based on a simplified version of the prognostic equation for the potential temperature θ relating the change of the mean quantity with time to the flux divergence. After horizontally averaging and vertically integrating from the height z to h F0 , where h F0 is the height at which the flux is zero, assuming horizontal homogeneity, and neglecting diabatic processes, mean vertical motion and molecular diffusivity, then the sensible heat flux ...
... This level, which is typically several tens to a few hundred meters higher than the mixed-layer top itself, is the entrainment-zone top at z = h E Z T . We assume that the instantaneous inversion zone separating the mixed layer and the free atmosphere is quite thin for a snap-shot profile (Deardorff et al. 1980), and define h E Z T = 1.2h as a compromise between being sure to be out of the entrainment zone, but still have a substantial part of the free atmosphere covered. Above this height, we expect to find a steady change in temperature over time, and typically also distinct wind direction and/or wind-speed changes. ...
Profiles of the sensible heat flux are key to understanding atmospheric-boundary-layer (ABL) structure and development. Based on temperature profiling by a remotely-piloted aircraft system (RPAS), the Small Unmanned Meteorological Observer (SUMO) platform, during the Boundary Layer Late Afternoon and Sunset Turbulence (BLLAST) field campaign, 108 heat-flux profiles are estimated using a simplified version of the prognostic equation for potential temperature \(\theta \) that relates the tendency in \(\theta \) to the flux divergence over the time span between two consecutive flights. We validate for the first time RPAS-based heat-flux profiles against a network of 12 ground-based eddy-covariance stations (2–60 m above ground), in addition to a comparison with fluxes from a manned aircraft and a tethered balloon, enabling the detailed investigation of the potential and limitations related to this technique for obtaining fluxes from RPAS platforms. We find that appropriate treatment of horizontal advection is crucial for obtaining realistic flux values, and present correction methods specific to the state of the ABL. Advection from a mesoscale model is also tested as another correction method. The SUMO heat-flux estimates with appropriate corrections compare well with the reference measurements, with differences in the performance depending on the time of day, since the evening period shows the best results (94\(\%\) within the spread of ground stations), and the afternoon period shows the poorest results (63\(\%\) within the spread). The diurnal cycle of the heat flux is captured by the SUMO platform for several days, with the flux values from the manned aircraft and tethered balloon coinciding well with those from the SUMO platform.
... Observations and laboratory experiments show that the evolution of the CBL height as a whole is well described by integral (bulk) relationships [6][7][8], so refining the existing parametrizations of convection on their basis is reasonable. The integral CBL models are based on a set of equations whose unknown variables proportionality constants of the turbulent TKE flux from the entrainment layer to the free atmosphere for free convection and sheared convection, respectively constant of proportionality between average TKE in the CBL ...
... The values of the entrainment coefficient measured in the atmosphere and in laboratory experiments lie in an approximate range of (see Table 1 in [21]), i.e., in the nearly whole interval between the limiting regimes [18] and [22]. Naturally, with scatter like this, Eq. (3) involving the constant is generally unsatisfactory, although the observed values in atmospheric CBLs are usually close to [6,8,21,23]. It will be shown below that results from the analysis of the turbulence kinetic energy balance for a well-developed CBL in free convection under the assumption that the CBL integral buoyancy generation of turbulent kinetic energy (TKE) is completely compensated by dissipation. ...
... Assuming, after [27], that , we obtain (7) Given the linearity of the buoyancy flux profile (see Fig. 1), , we have the integral TKE balance equation for free convection (8) where and C 1 = 1 -2α 1 = are the dimensionless energy constants. If (4) is simplified by assuming that the amount of TKE in the CBL does not vary and ...
This paper discusses approaches to constructing bulk convective boundary layer (CBL) models
based on the concept of complete mixing. Large-eddy simulation (LES) results are used to test the basic similarity hypotheses. The empirical constants of the bulk CBL model that are obtained from LES data for the
case of free convection agree well with previously published data from laboratory experiments. It is also shown
that the flux of kinetic energy from the upper CBL boundary transported by gravity waves is small compared
with other components of the balance of turbulence kinetic energy (TKE) in the convective layer. The parametrization of TKE generation for the case of a sheared CBL in terms of the friction velocity and the average
wind velocity in the CBL is derived; all dimensionless constants of the theoretical model are obtained from
LES data. The results allow us to formulate an integral model of the sheared CBL suitable for practical use.
... Entrainment processes are complicated and are often associated with shear, convection, internal waves breaking etc (Thorpe, 1973;Lin and Linden, 2005). However, it is difficult to measure the entrainment rate directly (Gryning and Batchvarova, 1994;Deardorff et al., 1980;Bretherton et al., 1999;Flamant et al., 1997;Mok and Rudowicz, 2001;De Rooy and Siebesma, 2010;De Rooy et al., 2013;Jonker and Jimenez, 2014). ...
... The entrainment of a stably stratified layer into a turbulent mixed layer in a confined region has been studied in laboratory for different Richardson numbers (Kato and Philips, 1969;Cardoso and woods, 1993). The internal waves generated at the interface are transmitted into the stratified fluid (Deardorff et al., 1980). The modal structure of these waves appears to interact with the turbulence processes near the interface creating a nonuniform entrainment rate usually in steps. ...
... This may be related to the vertical wave number of the dominant wave which is dependent on the depth of the stratified layer as well as the horizontal cross section of the tank. A similar behavior is also observed in the deepening of plume outflow entering a preexisting stratified fluid in a confined region (Deardorff et al., 1980). Density interface (DI) between mixed regions and stratified fluids is ubiquitous in geophysical fluids as in atmospheric mixed layer during day or oceanic mixed layer. ...
In this paper a simple qualitative model of growth of a mixed layer adjacent to a uniform layer with a stably stratified layer is presented. The entrainment of a stably stratified layer into a turbulent mixed layer in a confined region was studied in laboratory for different Richardson numbers. The results for entrainment near a density stratified layer show that the entrainment rate is a weaker function of Ri than the case with a step density profile. It is also shown that the internal waves in the stratified region, with typical buoyancy period of about 10 s may interact with turbulence near the interface and create a non-uniform entrainment rate as an oscillatory behavior with a typical time scale of 150 s. The process is qualitatively consistent with processes associated with internal waves interaction with turbulence and create a momentarily buoyancy flux with different signs. Results of lidar observations of atmospheric boundary layer also show that the oscillation of aerosol layer is probably due to non-uniform entertainment in the interface between the mixed layer and free atmosphere. Although there seems to be a qualitative similarity between entrainment behavior at the top of the atmospheric mixed layer and laboratory experiments "mixing box", but the two are quite different as lab experiments are in an enclosure without mean flow, while the top of the mixed layer is a free solid boundary flow which may be associated with mean flow shear.
... We determined O 3 fire LFT by first averaging TOPAZ Δβ data vertically over 50 m just above the entrainment zone and then converted Δβ to LFT fire O 3 using Equation 1. Following Deardorff et al. (1980), we assumed an entrainment zone symmetric around z i with a thickness of 0.2 z i . Thus, we averaged the TOPAZ Δβ data between 1.1 × z i and 1.1 × z i + 50 m. ...
... The MDA8 wildfire contribution was chosen as the "8-hr" wildfire BL O 3 value for the same hour when MDA8 O 3 at the Rocky Flats site was reached. Our calculations suggest that entrained wildfire smoke increased the MDA8 concentrations in the Boulder/Rocky Flats area by ≈ 12 ± 1 ppbv on 12 July, with the error bar determined primarily by the uncertainties in Equation 1 and an estimated uncertainty of ±30% in the assumed baseline for β and to a lesser extent the assumed entrainment zone thickness (z i ) (Deardorff, 1980). ...
Ground‐level ozone (O3) was unusually high in northern Colorado in the summer of 2021 with maximum daily 8‐hr average (MDA8) concentrations 6 to 8 parts‐per‐billion by volume (ppbv) higher than in 2019, 2020, or 2022. One or more of the monitors on the Colorado Front Range exceeded the 2015 U.S. National Ambient Air Quality Standard (NAAQS) of 70 ppbv on 66 of the 122 days from 1 June to 30 September, and this record number of exceedances coincided with the near daily presence of dispersed smoke haze from wildfires in Arizona, California, and the Pacific Northwest. In this paper, we use regulatory and non‐regulatory surface O3 and PM2.5 measurements in conjunction with ground‐based lidar observations to estimate how much O3 was associated with the wildfire smoke. Analyses of the surface measurements suggest that pyrogenic O3 transported to northern Colorado with the smoke increased the surface concentrations in northern Colorado by an average of 8 ppbv in July, 3 ppbv in August, and 2 ppbv in September. Analysis of the lidar measurements showed these contributions to be as large as 12 ppbv on some days. Production of O3 from reactions of pyrogenic VOCs and locally emitted NOx appears to have been minimal (<3 ppbv) in the Boulder area, but may have been much larger in the suburbs southwest of downtown Denver.
... Relating the boundary-layer height with the depth of the aerosol layer has fostered the development of a multitude of methods to determine the boundary-layer depth focusing on the mid-latitude with a clear daily variation in the surface fluxes. These methods are fundamentally based on tank experiments by Deardorff et al. (1980) on the structure of the convective boundary layer. Deardorff et al. (1980) found the top of the mixed-layer "to agree roughly with the height at which mixed-layer fluid occupies one-half the area." ...
... These methods are fundamentally based on tank experiments by Deardorff et al. (1980) on the structure of the convective boundary layer. Deardorff et al. (1980) found the top of the mixed-layer "to agree roughly with the height at which mixed-layer fluid occupies one-half the area." In the threshold method, which was proposed by Melfi et al. (1985), the top of the aerosol layer (boundary layer) is assigned to the height of the layer close to the ground, where the attenuated backscatter reaches a fixed threshold. ...
The depth of the aerosol layer at the Villum Research Station at Station Nord in the high Arctic is analysed based on 8 years of observations from a ceilometer and one full year from a wind lidar. The layer is of particular interest for aerosol process modelling and atmospheric chemistry studies. The depth of the aerosol layer is assigned to the inflection point in the attenuated backscatter profile by two methods; one is based on polynomial approximation of the profile and the other is direct numerical differentiation. The analysis is based on two types of hourly profiles; one consists of averaging the attenuated backscatter observations and the other by computing the median. Due to sporadic occurrence of outliers in the ranges around 50 m in the ceilometer observations, this part of the profile is not used in this study. Restricting the observations to heights above 100 m, the depths of the aerosol layer are found to be typically ≈230 m. It varies little between winter and summer, but the spread in the depth is larger during the winter as compared to summer. To extend the study of the aerosol‐layer depth below 100 m, a method is applied that combines the ceilometer measurements with the carrier‐to‐noise ratio from the wind lidar. The results are available for 2018 only, and they show aerosol‐layer depths below ≈80 m as well as depths around 230 m and they show few observations between ≈80 and ≈230 m. Near the ground, the observed backscatter exhibits a pronounced seasonal variation, having low values during the summer and high values during the winter. The strength of the seasonal variability decreases with height, especially above the aerosol‐layer depth, and is virtually absent at 1 km.
... Since erosion proceeds from below, we assume that the gradient of composition inside the layer does not change over time. This approximation is common in laboratory experiments (Deardorff et al., 1980;Kato & Phillips, 1969;Levy & Fernando, 2002;Turner, 1986) and is well verified in our simulations, though to a lesser extent in the presence of double-diffusive motions ( Figure S4). With this assumption, the mass balance in the convective region writes 4 3̄c onv (t) ...
... The disperion of our data in Figure 3b, measured as the relative standard deviation to the power law (5) in logarithmic scale, is 15%. Such a large dispersion is common in previous investigations (see for instance scaling laws by Deardorff et al., 1980;Kato & Phillips, 1969;Strang & Fernando, 2001). This may originate from flows inside the layer, which modify the initial compositional profile, or from bursts in the convective velocity, which induce sudden variations in the erosion rate. ...
Seismic and geomagnetic observations suggest the presence of a stratified layer atop Earth's core. Previous laboratory experiments showed that this layer could be primordial, produced by a collision between the primitive Earth and a giant impactor. However, paleomagnetic data require turbulent flow motions in the core for the last 3.4 Ga. Such flows can erode an existing stratification. It is therefore unclear whether a primordial stratification still exists nowadays. Here, we use numerical simulations to investigate the erosion by thermal convection of a chemical layer atop Earth's core. Our scaling law predicts that a primordial layer thicker than 1 km with a density anomaly above 0.01% can survive 4.5 Ga of convective erosion. We conclude that the observed present‐day stratification could be a vestige of core formation. We also observe strong double‐diffusive flows in the layer. These might reconcile the existence of a stratification with the present‐day structure of the geomagnetic field.
... where b is the buoyancy of the parcel, assumed to be equal to the mixed layer value and b is the area mean buoyancy profile in the transition layer. This equation holds if the mean buoyancy profile is in hydrostatic balance and the area occupied by sinking plumes is small compared to the total area (Deardorff et al., 1980). Integrating from z = −h+ ∆h, where w ≡ w e , to z = −h, where the turbulence and particle descent vanish and hence w = 0, gives, ...
... The LES simulation described in section 2.1, and many previous studies of penetrative convection, e.g. (Van Roekel et al., 2018;Deardorff et al., 1980), show that the boundary layer depth grows as √ t. N h would have to scale as h 2/3 for KPP to correctly predict that deppening rate of the boundary layer, but this scaling is not observed in the LES simulations nor supported by theory. ...
... The latent heat consumed by sublimation of ice/snow particles (and in some cases by evaporation of water particles) falling into the dry air below the cloud base cools the air, making it heavier, thus giving rise to convective instability. Unlike the convective boundary layer (CBL) studied intensively since the 1960s (e.g., Ball, 1960;Betts, 1973;Deardorff, 1970;Deardorff et al., 1969Deardorff et al., , 1980Farmer, 1975;Kantha, 1980;Stull, 1973;Willis & Deardorff, 1974) and convection driven by cloud top cooling (Deardorff, 1976(Deardorff, , 1980, very little attention has been paid to Midlevel Cloud-base Turbulence (MCT), the term coined by Kudo (2013) to describe this phenomenon, although Below Cloud-base Turbulence (BCT) may be better in some ways. Most investigations of mixing in the free troposphere have focused on mixing induced by Kelvin-Helmholtz (K-H) instabilities driven by wind shear in a stably stratified atmosphere. ...
... (1) as shown by classical laboratory experiments by Deardorff et al. (1969Deardorff et al. ( , 1980 and Willis and Deardorff (1974). This changes somewhat when the entrainment is taken into account. ...
Midlevel Cloud‐base Turbulence (MCT) caused by ice/snow precipitation from midlevel clouds falling into dry air below the cloud base and sublimating is investigated. MCT phenomena in the lower troposphere as revealed by the Middle and Upper atmosphere (MU) radar in Shigaraki, Japan, during the Shigaraki unmanned aerial vehicle and radar Experiment campaigns in the spring‐summer of 2015 and 2016 are described. The MU radar was operated in a high‐resolution (~20‐m) range imaging mode and hence revealed the structure of these MCTs in great detail. These MCT layers grew to hundreds of meters in thickness, often reaching nearly 2,000 m in depth, lasting often for as much as 24 hr. A simple analytical model and a second‐moment closure‐based turbulent mixing model are used to estimate the levels of turbulence kinetic energy and its dissipation rate in the MCT layer and compare them to those measured by the MU radar. The study shows that MCT can give rise to moderate levels of turbulence of potential interest to aviation, confirming conclusions reached by earlier pioneering studies. However, to our knowledge, this important process has not received the attention it deserves by the atmospheric community so far, and therefore, it is the principal goal of this paper to not only present some observations and preliminary modeling results, but also redraw the attention of atmospheric scientists to this important process.
... Another aspect of the CBL entrainment that has not been systematically studied is associated with the limiting value of the entrainment rate in the regime of so-called free encroachment (also called the free entrainment in some earlier works), when the CBL is growing in the neutrally stratified atmosphere with N = 0 and with zero entrainment heat flux (hence, encroachment instead of entrainment; although the word entrainment is kept in the names of some parameters used to describe this regime). The growth of CBL by free encroachment was studied in laboratory experiments by Deardorff (1974) and Deardorff et al. (1980), and by means of numerical simulations in Sorbjan (1996) and Mellado (2012). These studies obtained rather varying estimates for the free-encroachment value of the dimensionless entrainment rate E = w * −1 (dz i /dt), where w * = [(g/ 0 )z i Q s ] 1/3 is the Deardorff convective velocity scale, g is acceleration due to gravity, and 0 is a constant reference temperature value (300 K in this study). ...
... Deardorff (1974) made a first estimate of the dimensionless entrainment rate E = (dz i /dt)/w * in a regime of free encroachment from the evolution of a morning-time temperature profile and found it to be constant with a value about 0.2. Deardorff et al. (1980) further quantified this value in a laboratory-tank experiment and obtained an approximate constant value of E = 0.24. Zilitinkevich's (1991) ZOM theory also predicted constancy of E in the regime of free encroachment. ...
... where z i is the boundary layer height; A e is the entrainment flux ratio, which is defined as the ratio of the downward heat flux at the CBL top to the upward heat flux at the surface, and is approximately a constant of 0.2 (Stull, 1976;Deardorff et al., 1980;Fedorovich et al., 2004;Sun, 2009); w θ s is the surface kinematic heat flux; γ is the lapse rate of the potential temperature in the free atmosphere above the CBL; and β is a parameter characterizing the relative stratification of the entrainment zone at the CBL top, which is approximately a constant of 0.9 for a purely buoyancy-driven CBL (Deardorff et al., 1980;Fedorovich et al., 2004;Sun, 2009). Rewriting Eq. (1) gives the prediction formula of the PBLH as follows: ...
... where z i is the boundary layer height; A e is the entrainment flux ratio, which is defined as the ratio of the downward heat flux at the CBL top to the upward heat flux at the surface, and is approximately a constant of 0.2 (Stull, 1976;Deardorff et al., 1980;Fedorovich et al., 2004;Sun, 2009); w θ s is the surface kinematic heat flux; γ is the lapse rate of the potential temperature in the free atmosphere above the CBL; and β is a parameter characterizing the relative stratification of the entrainment zone at the CBL top, which is approximately a constant of 0.9 for a purely buoyancy-driven CBL (Deardorff et al., 1980;Fedorovich et al., 2004;Sun, 2009). Rewriting Eq. (1) gives the prediction formula of the PBLH as follows: ...
Radiative aerosols are known to influence the surface energy budget and hence the evolution of the planetary boundary layer. In this study, we develop a method to estimate the aerosol-induced reduction in the planetary boundary layer height (PBLH) based on two years of ground-based measurements at a site, the Station for Observing Regional Processes of the Earth System (SORPES), at Nanjing University, China, and radiosonde data from the meteorological station of Nanjing. The observations show that increased aerosol loads lead to a mean decrease of 67.1 W m−2 for downward shortwave radiation (DSR) and a mean increase of 19.2 W m−2 for downward longwave radiation (DLR), as well as a mean decrease of 9.6 Wm−2 for the surface sensible heat flux (SHF) in the daytime. The relative variations of DSR, DLR and SHF are shown as a function of the increment of column mass concentration of particulate matter (PM2.5). High aerosol loading can significantly increase the atmospheric stability in the planetary boundary layer during both daytime and nighttime. Based on the statistical relationship between SHF and PM2.5 column mass concentrations, the SHF under clean atmospheric conditions (same as the background days) is derived. In this case, the derived SHF, together with observed SHF, are then used to estimate changes in the PBLH related to aerosols. Our results suggest that the PBLH decreases more rapidly with increasing aerosol loading at high aerosol loading. When the daytime mean column mass concentration of PM2.5 reaches 200 mg m−2, the decrease in the PBLH at 1600 LST (local standard time) is about 450 m.
... Because the equation of state around T md is nonlinear, this warming beneath the surface layer has the effect of increasing the local density (Chen and Millero 1986); thus, the incoming solar radiation acts as a destabilizing flux and works to form a region of reduced density stratification (Fig. 1b). Denser water lies above less dense water, creating an instability that leads to the formation of a convective mixed layer (h; Fig. 1c) where convective mixing occurs (Farmer 1975, Deardorff et al. 1980, Wells et al. 1999. ...
... Numerous studies during the open-water season have investigated convective mixing processes as a function of Ri (Deardorff et al. 1980, Ching et al. 1993, Wells et al. 1999. Laboratory experiments demonstrate mixing for Ri ≤ 1 (Ching et al. 1993); thus, when b > 0 (α < 0) and values of Ri are ≤1, a convective mixed layer will form. ...
Temperate lakes are ice covered for much of the year; however, winter lake conditions have not been well studied and are undergoing rapid change. Using data collected during ice-on periods from 4 north-temperate water bodies, we report observations of stable surface layers, solar-induced convective mixed layers, and their potential impacts on phytoplankton. The convective mixed layer is defined as the region where the convective Richardson number (Ri) is ≤1. In the absence of a convective mixed layer, peaks in chlorophyll a were near the ice–water interface. Light conditions here seemed sufficient to support phytoplankton biomass accrual in the short-term in 50% of our measurements, although snow depths >13.5 cm may lead to light limitation. When a convective mixed layer was present, light conditions were sufficient for biomass accrual in 37.5% of cases. The frictional timescale for damping averaged 15 minutes, indicative of a lack of mixing at night. Convective mixing depths and velocity increased as snow declined, and results demonstrated the potential for rapid convective mixed layer deepening (up to 6.6 m h −1), underscoring the highly dynamic physical environment under ice. Although declining periods of ice cover have been subject to much attention, changes in snow cover may have equally important implications for primary producers and the potential for under-ice blooms. This link between physics and biology must be further explored to better understand how changing winters will affect water bodies.
... Large and more energetic scales are explicitly resolved by the model's dynamical core, whereas smaller-dissipative scales are treated implicitly by the subgrid scales (SGS) models. Despite the extensive use of linear schemes, such as Smagorinsky [31] or Deardorff [32], they are unable to capture the dynamics of non-neutral boundary layers, especially in nighttime conditions subject to complex turbulence intermittency and shear instabilities. Therefore, we make use of a non-linear scwheme, the so-called nonlinear backscatter and anisotropy (NBA) SGS model [33], which has been recently assessed in Martian large-eddy simulations via MarsWRF framework [18]. ...
The Planetary boundary Layer (PBL) is the region which governs the interactions between the surface and atmosphere. Martian daytime PBL has been shown to have strong turbulent mixing similar to the Earth. Nighttime Martian PBL, yet to be explored further, has been assumed to form under very weak turbulent mixing conditions so far. Here we show that temperature fluctuations caused by large-scale atmospheric variations can induce strong local turbulent mixing and remarkably affect surface-atmosphere exchange processes. Temperature fluctuations as low as 0.5 K can increase the surface momentum flux up to an order of magnitude. Our results reveal the feedback between global/mesoscale atmospheric dynamics and the microscale boundary-layer meteorology, with implication for nighttime dust lifting on Mars due to increased near-surface wind stress.
... The authors found that the flow became vertically mixed after a distance L x and ran out of energy to propagate further. We posit that the propagation distance is controlled by penetrative convection during the C-phase and scales as L x ∼ U s h d /w e , where w e = A W a /Ri c = A B 0 h a /(g′h d ) is the convective entrainment velocity, with A an empirical coefficient (Deardorff et al., 1980). This distance represents how far the gravity current propagates before being entirely eroded by penetrative plumes. ...
Gravity currents contribute to the transport of heat and mass in atmospheric and aquatic environments. In aquatic systems subject to daily surface cooling, gravity currents propagate through turbulent convective surroundings. Yet, the effects of thermal convection on aquatic gravity currents remain to be quantified. This paper demonstrates how the interaction between penetrative convection and downslope gravity currents impacts the fluid dynamics and transport across littoral aquatic systems. We performed field experiments in a wind-sheltered lake experiencing differential cooling to resolve the dynamics of thermally driven gravity currents in convective environments. Our in situ observations reveal that convective plumes penetrate gravity currents, generating large vertical fluctuations that foster the erosion of the stratified layer. This enhanced vertical mixing destroys the stratified downslope flow and limits the basin-scale transport. Our results demonstrate that the interaction between penetrative convection and downslope gravity currents controls the littoral-pelagic connectivity in aquatic ecosystems.
... Ceilometers derive the BLH from vertical aerosol profiles, which are defined by Deadorff [34] as the height where there are equal areas of clear air above and particulates below. As a result, the BLH is regarded as the midpoint of the transition zone between the areas of elevated and diminished backscattering, i.e., the top of the aerosol layer [19]. ...
A comparative study and evaluation of boundary layer height (BLH) estimation was conducted during an experimental campaign conducted at the Cape Grim Air Pollution station, Australia, from 1 June to 13 July 2019. The temporal and spatial distributions of BLH were studied using data from a ceilometer, sodar, in situ meteorological measurements, and back-trajectory analyses. Generally, the BLH under continental sources is lower than that under marine sources. The BLH is featured with a shallow depth of 515 ± 340 m under the Melbourne/East Victoria continental source. Especially the mixed continental sources (Melbourne/East Victoria and Tasmania direction) lead to a rise in radon concentration and lower BLH. In comparison, the boundary layer reaches a higher averaged BLH value of 730 ± 305 m when marine air is prevalent. The BLH derived from ERA5 is positively biased compared to the ceilometer observations, except when the boundary layer is stable. The height at which wind profiles experience rapid changes corresponds to the BLH value. The wind flow within the boundary layer increased up to ∼200 m, where it then meandered up to ∼300 m. Furthermore, the statistic shows that BLH is positively associated with near-surface wind speed. This study firstly provides information on boundary layer structure in Cape Grim and the interaction with wind, which may aid in further evaluating their associated impacts on the climate and ecosystem.
... The thickness of the entrainment layer, Δz (Δz = z 2 -z i ), quantifies the effect of various factors influencing the entrainment process. Deardorff et al. (Deardorff, 1980;Deardorff et al., 1980;Deardorff and Willis, 1985) measured the vertical distribution of the horizontal mean potential temperature (θ) and buoyancy flux (B) in a stratified flume without shear and found that the entrainment zone thickness Δz was about 20-40% of the mixed zone thickness. They obtained the following correlation between Δz/z i and the bulk convective Richardson number Ri p as follows: ...
A stratified saline flume experimental apparatus was set up in this study to experimentally simulate the entrainment process of the atmospheric convective boundary layer with vertical wind shear, of which the entrainment characteristics are quite different from those of the shear-free convective boundary layer. Entrainment occurs at the interface of the flume inlet until the velocity difference between the upper and lower layers reaches 0.04 m/s, and a thin stable entrainment zone is formed at a 12z i distance from the flow inlet, where z i is the height of the entrainment zone. Shear in the entrainment zone induces the counter-gradient momentum transport process, and a series of large-scale vortices with a characteristic length of about (1.0–1.5)z i fills this region. The data analysis shows that the velocity difference and buoyancy flux of the bottom plume promote the occurrence of entrainment, while the density difference between the upper and lower layers inhibits it. The contribution of the shear effect to the entrainment process was introduced into the characteristic velocity scale, and a new scaling relation between the dimensionless thickness of the entrainment zone and the corrected Richardson number was obtained as Δz/z i = 1.17Ri NC −1/2 from the experimental results, which agrees well with the available radar data and the numerical simulation data.
... 96,97,98] developed parameterization models in terms of the potential temperature lapse rate in the free atmosphere Γ θ . Using the data from [99] and [100], [98] obtained the following parameterization model: ...
... 2005) developed parameterization models in terms of the potential temperature lapse rate in the free atmosphere . Using the data from Deardorff et al. (1980) and Boers and Eloranta (1986), Sun et al. (2005) obtained the following parameterization model: ...
Analytical solution for two-dimensional thermal plume updraft velocity is obtained under the assumption of a uniform temperature excess inside the plume. In this way, the thermal plume motion is modeled in both mixed layer and entrainment zone. Also, a semi-analytical solution is obtained using an empirical model for the plume temperature excess in the mixed layer. In addition, an analytical model for entrainment zone thickness is obtained by computing the overshoot distance of the modeled plumes, and a semi-analytical model by using the empirical model for plume temperature. By using a nonlinear profile for the lapse rate in the surface layer based on the Monin–Obukhov similarity theory, our model predicts that the characteristics of the surface layer plays an important role in the structure of the entrainment zone. Finally, our solutions for plume velocity allow us to consider the effect of the lateral entrainment on the plume excess temperature and velocity in the convective boundary layer. It is shown that the lateral entrainment has an important role on the plume dynamics and the solutions in the zero entrainment limit offer large overestimated values for the plume velocity, which also result in overestimated values of the entrainment zone thickness.
... Following the gradient method, z i is defined as the vertical location of the maximum vertical potential temperature gradient. Sullivan et al. (1998) also showed that z i obtained via the flux method is, in general, lower than with the other methods, which corresponds with results of laboratory investigations by Deardorff et al. (1980). Furthermore, Sullivan et al. (1998) found that the flux method underestimated both z i and turbulence in the inversion. ...
A non‐eddy‐resolving microscale model is applied to simulate convection over three different leads (elongated channels in sea ice), which were observed by aircraft over the Arctic Marginal Ice Zone in 2013. The study aims to evaluate the quality of a local and a non‐local turbulence parametrization. The latter represents a lead‐width‐dependent approach for the turbulent fluxes designed for idealised conditions of a lead‐perpendicular, near‐neutral inflow in an atmospheric boundary layer (ABL) capped by a strong inversion at around 250 to 350 m height. The observed cases considered here are also characterised by an almost lead‐perpendicular flow but, in comparison to the idealised conditions, our analysis covers effects in stable inflow conditions and a much shallower ABL. The model simulations are initialised with observed surface parameters and upwind profiles, and the results are compared with measurements obtained above and downwind of the leads. The basic observed features related to the lead‐generated convection can be reproduced with both closures, but the observed plume inclination and vertical entrainment near the inversion layer by the penetrating plume are underestimated. The advantage of the non‐local closure becomes obvious by the more realistic representation of regions with observed vertical entrainment or where the observations hint at counter‐gradient transport. It is shown by comparison with the observations that results obtained with the non‐local closure can be further improved by including the determination of a fetch‐dependent inversion height and by specifying a parameter determining the plume inclination as a function of the upwind ABL stratification. Both effects improve the representation of fluxes, boundary‐layer warming, and vertical entrainment. The model is also able to reproduce the observed vanishing of a weak low‐level jet over the lead, but its downwind regeneration and related momentum transport are not always well captured, irrespective of the closure used.
... In the class of unsteady problems with two independent variables are problems that develop slowly in time in one spatial dimension z or r. These are problems such as penetrative convection (Mellado 2012;Holzner & van Reeuwijk 2017), convective and stable boundary layers (as relevant to the atmospheric boundary layer and the oceanic mixed layer; Kato & Phillips 1969;Deardorff et al. 1980;Sullivan et al. 1998;Jonker et al. 2013;Garcia & Mellado 2014), stratocumulus clouds (Mellado 2017), but also include temporal jets (Da Silva & Pereira 2008;van Reeuwijk & Holzner 2014), plumes (Krug et al. 2017), gravity currents (van Reeuwijk et al. 2018(van Reeuwijk et al. , 2019, wakes (Redford et al. 2012;Watanabe et al. 2016), mixing layers (Watanabe et al. 2018a) and compressible reacting mixing layers (Jahanbakhshi & Madnia 2018). These temporal flows are not generally encountered in nature but share many of the features of their 2D steady cousins. ...
... The small multi-function research and teaching Sonde application proved the reliability of temperature and humidity measurements from UAV platforms for the estimation of sensible heat flux. 98,99 Another recent research related to surface flux estimations revealed that the wind speed, temperature, and relative humidity from UAVs were in good agreement with ground-based values and the data quality was sufficient for the computation of the bulk heat transfer coefficient. 100 ...
... The small multi-function research and teaching Sonde application proved the reliability of temperature and humidity measurements from UAV platforms for the estimation of sensible heat flux. 98,99 Another recent research related to surface flux estimations revealed that the wind speed, temperature, and relative humidity from UAVs were in good agreement with ground-based values and the data quality was sufficient for the computation of the bulk heat transfer coefficient. 100 ...
We recapitulate the approaches of sensible heat flux (H) estimation, which is a critical parameter in the remote sensing (RS)-based evapotranspiration (ET) models. We propose a classification scheme for the ET models considering their distinctions in approaches for the estimation of H. Adhering to the proposed classification scheme, the theoretical backgrounds of H estimation in the single-source and two-source RS-based ET models are discussed in brief, along with their unique characteristics. We addressed the role of critical parameters that influenced the H computation under each model and presented the related progress in the research. The importance of data assimilation techniques, as well as the application of un-manned aerial vehicles for the uninterrupted estimation of turbulent heat flux, are discussed in the context of single-source and two-source models. The influence of scale on the validation of the models and the impact of the aggregation methods are discussed. We compared the performance of the popular ET models for the estimation of H, utilizing the information obtained from peer-reviewed articles. The limitations related to the RS datasets in terms of spatial and temporal resolution and the scope of alleviating the shortcomings using the future satellite missions are discussed. We conclude by pointing toward the current challenges and the prospective domain of research, which needs to be addressed critically in the future.
... Deardorff's work was a proof of concept, informing about closure assumptions and making the flow organization visible. J. D. Deardorff was not only a pioneer in illustrating how LES can be applied to engineering and environmental problems, but he also performed seminal work on laboratory studies of the unstable ABL [11,12,39], and the convective scales that he introduced for the characterization of convection have been used ever since [7]. ...
The atmospheric boundary layer (ABL) is the lower part of the atmosphere, the part that is in contact with the surface and responds to changes in surface properties in a few hours.
... Ceilometers provide the PBLH from vertical aerosol profiles based on the Deadorff's definition of M ing L (or M ed L), which is the "height where there are equal areas of clear air above and particulates below" (Deardorff et al., 1980). Therefore, the PBLH "is taken to be the midpoint of the transition region between the areas of higher and lower backscattering", i.e. the top of aerosol layer. ...
The Planetary Boundary Layer (PBL) is an important part of the atmosphere that is relevant in different atmospheric fields like pollutant dispersion, and weather forecasting. In this study, we analyze four and five-year datasets of measurements gathered with a ceilometer and a microwave radiometer to study the PBL structure respectively, in the mid-latitude urban area of Granada (Spain). The methodologies applied for the PBL Height (PBLH) detection (gradient method for ceilometer and the combination of parcel method and temperature gradient method for microwave radiometer) provided a description in agreement with the literature about the PBL structure under simple scenarios. Then, the PBLH behavior is characterized by a statistical study of the convective and stable situations, so that the PBLH was obtained from microwave radiometer measurements. The analysis of the PBLH statistical study shows some agreement with other PBLH studies such as daily pattern and yearly cycle, and the discrepancies were explained in terms of distinct latitudes, topography and climate conditions. Finally, it was performed a joint long-term analysis of the residual layer (RL) provided by ceilometer and the stable and convective layer heights determined by microwave radiometer, offering a complete picture of the PBL evolution by synergetic combination of remote sensing techniques. The PBL behavior has been used for explaining the daily cycle of Black Carbon (BC) concentration, used as tracer of the pollutants emissions associated to traffic.
... We used a fifth-order advection 236 scheme (Wicker and Skamarock, 2002), and a third-order Runge-Kutta timestep scheme 237 (Williamson et al., 1980). The 1.5-order flux-gradient sub-grid closure solves a prognostic 238 equation for the turbulence kinetic energy (Deardorff, 1980 We run PALM with fixed external forcing for each considered case. The temperature 248 filed in the model is initialized with corresponding idealized temperature profiles from the MTP 249 observations. ...
Detailed temperature maps are required in various applications. Any temperature interpolation over complex terrain must account for differences in land cover and elevation. Local circulations and other small-scale factors can also perturb the temperature. This study considers the surface air temperature, T, mapping with geo-statistical kriging. The kriging methods are implemented for both T, and temperature anomalies, Δ T, defined as difference between T at a given location and T at the same elevation in the free atmosphere. The study explores the large-eddy simulation (LES) model PALM as a source for variogram and external drift in the kriging methods. Ten kriging methods for the temperature mapping have been considered: ordinary kriging (OK) of T and Δ T with variogram derived from the observations (methods 1 and 2, correspondingly); OK of T and Δ T with variogram derived from LES data (3 and 4); universal kriging with external drift (KED) that utilizes the LES data (5 and 6); a weighted combination of KED of T and Δ T (method 7); and the methods (5), (6) and (7) enhanced with additional “virtual” points in remote areas (methods 8, 9 and 10). These ten methods are evaluated for eight typical weather situations observed in Bergen, Norway. Our results demonstrate considerable added value of the LES information for the detailed meteorological temperature mapping. The LES data improves both the variogram and the resulting temperature maps, especially in the remote mountain parts of the domain and along the coast.
... In the class of unsteady problems with two independent variables are problems that develop slowly in time in one spatial dimension z or r. These are problems such as penetrative convection (Mellado 2012;Holzner & van Reeuwijk 2017), convective and stable boundary layers (as relevant to the atmospheric boundary layer and the oceanic mixed layer; Kato & Phillips 1969;Deardorff et al. 1980;Sullivan et al. 1998;Jonker et al. 2013;Garcia & Mellado 2014), stratocumulus clouds (Mellado 2017), but also include temporal jets (Da Silva & Pereira 2008;van Reeuwijk & Holzner 2014), plumes (Krug et al. 2017), gravity currents (van Reeuwijk et al. 2018(van Reeuwijk et al. , 2019, wakes (Redford et al. 2012;Watanabe et al. 2016), mixing layers (Watanabe et al. 2018a) and compressible reacting mixing layers (Jahanbakhshi & Madnia 2018). These temporal flows are not generally encountered in nature but share many of the features of their 2D steady cousins. ...
Integral equations are derived that describe turbulent free shear flows developing in space and/or time. The description clarifies the connection between the local (small-scale) and global (integral) descriptions of turbulent entrainment, and provides a seamless connection between the implicit description of the turbulent-nonturbulent interface (TNTI) required for the former and the explicit description of the TNTI usually adopted for the latter. The description is applied to the axisymmetric jet, the planar wake, temporal jet and unsteady jets and plumes.
... As the CBL broadens, the upper sublayer becomes thinner compared to the lower sublayer. This two-layer structure rationalizes the observation that the entrainment-zone thickness deviates from a constant fraction of the CBL depth as the CBL grows (Deardorff, Willis & Stochton 1980;Sullivan et al. 1998), and that the variance correlates with the local gradients and not with the convective scales that characterize the CBL interior (Deardorff 1974;Sorbjan 2005). This two-layer structure also helps explain the observed dependence on weak and strong stratification regimes of the minimum buoyancy flux, and of the relationship between the mean entrainment velocity and the convective Richardson number. ...
Direct numerical simulations are used to characterize wind-shear effects on entrainment in a barotropic convective boundary layer (CBL) that grows into a linearly stratified atmosphere. We consider weakly to strongly unstable conditions $-z_{enc}/L_{Ob}\gtrsim 4$ , where $z_{enc}$ is the encroachment CBL depth and $L_{Ob}$ is the Obukhov length. Dimensional analysis allows us to characterize such a sheared CBL by a normalized CBL depth, a Froude number and a Reynolds number. The first two non-dimensional quantities embed the dependence of the system on time, on the surface buoyancy flux, and on the buoyancy stratification and wind velocity in the free atmosphere. We show that the dependence of entrainment-zone properties on these two non-dimensional quantities can be expressed in terms of just one independent variable, the ratio between a shear scale $(\unicode[STIX]{x0394}z_{i})_{s}\equiv \sqrt{1/3}\unicode[STIX]{x0394}u/N_{0}$ and a convective scale $(\unicode[STIX]{x0394}z_{i})_{c}\equiv 0.25z_{enc}$ , where $\unicode[STIX]{x0394}u$ is the velocity increment across the entrainment zone, and $N_{0}$ is the buoyancy frequency of the free atmosphere. Here $(\unicode[STIX]{x0394}z_{i})_{s}$ and $(\unicode[STIX]{x0394}z_{i})_{c}$ represent the entrainment-zone thickness in the limits of weak convective instability (strong wind) and strong convective instability (weak wind), respectively. We derive scaling laws for the CBL depth, the entrainment-zone thickness, the mean entrainment velocity and the entrainment-flux ratio as functions of $(\unicode[STIX]{x0394}z_{i})_{s}/(\unicode[STIX]{x0394}z_{i})_{c}$ . These scaling laws can also be expressed as functions of only a Richardson number $(N_{0}z_{enc}/\unicode[STIX]{x0394}u)^{2}$ , but not in terms of only the stability parameter $-z_{enc}/L_{Ob}$ .
... In the last two decades, elastic lidar (EL) systems have been widely applied in PBL studies (Flamant et al., 1997;Menut et al., 1999;Davis et al., 2000;Brooks, 2003;Morille et al., 2007;Münkel et al., 2007;Baars et al., 2008;Pal et al., 2010;De Tomasi et al., 2011;Haeffelin et al., 2017;Wang et al., 2012;Granados-Muñoz et al., 2012;Lange et al., 2014;Fedele et al., 2015;Banks and Baldasano, 2016;Bravo-Aranda et al., 2017;Liu et al., 2018;Zhu et al., 2018). The detection of the PBLH using EL (PBLH elastic ) is based on the definition provided by Deardorff et al. (1980) for this variable: "the altitude where there are equals areas of clear air below and particulates above", e.g. considering an ideal lidar return the PBLH is at the midpoint where an inflexion occurs and the areas below and above the lidar return curve are equal (Kovalev and Eichinger, 2004). ...
The Planetary Boundary Layer (PBL) is a relevant part of the atmosphere with a variable extension that clearly plays an important role in fields like air quality or weather forecasting. Passive and active remote sensing systems have been widely applied to analyze PBL characteristics. The combination of different remote sensing techniques allows obtaining a complete picture on the PBL dynamic. In this study, we analyze the PBL using microwave radiometer, elastic lidar and Doppler lidar data. We use co-located data simultaneously gathered in the framework of SLOPE-I (Sierra Nevada Lidar aerOsol Profiling Experiment) campaign at Granada (Spain) during a 90- day period in summer 2016. Firstly, the PBL height (PBLH) obtained from microwave radiometer data is validated against PBLH provided by analyzing co-located radiosondes, showing a good agreement. In a second stage, active remote sensing systems are used for deriving the PBLH. Thus, an extended Kalman filter method is applied to data obtained by the elastic lidar while the vertical wind speed variance method is applied to the Doppler lidar. PBLH′s derived by these approaches are compared to PBLH retrieved by the microwave radiometer. The results show a good agreement among these retrievals based on active remote sensing in most of the cases, although some discrepancies appear in instances of intense PBL changes (either growth and/or decrease).
... It was postulated that the entrainment is manifested by the engulfment of non-turbulent fluid by the integral eddies near the interface. Such an entrainment mechanism is akin to that observed by Deardorff et al. 16 . Therefore, an entrainment hypothesis was used to estimate . ...
Double-diffusive convection in a linearly stratified fluid in the presence of radiative cooling at the surface has been investigated experimentally and theoretically. The stratification strength, which was varied in the experiments, is characterized by the buoyancy frequency of a stable environment defined as N² = (g/ρ0)/ (dρ/dz). The surface radiative cooling mimics buoyancy forcing incumbent at the surface of the ocean during the boreal winter months. The significant parameters governing the mixing dynamics for such a system were identified to be the Richardson number (Ri) and flux Rayleigh number (Raf). Controlled experiments were performed for Ri = 0-6, while maintaining a constant Raf = 2.58 × 10⁷. This indicates that the stratification strength N was changed while the cooling flux Q was fixed. The mixing and barrier layers were visualized using a commercial dye solution. The thickness of the mixing layer was quantified from the flow evolution images. It was found that the mixing layer decays exponentially with increase in the stratification strength owing to suppression of downward convective motion due to the buoyancy force. A similar trend was observed for the entrainment velocity. A scaling law was proposed as follows: Δ = CRi-3/4, where Δ is the mixing layer depth and C is a constant. The experimental results were compared with theoretical analysis and reasonable agreement was found. The results would be useful in parameterizing the mixing and barrier layers in strongly stratified environments such as the Bay of Bengal.
... But research protocols mixing the two approaches -numerical and experimental -are also considered. For example, Jonker and Jiménez (2014) tried to reproduce the water tank experiments of Deardorff et al. (1980) which provided commonly accepted values of the buoyancy entrainment ratio. They found significantly different values of this parameter and recommend to further explore the matter with DNS (Direct Numerical Simulations). ...
A meteorological numerical model can be a powerful tool to complement laboratory experiments applied to atmospheric sciences, but it needs to be adapted in order to represent flows generated in laboratory. This paper presents such an adaptation of the atmospheric non-hydrostatic model Meso-NH. The usually neglected viscous diffusive fluxes have been added to the model’s equations, along with the coding of an explicit bottom no-slip boundary condition was implemented. These implementations are validated against exact solutions of ideal flows. Meso-NH is then used in a configuration matching a laboratory experiment performed in the CNRM large stratified water flume meant to reproduce a neutral atmospheric boundary layer. The model is run for the first time in an explicit mode (Direct Numerical Simulation – DNS) at a very high resolution (1 mm) over a large grid. The comparison with the experimental data shows that the boundary layer height and vertical profiles of mean velocity are well captured by the model. This result further validates the implementations carried out in Meso-NH which can now be used in a DNS mode to simulate channel flows. The joint use of Meso-NH and laboratory experiments, along with the possibility to run DNS with Meso-NH, could lead to new findings or improvements in the field of atmospheric sciences.
... Second, we assume that b z i,gb is a linear combination of b ml = βN 2 z enc and (b bg ) z i,gb = N 2 z i,gb , where the first contribution represents the mean buoyancy at z = z i,gb inside the penetrating thermals and the second contribution represents the mean buoyancy outside them. The weighting factors of this linear combination would be the area fraction occupied by each region (Deardorff et al., 1980). As a first approximation, we have considered an area fraction of 0.5, which explains the term 0.1 z enc in Eq. (32) because then ...
We use dimensional analysis and direct numerical simulations to characterize specific-humidity statistics in the equilibrium (quasi-steady) entrainment regime of cloud-free convective boundary layers that grow into linearly stratified free atmospheres. The first three moments and the mean vertical flux are studied for arbitrary combinations of free-atmosphere lapse-rates and surface fluxes of buoyancy and specific humidity. First, we find the combination of these parameters that distinguishes between the entrainment-drying regime and the surface-moistening regime. We also provide a zero-order model describing both regimes. Second, we parametrize the variances in the mixed layer and in the entrainment zone separately, based on convective and entrainment-zone scales, respectively. We show that the large variances in the entrainment zone are not only due to large production rates, but also due to low dissipation rates. Third, we provide the skewness for any regime between the pure drying limit and the pure moistening limit. The variation of the skewness indicates that knowing the sign of the skewness near the surface is often insufficient to distinguish between drying and moistening regimes, in contrast to previous conjectures. On a more general context, this paper further supports the applicability of direct numerical simulations to investigate the atmospheric boundary layer, as inferred from the degree of Reynolds number similarity observed in the results and from the consistency of the derived parametrizations with field measurements.
We develop innovative analytical expressions for the mean wind and potential temperature flux profiles in convective boundary layers (CBLs). CBLs are frequently observed during daytime as Earth’s surface is warmed by solar radiation. Therefore, their modeling is relevant for weather forecasting, climate modeling, and wind energy applications. For CBLs in the convective-roll-dominated regime, the mean velocity and potential temperature in the bulk region of the mixed layer are approximately uniform. We propose an analytical expression for the normalized potential temperature flux profile as a function of height, using a perturbation method approach in which we employ the horizontally homogeneous and quasi-stationary characteristics of the surface and inversion layers. The velocity profile in the mixed layer and the entrainment zone is constructed based on insights obtained from the proposed potential temperature flux profile and the convective logarithmic friction law. Combining this with the well-known Monin–Obukhov similarity theory allows us to capture the velocity profile over the entire boundary layer height. The proposed profiles agree excellently with large-eddy simulation results over the range of − L / z 0 ∈ [3.6 × 10 ² , 0.7 × 10 ⁵ ], where L is the Obukhov length and z 0 is the roughness length.
This paper describes the structure and mechanisms of the convective roll vortices seen by airborne lidar scattering from sea salt aerosols and measured directly by instruments on another aircraft. The observations were taken off the east coast during a cold air outbreak. In addition, we discuss the ways in which the lidar may be used to estimate some of the key parameters related to the surface heat flux. Much of what follows is based upon the work of Chou and Atlas, 1982; Melfi et al, 1984; and Atlas, 1985.
This paper investigates the performance of seven methods of retrieving the planetary boundary layer height (PBLH) from lidar measurements carried out in the Metropolitan Region of São Paulo (MRSP) during two MCITY-BRAZIL field campaigns of 2013. The performance is objectively assessed considering as reference the PBLH retrieved from rawinsonde carried out every 3 h during these campaigns. The role of clouds and aerosol load in the performance of the seven methods is analysed considering three case study scenarios representative of typical atmospheric conditions in the MRSP: (a) winter clean atmosphere, (b) summer low clouds and aerosol multilayers, (c) summer sea-breeze intrusion. Corroborating the case study results, the objective analysis indicated that most of the lidar methods retrieved PBLH closer to the top of the entrainment zone than the mixed layer, contradicting their definition. During daytime, the Wavelet Covariance Transform Method performs better than all the other six methods. The Inflexion Point Method performed better to estimate the Residual Layer height during night-time. In average, the diurnal evolution of the PBLH and its local rate of change based on lidar and rawinsonde measurements are in agreement.
Au regard de l’importance des lacs sur le climat et de leur rôle sociétal, il estpertinent de les implémenter dans les modèles de climats pour comprendre leur influence sur les différents cycles comme ceux de l’eau, du carbone, du méthane ou encore leur interaction avec la couche limite de l’atmosphère. Cette thèse vise à implémenter les lacs dans le modèle de surface continental ORCHIDEE. Nous avons choisi le modèle à une dimension Flake qui simule le bilan d’énergie des lacs.Dans une première partie de cette thèse nous avons réalisé une analyse de sensibilité des différents paramètres su modèle Flake. Nous avons mis en avant que les températures de surface des lacs et les flux de chaleur de surface sont d’abord sensibles à la profondeur. Cependant selon l’intervalle de profondeur choisie (peu ou très profond), on remarque que l’influence de la profondeur est plus important pour les lacs peu profond. Le coefficient d’extinction qui mesure la pénétration du rayonnement solaire dans l’eau est lui aussi influent pour les lac de faible profondeur.Dans la suite du travail, nous avons couplé ORCHIDEE avec FLake et testé plusieurs stratégies d’agrégation des profondeurs à plusieurs résolutions (0.25 et 0.5 degrés). Nous avons utilisé la base de données GloboLakes pour valider les températures de surface de lac et la base de données « Global Lake and River Ice Phenology Database » pour valider les périodes de gel. Nous avons utilisé 5 forçages atmosphériques différents et nous avons remarqué la forte sensibilité du couplage aux forçages choisis. La stratégie d’agrégation des profondeurs des lacs à l'échelle de la maille de calcul, quant à elle, influence peu les résultats.Le modèle couplé a finalement montré de bons résultats. Pour chaque série, la médiane des erreurs obtenues sur les températures à varie entre 2.7 K et 3.2 K. Les périodes de gel sont en général surestimées. La médiane des erreurs sur la période de gel varie entre 20 et 41 jour selon le forçage utilisé.Des pistes d’amélioration du couplage sont envisagées comme la paramétrisation spatiale du coefficient d’extinction et l’évolution temporelle des profondeurs contraintes par les mesures satellitaires du futur instrument SWOT. Enfin, dans une perspective à plus long terme, il est envisagé de coupler le modèle ORCHIDEE-FLake avec le modèle atmosphérique LMDZ.
The use of experimental techniques is one method of designing, testing, and commissioning ventilation systems. Various complex problems are encountered in the broad field of industrial ventilation, and visualization techniques or measurements are one way to get answers to these questions. This chapter introduces measurement and visualization techniques that can be used for industrial ventilation problems. Then three main sections are introduced: Section 4.2 firstly introduces visualization techniques for determining the characteristics and properties of phenomena/problems when quantitative information (numbers) are not required. Section 4.3 describes measurement techniques and methods from which quantitative variations and characteristics could be obtained. Section 4.4 introduces scale model experiments for the determination of airflow in large spaces and also in the study of local ventilation around a working area in the industrial environment. Through this chapter, readers can fully understand the visualization techniques, measurement techniques, and scale model experiments to deal with various complex problems in industrial ventilation.
Water reservoirs in western Japan have a low temperature around the bottom area during summer, and they can be used as possible renewable heat sources in heat pump systems. Predicting the temperature of the heat source is a significant concern because it directly affects the system efficiency. Although many previous studies have investigated the thermal characteristics of heat exchangers in heat-release processes, little has been reported on the influence of heat release on the thermal stratification of the heat source. In this study, we conducted laboratory experiments involving thermal layers with two different temperatures and measured the temperature variations of the heat source and boundary of the thermal layers. We found that natural convection with a velocity of approximately 1 cm/s, caused by a heat release of 0.7–4.5 kW/m² from the bottom, resulted in an increase of the boundary by entrainment, warming only the lower layer uniformly. The measured variations of the lower-layer temperature were reproduced using the entrainment law, which is originally defined for natural phenomena in lakes, with an accuracy of ±0.7 °C. Using the entrainment law, the heat source temperature in the reservoir-source heat pump systems may be predicted easily without turbulent transfer models.
Destratification of thermally stratified turbulent open-channel flow by surface cooling - Volume 899 - Michael P. Kirkpatrick, N. Williamson, S. W. Armfield, V. Zecevic
Entrainment is critical to the development of the atmospheric convective boundary layer (CBL), but little is known about how entrainment is impacted by the aerosol radiative effect. An aerosol radiation transfer model is used in conjunction with large eddy simulation (LES) to quantify the impact of aerosol shortwave radiative heating on entrainment and thermodynamics of an idealized dry CBL under aerosol-loading conditions. An entrainment equation is derived within the framework of zero-order model (ZOM) with the aerosol radiative heating effect included; the equation is then examined against the LES outputs for varying aerosol optical depth (AOD) and free-atmosphere stratification scenarios. The results show that the heat flux profiles become more nonlinear in shape as compared to the case of the clean (no aerosol pollution) CBL, with degree of nonlinearity being highly dependent on the AOD of the layer for the given type of radiation-absorbing aerosols. As AOD increases, less solar radiation reaches the surface, thus the surface heat flux becomes smaller, and both actual (LES) and ZOM-derived entrainment flux ratios decrease. This trend is opposite to the clean CBL where the LES-predicted flux ratios show an increasing trend with diminishing surface heat flux, while the ZOM-calculated flux ratio remains constant. The modified dimensionless entrainment rate closely follows the −1 power law with a modified Richardson number. The study suggests that including the aerosol radiative effect may improve numerical air quality predictions for heavy air pollution events.
A new three-dimensional (3D) turbulent kinetic energy (TKE) subgrid mixing scheme is developed using the Advanced Research version of the Weather Research and Forecasting (WRF) Model (WRF-ARW) to address the gray-zone problem in the parameterization of subgrid turbulent mixing. The new scheme combines the horizontal and vertical subgrid turbulent mixing into a single energetically consistent framework, in contrast to the conventionally separate treatment of the vertical and horizontal mixing. The new scheme is self-adaptive to the grid-size change between the large-eddy simulation (LES) and mesoscale limits. A series of dry convective boundary layer (CBL) idealized simulations are carried out to compare the performance of the new scheme and the conventional treatment of subgrid mixing to the WRF-ARW LES dataset. The importance of including the nonlocal component in the vertical buoyancy specification in the newly developed general TKE-based scheme is illustrated in the comparison. The improvements of the new scheme with the conventional treatment of subgrid mixing across the gray-zone model resolutions are demonstrated through the partitioning of the total vertical flux profiles. Results from real-case simulations show the feasibility of using the new scheme in the WRF Model in lieu of the conventional treatment of subgrid mixing.
Entrainment behavior on a density interface of stratified fluids is very important for the design of innovative nuclear reactors. In the present study, the turbulent energy in the upper stratified fluid was supplied by an injection and extraction flow. The turbulent intensity in the upper fluid was proportional to the injection and extraction velocity at the nozzle. The entrainment was done by liftup of filaments from peaks of the interfacial wave. The entrainment velocity was inversely proportional to the overall Richardson number. These results could be obtained when the turbulent energy released from the energy-containing eddy was proportional to the energy consumption by the entrainment.
The spatial structures of atmospheric mixed and transition layers were investigated using the image data of aerosol distribution observed by a scanning Mie lidar. The mixed layer height, the transition layer thickness and the horizontal scale of convective cell structures in the transition layer as well as their time variation were analyzed. The main results are : the mixed layer height reaches its maximum at about 13h and its rising speed is 100-300m/h in the period of 8-12h. The transition layer thickness increases in the morning and takes a constant value thereafter. The aspect ratio of the convective cell structure is estimated about 2-4 in the early morning and reaches about unity as the mixed layer develops.
This paper discusses the thermodynamic transports of heat, liquid water and (briefly) water vapour by non-precipitating cumulus convection. It is shown that because of the irreversible mixing between cloud and environment, there is a downward transport of enthalphy in the cumulus layer. A lapse-rate adjustment model relates stratification to the life-cycle of a model cloud parcel. A sub-cloud layer model specifies the lower boundary of the lapse-rate model, and the convective transports through cloud-base. Budget equations together with the lapse-rate model, and its time dependent boundary conditions, predict the time development of the cumulus layer, and show the dependence on large-scale mean vertical motion, cloud-base variations, and the surface sensible heat flux.
The sensitivity of models of cloud-topped mixed layers to various
specifications of the radiative cooling rate near the cloud top is
investigated. It is found that for the `dry cloud' case an assumed
distributed cooling rate leads to a shallower mixed layer and more
positive surface turbulent heat flux than does a discontinuous radiative
flux model.
There is significant vertical transport of mass both within and across the base of the U.S. west coast temperature inversion. The vertical flux has been determined from a variety of observations made on Mt. Sutro Tower, in the heart of San Francisco: (1) increased concentration of trace elements in aerosols above the inversion base; (2) correlation between the diurnal variations of the concentration of condensation nuclei below and just above the inversion base; (3) a rate of decrease with height in the concentration of sea salt nuclei that does not change significantly above the inversion base; and (4) mixing of fluorescent particles, released upwind of the tower both below and above the inversion base, across and within the inversion. The vertical transport, approximately 15 cm s−1 is ascribed to the action of stable internal gravity waves moving through a layer of strong vertical shear of the horizontal wind. Horizontal mixing near their crests results in a net vertical pumping of mass. The apparent vertical diffusion coefficient is larger than would be expected for the observed Richardson number, although it decreases with increasing Richardson number.
A scanning lidar system has been used to observe convection in the atmospheric boundary layer. In particular, cell sizes and geometry have been determined and circulation patterns in and around the cells have been measured. The lidar data show that the preferred form of convective cells are plumes with roots near the surface. The majority of these plumes have aspects ratios between 0.5 and 1.5. The measurements of circulation patterns show the strongest rising motion on the upwind side of the cell with sinking motion on the downwind side. These observations show that lidar is a powerful tool for observing convection. (A)
A stable layer of fluid which is suddenly heated at the bottom is studied numerically in two dimensions. Internal waves are soon set in motion by penetrative convection elements, and are found to transport heat downward, on the average, even at heights well above the interface separating the stable and convective layers. This heat transport is found to be associated primarily with a finite‐amplitude effect, to a lesser extent with the increase of internal wave amplitudes with time, and only slightly associated with processes of molecular diffusion.
The stability of the mixing layer is of primary importance in short-range pollution studies, and the ability to specify the diurnal cycle of boundary-layer evolution becomes important when dealing with pollutants tracked for several days on a regional scale. This chapter describes the general results and limitations of the simple thermal approach, and provides a combined dynamical and thermal approach to the parameterization of the entrainment process and the development of the convectively unstable boundary layer. Observations of the boundary layer in convective situations show that in general it is a diurnally evolving system with discontinuities around sunrise and sunset. Two main factors, which control the development of the convective layer, are (1) the flux of sensible eddy heat entering the boundary layer at the ground and (2) a turbulent mixing process occurring at the interface between the well-mixed boundary layer air and the nonturbulent air in the capping stable layer. Recent observations indicate that wind shear at the interface may be of fundamental importance not only to the entrainment of eddy momentum but also of eddy sensible heat.
An experiment was designed to measure the position of a front separating turbulent and nonturbulent fluid as the front moves away from an oscillating grid located near the plane z=0. The theory predicts D∝ (Kt)1/2, where D is the distance of the front from z=0, t=0 is time at which the oscillation begins, and K is a quantity of the dimensions and character of eddy viscosity, called the ’’action’’ of the idealized plane energy source that replaces the grid in the theoretical model. The experimental results support the theory.
The structure and dynamics of a rain-formed mixed layer (ML) are studied using hourly STD and profiling current meter casts. Because the fluid beneath the rain-formed ML was vertically homogeneous, the ML buoyancy g′ and horizontal velocity difference δV were easily observable as the ML depth h increased by entrainment from 7 to 18 m in a period of 8 h. The overall Richardson number of the mixed layer g′(h + d/2)/δV2 ≈ 0.7 during that period, where d is the thickness of the transition layer at the base of the ML. The entrainment rate was consistent with that of a laboratory surface half-jet (Ellison and Turner, 1959). The transition layer thickness was an appreciable fraction of the ML thickness, roughly d ≈ h/3. The density profile through the transition layer was linear and symmetric, and the overall Richardson number of the transition layer g′d/δV2 ≈ 1/4.
Turbulent fluctuations in active mixed layers can excite internal waves in stably stratified fluid regions adjoining them. Expressions are derived for the energy and momentum fluxes radiated away by internal waves from an oceanic mixed layer, in terms of the spectrum of the static pressure fluctuations imposed at the base of the mixed layer by the turbulent eddies. The role of these internal wave fluxes in questions such as the determination of the rate of deepening of the layer due to an applied surface stress and the origin of internal waves in the deep ocean is discussed.
The dispersal of pollutants when released into the environment is often affected by the action of buoyancy forces either because the pollutant has a different density from its immediate environment, or because there is stratification already present in the environment, or both. This chapter describes the turbulent motions produced by the vertical oscillation of horizontal grids that are imposed on a density interface and determines the role of molecular diffusion at such an interface. This method of production of turbulence is convenient, because it allows the properties of the turbulence and the interface to be set independent of one another; however, there are certain drawbacks, such as the properties of the turbulence may be related to the special geometry of the tank and grid, or the experiments are not completely steady. A thick interface suggests that the centre of the interface consists of a diffusive core which provides a flux, by molecular diffusion alone, which balances the entrainment flux from the edges of the interface into the turbulent layers. However, when the interface is thin, it is not possible to provide a large enough flux by diffusion, and mechanical breakdown with direct mixing of fluid from each layer must occur. One aspect of pollutant disposal is the effect of double-diffusion convection on sewage deposited in the sea, and that in some circumstances vigorous salt-finger convection could occur enhancing the vertical spread of the sewage cloud. This implies that in circumstances, where the finger convection is vigorous, it may be found that even in the ocean the interface acts as though it is a low Peclet number structure.
An acoustic sounding system placed on the NOAA Ship Oceanographer during GATE provided a unique meteorological data set. Examples of three distinct boundary-layer situations are discussed as they appear on the facsimile records of backscattered acoustic intensity: 1) ubiquitous plume echoes associated with undisturbed conditions, 2) cool-air outflows (or wakes) from either squall-line or isolated cumulonimbus activity associated with disturbed conditions and 3) “hat”- or “hummock” -shaped echoes associated with low-level cumulus clouds usually occurring during weakly disturbed conditions. Profiles of potential temperature and mixing ratio from radiosonde flights launched from the Occonograph are compared with the acoustic data. Convective plumes observed during GATE were less vigorous than those seen over land. Bulk aerodynamic fluxes of surface sensible and latent heat varied in time with the passage of thermal plumes. This indicates a minimum averaging time for valid flux estimates of about 30 ...
The turbulent temperature structure and winds in thermal convective
plumes over prairie grassland have been investigated with an acoustic
echo sounder system. Three spaced acoustic antennas, with two inclined
at 45° elevation, were used to provide plume shape information and
Doppler-derived total wind-vector patterns between heights of 70 and 500
m. Supporting in situ measurements were made on a 15 m tower, with a
tethered balloon-supported Boundary Layer Profiler, and from a light
aircraft. The most probable orientation of the plumes was nearly
vertical, but frequent upwind and downwind tilts were also observed.
Maximum positive vertical velocities in the plumes at midday were near 2
m s1, while maximum downward currents were one-half this
value. Acoustic echoes from regions above the mixed layer, corresponding
in height to an elevated temperature inversion, correlate well with
regions of maximum wind shear.
A study is made of the entrainment interface in a two-layer flow with one layer turbulent owing to an imposed surface stress. Turbulent and wave parameters were measured from films of an experiment carried out by Kantha, Phillips & Azad (1977) and are analysed to determine relationships between wave and turbulent length and velocity scales and bulk scales. A measure of interface distortion is calculated and it is found to be related to the mixed-layer depth only at small overall Richardson number. The local velocity of advance of the interface is determined and is found to vary with overall Richardson number tending to the Kolmogorov scale at small Ri and to Phillips’ (1966) quasilaminar scale at large Ri. Kelvin-Helmholtz type instabilities are observed and their wavelength, amplitude and lifetime are measured. The wavelength is not found to be related to the mixed-layer depth but some dependence on overall Richardson number is observed. An interfacial mean flow Richardson number is estimated and the variation of wave slope at maximum amplitude with this Richardson number is found to be comparable with observations of Thorpe (1973a) in a laminar two-layer flow. A relationship between the wavelength of an instability and the distortion length scale is found and is discussed.
A theory is developed to describe the evolution of the entrainment interface in turbulent flow, in which the surface is convoluted by the large-scale eddies of the motion and at the same time advances relative to the fluid as a result of the micro-scale entrainment process. A pseudo-Lagrangian description of the process indicates that the interface is characterized by the appearance of ‘billows’ of negative curvature, over which surface area is, on average, being generated, separated by re-entrant wedges (lines of very large positive curvature) where surface area is consumed. An alternative Eulerian description allows calculation of the development of the interfacial configuration when the velocity field is prescribed. Several examples are considered in which the prescribed velocity field in the z direction is of the general form w = Wf(x – Ut), where the maximum value of the function f is unity. These indicate the importance of leading
points on the surface which are such that small disturbances in the vicinity will move away from the point in all directions. The necessary and sufficient condition for the existence of one or more leading points on the surface is that U [less-than-or-eq, slant] V, the speed of advance of an element of the surface relative to the fluid element at the same point. The existence of leading points is accompanied by the appearance of line discontinuities in the surface slope re-entrant wedges, In these circumstances, the overall speed of advance of the convoluted surface is found to be W + (V2 – U2)[fraction one-half], where W is the maximum outwards velocity in the region; this result is independent of the distribution f.
In this paper two aspects of the deepening of a mixed layer in a stratified fluid are examined in the laboratory. The first is the deepening of a layer into a region of constant density gradient. Turbulence is produced by an oscillating grid which generates a horizontally homogeneous field of motion with no significant mean flow. It is found that the rate at which the potential energy of the basic stratification is increased by the mixing does not bear a simple relationship to the rate of energy input by the grid. On the other hand, when allowance is made for the decay of turbulent energy away from the grid and only that portion to reach the bottom of the mixed layer is considered, the rate of potential energy increase is found to be proportional to this available energy. The second aspect to be discussed is the effect of energy radiation by internal waves in the region below the mixed layer. Estimates are made of the possible loss of energy to these waves, which reduces the amount available to deepen the layer. An experimental demonstration of up to 50 % reduction in the mixing rate due to the presence of internal waves is given. Finally, the implications of these results are discussed in the light of current theoretical models of the deepening process.
Some experiments are described in which steady-state shearing flows are developed in stratified brine solutions contained in a cyclically continuous tank of rectangular cross-section. Over the range of overall Richardson numbers studied, the results suggest that whenever turbulent layers are present on either side of a region of fluid with a gravitationally stable density gradient, they cause erosion of this region to occur. The erosion leads to the formation of two homogeneous layers separated by a thin layer of strong density and velocity gradients. The gradient Richardson number, computed by using the velocity and density gradients in this transition layer, tends to have a value of order one.
If we define an overall Richardson number Ri * by averaging the velocity and density gradients over the entire depth of fluid in the tank, we find that the non- dimensional buoyancy flux, Q , is functionally related to Ri * by an equation of the form Q = C 1( Ri *) ⁻¹ where C 1 is a constant, approximately, and Ri * ranges in value between one and thirty.
To check the effect of a large variation of the molecular diffusivity coefficient on flow conditions, we ran a limited number of experiments with thermally stratified fluid. Over a restricted range, 1·0 < Ri * < 5·0, velocity profiles very similar to those measured in the brine-stratified experiments at like values of Ri * were obtained. This suggests that the coefficient of molecular diffusion is not an important parameter in either type of experiment.
Other experiments, made in the same apparatus, describe the entrainment by a turbulent, homogeneous layer of an initially quiescent layer of fluid with a linear density gradient. The depth of the turbulent layer, D , increases with time, t , according to the relation. \[ D^3\propto t. \] This result is consistent with that found by Kato & Phillips (1969), although the turbulent layer in the present experiment is generated in a different manner.
The first-order jump model for the potential temperature or buoyancy
variable at the capping inversion atop a convectively mixed layer is
reexamined and found to imply existence of an entrainment rate equation
which is unreliable. The model is therefore extended here to allow all
the negative buoyancy flux of entrainment to occur within the
interfacial layer of thickness h and to allow realistic thermal
structure within the layer. The new model yields a well behaved
entrainment rate equation requiring scarcely any closure assumption in
the cases of steady-state entrainment with large-scale subsidence, and
pseudo-encroachment. For nonsteady entrainment the closure assumption
need only be made on d(h)/dt in order to obtain the entrainment rates at
both the outer and inner edges of the interfacial layer. A particular
closure assumption for d(h)/dt is tested against five laboratory
experiments and found to yield favorable results for both h and the
mixed-layer thickness if the initial value of h is known. It is also
compared against predictions from two zero-order jump models which do
not attempt prediction of h and one first-order jump model.
An experiment is described in which a constant stress is applied to the surface of an initially quiescent tank of fluid with a uniform density gradient. The development of the turbulent layer by entrainment of the underlying fluid is described and it is found that the entrainment coefficient E, the ratio of the entrainment velocity ue to the friction velocity u* is given in terms of the depth D of the mixed layer and the density jump across the entrainment interface by the relation\[E = \frac{u_e}{U_{*}} = 2.5\frac{\rho_0u^2_{*}}{g\delta\rho D}.\]The rate of increase of potential energy of the stratified fluid was found to be proportional to the rate of dissipation of kinetic energy per unit area in the turbulent layer. The form of these results is consistent with those found by Turner with an agitation tank, but the parameters used here allow direct application to entrainment in the ocean.
Turbulent entrainment at the density interface of a stable two-layer stratified fluid is studied in the laboratory, a constant surface stress being applied at the free surface. Conservation of mass requires that the overall Richardson number Ri = Dg/ the buoyancy difference and u* the friction velocity. If the entrainment rate E = ue/u* is a function only of Ri, it is therefore constant in each experiment and can be measured with a greater accuracy than has previously been attained. The functional dependence of ue/u* on Ri is established over the range 30 < Ri < 1000; it is found not to follow any simple power law. The entrainment rates are considerably higher than those measured by Kato & Phillips (1969), for which the fluid below the mixed layer was linearly stratified. Such a condition allows internal gravity waves to be radiated downwards and the reduction in entrainment rate is consistent with that found by Linden (1975).
The forced entrainment rate at the top of a stratocumulus deck is derived from the assumption that the negative buoyancy flux there is a particular fraction (1/2) of the average buoyancy flux within the entire mixed layer. A portion of the cloudtop radiative cooling is allowed to occur below the inversion base, thus contributing to the maintenance of the mixed-layer turbulence. The derived equation clearly shows the dependence of the forced entrainment rate upon the surface heat and moisture fluxes, cloudtop radiative cooling rate, temperature and humidity jumps across the capping inversion, solar absorption rate within the mixed layer, and percentage of the mixed layer occupied by stratocumulus. The forced entrainment rate becomes inapplicable when the thermal jump at cloudtop becomes very small; then either encroachment or free entrainment occurs, and expressions are proposed for each. A useful criterion is that the entrainment rate is the minimum of the calculated rates for forced entrainment, encroachment, and free entrainment. The equation is tested satisfactorily against observations of coastal stratus off California and stratocumulus development over Lake Michigan.
The rate of mixing across a density interface between two layers of liquid has been measured in a laboratory experiment which allows a direct comparison between heat and salinity transports over the same range of density differences. Low Reynolds number turbulence was produced by stirring mechanically at a fixed distance from the interface, either in one or in both layers, and the results for these two sets of experiments are also compared. The measurements cover a factor of two in stirring rate and twenty in density. Over this range of conditions the ratio of entrainment velocity to stirring velocity can be expressed as functions of an overall Richardson number Ri, and in this form the results of the one and two stirred layer experiments are indistinguishable from one another. For density differences produced by heat alone, the functional dependence is close to Ri−1 except at small values of Ri where it approaches a finite limit. For experiments with a salinity difference across the interface, the mixing rate is the same as in the heat experiments at low values of Ri, but falls progressively below this as Ri is increased, with the approximate form $Ri^{\frac{3}{2}} $.
Laboratory experiments of non-steady penetrative convection in water are performed that closely simulate the lifting of an atmospheric inversion above heated ground. Vertical profiles of horizontally averaged temperature and heat flux are measured and interpreted. The rate at which kinetic energy is destroyed by the downward heat flux in the vicinity of the inversion base is found to be a very small fraction of the rate at which it is generated in the lower convective region. The interface separating the convective region from the stable region is examined and its rate of rise explained.
Using data obtained from a probe mounted on the flying cable of a tethered kite balloon, this paper presents a fairly comprehensive description of the structure of a ‘hummocky’ subsidence inversion and the associated air motions, including the formation and breakdown of billows at the crests of the hummocks. Below the inversion, the transfer of warm air downwards was detected and the rate at which this occurred estimated using the model proposed by Readings et al. (1973). This estimate is shown to be in good agreement with that derived from some radio-sonde ascents. The fluxes of potential heat downwards at the inversion and upwards at the ground are estimated and their ratio is shown to be about 0.25.
The heated boundary layer for DAY 33 of the Wangara data of southeast Australia (Clarke et al., 1971) is studied numerically with a three-dimensional model using 64000 grid points within a volume 5 km on a side and 2 km deep. Subgrid-scale transport equations were utilized in place of eddy-coefficient formulations. The rate of growth of the mixed layer is examined and parameterized, and the vertical profiles of heat flux, moisture flux and momentum fluxes are examined. The momentum boundary layer is found to coincide essentially with the mixed layer, and to grow with the latter during the hours of solar heating of the surface.
Radar observations of convective pattern types in clear atmosphere consisting of thermal- and Benard-like convention cells
Turbulent entrainment a t a bouyancy interface due to convective turbu-lence. Unpublished manuscript
- D A. M. T. P University
- Cambridge Kantha
D.A.M.T.P., University of Cambridge. KANTHA, L. H. 1979c Turbulent entrainment a t a bouyancy interface due to convective turbu-lence. Unpublished manuscript, Dept. of Earth and Plan. Sci., Johns Hopkins Univ., Baltimore, Maryland 21218. KANTHA, L. H., PHILLIPS, 0. M. & &AD, R. S. 1977 On turbulent entrainment at a stable density interface. J. FZuid Mech. 79, 753-768.
Observation and simulation of stonn
- J F Price
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- J. C.-Randall Van Leer
PRICE, J. F., MOOERS, C. N. K. & VAN LEER, J. C. 1978 Observation and simulation of stonn-RANDALL, D. A. 1980 Entrainment into a stratocumulus layer with distributed radiative cooling.
On the dissipation of tall cumulus clouds
- J Namias
NAMIAS, J. 1939 On the dissipation of tall cumulus clouds. Monthly Weather Rev. 67, 294-295.
The rise of a strong inversion caused by heating a t the ground
- R R Long
- L H Kantha
LONG, R. R. & KANTHA, L. H. 1978 The rise of a strong inversion caused by heating a t the ground. In Proc. 12th Naval Hydrodyn. Symp., Wash. D.C. National Academy of Sciences. MALKUS, J. S. 1958 On the structure of the trade wind moist layer. Papers in Phys. Oceunog. & Met. 13, M.I.T. and Woods Hole Oceanog. Inst. 1-48.
- Uthe