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Relations between surface fluxes and mean profiles of velocity, temperature and concentration, downwind of a change in surface roughness
Quarterly Journal of the Royal Meteorological Society
Abstract
Changes in surface fluxes (of momentum, heat, and mass) downwind of a surface roughness change, are related to changes in mean profiles (of velocity, temperature, and concentration). the theory assumes that changes in mean quantities are self-preserving. At fetches sufficiently large for the underlying surface to be specified by an aerodynamic surface roughness, the changes in surface fluxes are related to changes in this quantity. the theoretical results are supported by available experimental data.
... Second , the treated area should have no vegetative cover, or at least a very short one, so that virtually all of the horizontal flux occurs in the air layers above the surface. Then , the profile of horizontal flux density has a theoretically predictable shape which is determined by surface roughness, plot geometry and atmospheric stability (Philip 1959, Mulhearn 1977and Wilson et a/. 1982. ...
... The simplification in measurement technique which this permits is obviously very great. While the appropriate value of u p 9 /F at ZINST can be determined empirically by 'calibrating' experiments like those just described , it can also be calculated a priori from models of atmospheric dispersion from plane sources such as those ofPhilip (1959), Mulhearn (1977) and Wilson eta!. (1982). These analyses predict the development of the concentration profile downwind of a change in surface flux density. ...
... Comparisons between the model predictions and the flux densities measured over three days and nights are shown in Fig. 5.8. The models of Philip ( 1959) and Mulhearn ( 1977) tend to overestimate the surface flux slightly by day, while that of Wilson et a!. ( 1982) slightly underestimates it. However, all three models give predictions of quite acceptable accuracy, generally well within I 0% of the measured flux. ...
While it has been recognised for many years that gaseous transfer is an important pathway in the terrestrial N cycle, it is only in recent times that direct field measurements have been made of the exchanges of nitrogenous gases between soils, plants and the atmosphere. Methods of three general kinds have been employed: those using diffusion theory to calculate gas transport in the soil profile; enclosure methods in which the flux density of the gas at the soil or water surface is calculated from changes in gas concentration in an enclosure placed over the surface; and micrometeorological techniques in which the vertical flux density of the gas is measured in the free air above the surface.
... Over the past five decades there have been numerous experimental studies of turbulent boundary layers over surface roughness changes that have proved invaluable in improving our understanding of how flow adjusts to heterogeneous surface conditions (Elliot 1958; Bradley 1968; Luxton 1971, 1972; Schofield 1975; Mulhearn 1977 Mulhearn , 1978 Wood 1982; Avelino 2000; Cheng and Castro 2002 ). Many of these studies were limited to mean velocity statistics (Elliot 1958; Wood 1982) while those that measured turbulence statistics (e.g., Bradley 1968; Luxton 1971, 1972; Mulhearn 1977) were focussed on measuring variables relevant to the RANS (Reynolds-Averaged Navier-Stokes) numerical simulation approach, namely the Reynolds stresses and total turbulent kinetic energy. ...
... Over the past five decades there have been numerous experimental studies of turbulent boundary layers over surface roughness changes that have proved invaluable in improving our understanding of how flow adjusts to heterogeneous surface conditions (Elliot 1958; Bradley 1968; Luxton 1971, 1972; Schofield 1975; Mulhearn 1977 Mulhearn , 1978 Wood 1982; Avelino 2000; Cheng and Castro 2002 ). Many of these studies were limited to mean velocity statistics (Elliot 1958; Wood 1982) while those that measured turbulence statistics (e.g., Bradley 1968; Luxton 1971, 1972; Mulhearn 1977) were focussed on measuring variables relevant to the RANS (Reynolds-Averaged Navier-Stokes) numerical simulation approach, namely the Reynolds stresses and total turbulent kinetic energy. However, those experiments were not designed to measure subfilter-scale quantities (SFS stresses and SFS energy transfer rates) as defined in the context of LES. ...
A wind-tunnel experiment was designed and carried out to study the effect of a surface roughness transition on subfilter-scale
(SFS) physics in a turbulent boundary layer. Specifically, subfilter-scale stresses are evaluated that require parameterizations
and are key to improving the accuracy of large-eddy simulations of the atmospheric boundary layer. The surface transition
considered in this study consists of a sharp change from a rough, wire-mesh covered surface to a smooth surface. The resulting
magnitude jump in aerodynamic roughnesses, M=ln(z
01/z
02), where z
01 and z
02 are the upwind and downwind aerodynamic surface roughnesses respectively, is similar to that of past experimental studies
in the atmospheric boundary layer. The two-dimensional velocity fields used in this study are measured using particle image
velocimetry and are acquired at several positions downwind of the roughness transition as well as over a homogeneous smooth
surface. Results show that the SFS stress, resolved strain rate and SFS transfer rate of resolved kinetic energy are dependent
on the position within the boundary layer relative to the surface roughness transition. A mismatch is found in the downwind
trend of the SFS stress and resolved strain rate with distance from the transition. This difference of behaviour may not be
captured by some eddy-viscosity type models that parameterize the SFS stress tensor as proportional to the resolved strain
rate tensor. These results can be used as a benchmark to test the ability of existing and new SFS models to capture the spatial
variability SFS physics associated with surface roughness heterogeneities.
... These studies have shown that an internal boundary layer (IBL) forms at the roughness transition point, where the change in surface roughness affects the mean streamwise velocity and the turbulent fields. Several analytical models for the mean velocity [6,9,10,11,12,13] and for the turbulence intensity [4] behind an abrupt surface roughness jump have been developed. None of these studies considered the effect of surface roughness transition on the evolution of a wind turbine or wind farm wakes located nearby. ...
We evaluate the effect of an abrupt change in the surface aerodynamic roughness height on a wind farm sited on it using the large eddy simulation (LES). Compared to a wind farm sited on a uniformly rough surface, the alteration in aerodynamic surface roughness from a rough to smooth value leads to substantial changes in the first-order and second-order turbulent statistics. Specifically, the rough-to-smooth surface roughness transition leads to an acceleration of the flow downstream of it, which affects the wake recovery and wind farm power production. Different velocity deficits are formulated considering different definitions of “upstream” velocity. The usual deficit, i.e., the difference between the overall wind farm upstream velocities and downstream of a turbine, attains negative values near the ground, rendering it difficult to model within the usual Gaussian radial-shape framework. An alternative definition, i.e., the difference in velocity at the same location with and without turbines on a heterogeneous surface, consistently yields positive values and is amenable to Gaussian shape-based modelling. The power generation decreases as the step change in surface roughness progressively moves into the wind farm. Maximum power is produced when all turbines are placed downstream of the surface roughness jump and minimum power is generated for a homogeneously rough surface when the entire wind farm is placed on the rough surface.
... These investigations have demonstrated the formation of an internal boundary layer (IBL) at the roughness transition point, where the change in surface roughness modulates the mean streamwise velocity and turbulent fields. Several analytical models have been formulated for the mean streamwise wind speed 1,9,13,14,28,30 and for the turbulence intensity (TI) 27 over surfaces with heterogeneous roughnesses. ...
Large-eddy simulations (LES) are performed on the flow over a wind farm sited behind an abrupt rough-to-smooth surface roughness jump. The change in surface roughness affects both the first-order and second-order turbulent statistics. The usual deficit, i.e., the difference between the velocities upstream of the entire wind farm and downstream of a turbine, attains negative values close to the ground, which makes it difficult for modeling within the usual Gaussian radial-shape framework. A different definition, i.e., the difference in velocity at the same location with and without a turbine on a heterogeneous surface, is always positive and is amenable to Gaussian shape-based modeling. For the setup considered here, wind farms sited downstream of a surface roughness jump produce more power than a wind farm sited on a homogeneously rough surface. This increase is primarily because of the larger power generated by the downstream turbines and only slightly due to the increased power of the first-row turbine. The farm performance is affected by the distance between the abrupt change in surface roughness and the position of the first row of turbines. The wind farm performance is also dependent on the aerodynamic roughness upstream of the surface roughness jump. Two single-turbine analytical models and three wake-merging strategies are evaluated for their ability to predict the velocity deficits. A corrected form of the standard Gaussian model with a recently proposed wake-merging methodology, applicable for a varying background field, is found to be insensitive to the tunable model parameter and is consistently in line with the LES results.
... We consider a simple configuration wherein the aerodynamic roughness undergoes a step change from z 01 to z 02 in the direction that is normal to that of the mean flow. This configuration has been studied using theoretical [1,2,3,4], observational/experimental [5,6,7] as well as numerical [3,8,9] approaches. A critical evaluation of the existing literature shows that a bulk of these previous studies have focused on situations relevant to engineering applications as opposed to geophysical applications. ...
The flow in the atmospheric boundary layer behind an abrupt transition in the surface roughness is studied using large eddy simulations (LES). A key ingredient of the LES is the ‘wall model’ that prescribes the instantaneous shear stress at the bottom surface as a function of the velocity field at the lower-most computational grid point. Two previously-developed wall models are evaluated; the first (BZ) is based on filtering the velocity field and the second (APA) is based on a blending function. The axial evolution of the wall shear stress, and vertical profiles of several quantities such as the stream-wise velocity, turbulence intensity and the total shear stress are evaluated. The APA model is found to predict the shear stress at the surface more accurately than the BZ model when compared with previous experimental results. Not all statistics are found to be equally sensitive to the wall models. We also employ the LES to evaluate an empirical relation for the height of the internal boundary-layer (IBL), which is commonly used to derive analytical models for the mean velocity profiles and wall shear stresses. The empirical relation is found to be reasonably accurate when the IBL height is calculated based on the shear stress but not when it is calculated based on the streamwise velocity variance. These results suggest that the wall model in LES of heterogeneously rough surfaces plays a key role and should be selected carefully in view of the quantity of interest.KeywordsAtmospheric boundary layerSurface roughnessHeterogeneityLarge eddy simulationWall modelling
... Several simplified analytical models have also been developed for the mean streamwise wind speed for such a heterogeneously rough surface. 2,[5][6][7][8] In our recent work, described in Ghaisas,9 a fully predictive analytical model for the mean streamwise velocity downstream of an abrupt surface roughness jump was proposed. However, none of these studies have considered the effect of such a surface roughness transition on the evolution of a wind turbine wake sited in its vicinity. ...
The evolution of a wind turbine wake situated downstream of an abrupt change in surface roughness is investigated using large-eddy simulations (LES). The results are compared with the evolution of the wake of a turbine sited on a homogeneously rough surface, and with the flow over a surface undergoing an abrupt roughness transition without a turbine. The changed surface roughness affects the turbulent statistics such as streamwise velocity, turbulence intensity, and shear stress. Different velocity deficits can be constructed based on different definitions of `background' velocity. The usual definition, i.e. the difference between the velocity upstream and downstream of a turbine, attains negative values over a significant portion of the turbine wake, rendering it difficult to model using the usual Gaussian radial shape-based framework. An alternative definition, i.e. the difference between the velocity over a heterogeneous surface in the absence and in the presence of a turbine, has mostly positive values, and is amenable to modeling. A new model accounting for streamwise and vertical variations of the background velocity profile is developed. The new model yields more accurate predictions of the LES results than the existing Gaussian wake-shape model which is applicable only for turbines sited on homogeneously rough surfaces.
... The internal flow layer near the bed was found to be not at an energy equilibrium state. Mulhearn [8] conducted wind tunnel experiments to explore the influence of bed roughness on the flow owing to a sudden change in roughness from rough to smooth beds. He observed that when the upstream bed roughness level aligns with the downstream bed level, the flow near the smooth bed is affected by the wake downstream of the upstream roughness elements. ...
The turbulence characteristics in open-channel flow owing to a sudden change from smooth (upstream) to rough (downstream) bed are investigated experimentally using a Particle Image Velocimetry system. The upstream flow had a shear Reynolds number of 4.86, characterizing the hydraulically smooth flow, while the downstream flow had a shear Reynolds number greater than 70, characterizing the hydraulically rough flow. The Reynolds stress results reveal that for a given vertical distance, both the Reynolds shear and normal stresses in the downstream bed increase with the streamwise distance as compared to their upstream values. Their peaks appear at a distance of one-fifth of the flow depth from the bed. In addition, the bed shear stress enhances with the streamwise distance. The stress contours corroborate that the formation of a roughness-induced layer over the downstream bed thickens with the streamwise distance. The third-order correlations reveal that an arrival of slowly moving fluid streaks associated with an outward Reynolds stress diffusion prevails in the flow on the upstream bed, while an inrush of rapidly moving fluid streaks associated with an inward Reynolds stress diffusion governs the near-bed flow zone in the downstream bed. These results are in conformity with those obtained from the turbulent kinetic energy (TKE) fluxes and the bursting events. With regard to the TKE budget, the peaks of TKE production and dissipation rates appear near the downstream bed and are greater than those in the upstream bed. However, in the downstream bed, an enhanced negative TKE diffusion prevails near the bed.
... The conditions for the existence of self-similar solutions were laid out, and a method to determine the surface stress and velocity distributions was outlined, given an assumption for the form of the velocity profile. A very similar approach was outlined in Mulhearn (1977), with a specific form for the velocity profile. Both these theories also allowed for considering other types of surface heterogeneities, such as a gradually varying roughness length, and for predicting the temperature profile due to an abrupt change in the surface heat flux. ...
A simple analytical model is developed for the flow downwind of a step change of the aerodynamic roughness length in the atmospheric boundary layer. The region downwind of the roughness transition is assumed to be composed of two equilibrium layers, corresponding to the downwind and upwind conditions, and separated by a third, transition, layer. The key assumption in deriving the model is that the eddy viscosity in the transition region is composed of a linearly varying component and an augmentation, which is parabolic in the vertical coordinate. The model is fully predictive up to two parameters that need to be specified. The first parameter is the ratio between the equilibrium boundary-layer height and the internal boundary-layer height. The second parameter controls the degree of nonlinearity of the eddy viscosity augmentation. An empirical relation is developed for the first parameter, while a range of values (between 0.1 and 0.3) is recommended for the second. The model is tested with results from field observations, wind-tunnel experiments, and numerical simulations of the flow behind a sudden jump in surface roughness. These tests show that the flow field and surface stresses are predicted accurately for smooth-to-rough as well as rough-to-smooth transitions.
... Nosso estudoé ainda fortemente motivado pela observação feita por outros autores onde a taxa de variação das propriedades do escoamento varia consideravelmente de um caso distinto para outro. Como exemplo, citamos as investigações sobre escoamentos com variação brusca de rugosidade de Antonia e Luxton(1971, 1972, Mulhearn(1977), Ligrani e Moffat(1986) e Bandyopadhyay(1987Bandyopadhyay( , 1988. ...
... For example, local 2D advection in which there is a step change in the surface source strength of a passive scalar has been studied by Philip (1959) and further developed by Dyer (1963) to estimate the so-called fetch-height ratio and by Schmid (1994) for footprint analyses. 2D changes in scalar fluxes caused by step changes in surface roughness have also been studied (e.g., Mulhearn, 1977; Lee et al., 1999 ) and previously reviewed by Garratt (1990). Nevertheless, any guidelines developed from these previous studies, while helpful, cannot be used with assurance of eliminating either 2D and 3D effects or the concomitant possibility of biases in the measured fluxes. ...
This study derives from and extends the discussions of a US DOE sponsored workshop held on 30 and 31 May, 2000 in Boulder, CO concerning issues and uncertainties related to long-term eddy covariance measurements of carbon and energy exchanges. The workshop was organized in response to concerns raised at the 1999 annual AmeriFlux meeting about the lack of uniformity among sites when making spectral corrections to eddy covariance flux estimates and when correcting the eddy covariance CO2 fluxes for lack of energy balance closure. Ultimately, this lack of uniformity makes cross-site comparisons and global synthesis difficult and uncertain. The workshop had two primary goals: first, to highlight issues involved in the accuracy of long-term eddy covariance flux records; and second, to identify research areas and actions of high priority for addressing these issues. Topics covered at the workshop include different methods for making spectral corrections, the influence of 3D effects such as drainage and advection, underestimation of eddy covariance fluxes due to inability to measure low frequency contributions, coordinate systems, and nighttime flux measurements. In addition, this study also covers some new and potentially important issues, not raised at the workshop, involving density terms to trace gas eddy covariance fluxes (Webb et al., 1980). Wherever possible, this paper synthesizes these discussions and make recommendations concerning methodologies and research priorities.
... The adjustment is not immediate throughout thickness of the air layer. Bradley (1968) and Mulhearn (1977), describing the downwind velocity profiles within the internal boundary layer, suggested that it might be described through a modified logarithmic law. Far downwind of the roughness change, a new equilibrium may be visualized so that the stress everywhere is constant. ...
In some arid land, the irrigated fields are not contiguous and are surrounded by large patches of bare land. During the summer time and rainless season, the solar radiation flux is high and the surface temperature during daylight in the dry bare areas, is much higher than that of the air. The sensible heat generated over these areas may be advected to the irrigated fields. The crops are usually planted in rows and the irrigation systems used (trickle) do not wet the whole surface, the dry bare soil between the rows may develop high soil surface temperatures and lead to convective activity inside the canopy above the bare soil. Advection from the surrounding fields and convective activity inside the canopy affect the layer above the crop. We studied the surface layer above an irrigated tomato field planted in Israel´s Negev desert. The crop was planted in rows, trickle irrigated and the distance between the outer edges of two adjacent rows was 0.36 m at the time of measurement. The gradients in temperature and water vapor pressure were obtained at various heights above the canopy using a Bowen ratio machine. The residual in the energy balance equation was used as a criterion to determine the equilibrium layer. During the morning, unstable conditions prevail, and the equilibrium layer was between Z/h ~ 1.9 and 2.4. In some particular circumstances, in the late morning, the bare soil between the rows reached extremely high temperatures and during conditions with low wind speeds free convection was identified. During these hours the ‘‘residuals’’ of the energy budget to the heights Z/h = 1.5 and 2.4 were significantly different from zero and an extremely large variability was evident for the Z/h = 3.2 layer. Local advection took place during the afternoon resulting in an increase in the stability of the uppermost measured layer and propagated slowly downwards. The equilibrium layer was between Z/h ~ 1.5 to 2.4. The residuals were significantly different from zero for the uppermost layers Z/h = 2.7 and 3.2 during these periods. Our findings suggest that the depth and location of the internal equilibrium layer above trickle irrigated row crop fields surrounded by dry bare areas, vary in response to wind speed and the temperature of the soil in between the rows of the crop. For some time intervals, the computation of fluxes using the conventional flux-gradient approach measurements was not possible.
... The adjustment is not immediate throughout thickness of the air layer. Bradley (1968) and Mulhearn (1977), describing the downwind velocity profiles within the internal boundary layer, suggested that it might be described through a modified logarithmic law. Far downwind of the roughness change, a new equilibrium may be visualized so that the stress everywhere is constant. ...
Arid and semi-arid regions are heterogeneous landscapes in which irrigated fields are surrounded by arid areas. The advection of sensible heat flux from dry surfaces is a significant source of energy that has to be taken into consideration when evaluating the evaporation from crops growing in these areas. The basic requirement of most of the common methods for estimating evapotranspiration [Bowen ratio, aerodynamic and Penman-Monteith (PM) equation] is that the horizontal fluxes of sensible and latent heat are negligible when compared to the corresponding vertical fluxes. We carried out measurements above an irrigated tomato field in a desert area. Latent and sensible heat fluxes were measured using a four-level Bowen machine with aspirated psychrometers. Our results indicate that under advective conditions only measurements carried out in the lowest layer are satisfactory for the estimation of latent heat fluxes and that the use of the PM equation with an appropriately parameterized canopy resistance may be preferable.
ABSTRACT
Turbulence characteristics in a fully developed flow over a gradually varied bed roughness are investigated. The results of the Reynolds stress profiles indicate that they increase with an increase in bed roughness height. Their peaks occur within the wall-shear layer close to the bed. Besides, the bed shear stress rises in accordance with the roughness height. The roughness-induced layer grows as the roughness height increases with the streamwise distance. The velocity profiles fitted with the logarithmic law reveal that the zero-velocity level is elevated as the roughness height increases, but the zero-plane displacement is not influenced by the roughness. The turbulent kinetic energy (TKE) flux results indicate that an inrush of faster moving fluid parcels composing the sweep event is the dominant mechanism in the near-bed flow zone. The magnitude of the sweep event escalates, as the roughness height increases. On the other hand, a process of slowly moving fluid parcels forming the ejection event prevails in the outer flow layer. The TKE flux results agree with those obtained from the bursting analysis. Concerning the TKE budget, the peaks of the TKE production, dissipation, and pressure energy diffusion rates being positive appear near the bed and grow as the roughness height increases, whereas the peak of the TKE diffusion rate being negative behaves in the similar way as the other terms of the TKE budget behave.
One of the foremost challenges for ecologists is to integrate observations made at a range of scales so that they become useful to others working at a different scale. An example of this would be scaling observations of carbon and water exchange made at leaf or plot scale to be of direct use to global climate modelers. Micrometeorological techniques, which operate at intermediate scales to these two extremes, are being used increasingly to validate and parameterize such models (Baldocchi and Meyers 1998). In turn, micrometeorological techniques can be validated against suitably scaled observations at a smaller scale. Progress in closing the carbon budget for example, must rely on such an interdisciplinary approach. When made in combination with detailed biophysical field experiments, such observations can reveal the atmospheric and biophysical variables that control carbon and water exchange. In this review, we describe briefly the most common micrometeorological methods used to measure fluxes of carbon and water at the scale of the canopy, focusing in particular on the direct techniques of eddy covariance and eddy accumulation. We also describe flux measurements at related scales that are commonly used to give added value to canopy-scale fluxes.
In this article discussion of evapotranspiration is limited to plant communities. Principles underlying various techniques are discussed, rather than specific applications. The scope is not restricted to agricultural or horticultural crops, but extends to other plant communities including natural and transplanted shrublands and forest ecosystems. Recent advances in evapotranspiration are reviewed and a perspective from the author's view is presented. Both measurement and calculation techniques are discussed, with greater emphasis on techniques which consider water flow through the soil-plant-atmosphere system.
Theoretical descriptions of the atmospheric boundary layer have not changed substantially during the past four years. The Monin-Obukhov theory remains the most complete description of the surface layer. Rather idealized models of the deeper convective boundary layer are also reasonably accurate. The stable boundary layer is still poorly understood, and the controversy persists in several attempts to relate boundary layer motions to deeper tropospheric flow.
By definition the boundary layer is the layer of the atmosphere that
responds directly to the character of the earth's surface. Usually, the
land surface is heterogeneous on a variety of scales and this
heterogeneity is reflected in the boundary layer. We have classified
surface heterogeneity into three types: complex surfaces such as plant
canopies and urban areas, where the horizontal scale of heterogeneity is
small; changing surface cover such as that found in farmland or between
major changes in land use; and topography. For each class of
heterogeneity we compare the changes that occur in the boundary layer
with the canonical boundary layer over homogeneous flat terrain. Our
emphasis is on changes to the windfield and surface stress that occur in
near-neutral stratification and we do not discuss scalar fields or the
effects of changes in the surface energy balance. In discussing
topography we deal only with low hills whose influence on the flow is
confined within the boundary layer.
The turbulent wind flow passing from a surface of one roughness to another is investigated analytically. The wind flow is modelled by a deep atmospheric turbulent boundary layer that assumes the possibility of self-preserving development in the course of flow modification. Closed form solutions are obtained describing the entire flow development and the characteristics of the wind velocity, surface stress changes and frictional velocity changes. It is found that as the wind flows past the roughness discontinuity, the flow adapts to the new surface roughness through adjustment by a vertical displacement of streamlines. This leads to a change in boundary layer thickness and the length of the acceleration region, in which the adjustments depend obviously on the difference in roughness between the new and the original region. By including the effect of frictional velocity and higher-order terms, the theory also shows that a greatly different value of shear stress is possible in the new regime, as opposed to what Townsend [J. Fluid Mech. 26 (1966) 255] has predicted.
A simple physical model of the wind transformation on abrupt changes in surface roughness and temperature across a coastal line is suggested. The model is based on a concept of the internal boundary layer (IBL) growth with the fetch. It consistently describes both small scale (order of 1km) and mesoscale (order of 10-100 km) evolution of the IBL. The planetary boundary layer (PBL) problem is solved using the similarity approach, which is applied for the IBL confined to the surface boundary layer. The description of the Ekman part of the PBL is based on the analytical solution of the momentum and heat balance equations. A 3-layer eddy-viscosity model of the PBL is introduced for the description of the mesoscale evolution of the IBL. The PBL model takes into account the baroclinicity eects due to the temperature gradient across a coastal line. The model is verified against existing data of the wind transformation across the Dutch coast of the North Sea and a reasonable agreement with observations is obtained. The model can be used as a module in multi-component coupled models describing dynamical processes in the ocean and the atmosphere and is viewed as a tool for engineering applications in the coastal zone.
Reviews turbulent-boundary-layer characteristics emphasizing the distribution of time and length scales. This review suggests a classification scheme for different perturbations. Flows with more than one perturbation acting simultaneously, including shock-wave/boundary-layer interactions, are discussed separately.-from Authors
For surface fluxes of carbon dioxide, the net daily flux is the sum of daytime and nighttime fluxes of approximately the same magnitude and opposite direction. The net flux is therefore significantly smaller than the individual flux measurements and error assessment is critical in determining whether a surface is a net source or sink of carbon dioxide. For carbon dioxide flux measurements, it is an occasional misconception that the net flux is measured as the difference between the net upward and downward fluxes (i.e. a small difference between large terms). This is not the case. The net flux is the sum of individual (half-hourly or hourly) flux measurements, each with an associated error term. The question of errors and uncertainties in long-term flux measurements of carbon and water is addressed by first considering the potential for errors in flux measuring systems in general and thus errors which are relevant to a wide range of timescales of measurement. We also focus exclusively on flux measurements made by the micrometeorological method of eddy covariance. Errors can loosely be divided into random errors and systematic errors, although in reality any particular error may be a combination of both types. Systematic errors can be fully systematic errors (errors that apply on all of the daily cycle) or selectively systematic errors (errors that apply to only part of the daily cycle), which have very different effects. Random errors may also be full or selective, but these do not differ substantially in their properties. We describe an error analysis in which these three different types of error are applied to a long-term dataset to discover how errors may propagate through long-term data and which can be used to estimate the range of uncertainty in the reported sink strength of the particular ecosystem studied.
We investigate small changes to a two-dimensional turbulent boundary layer on a rough surface caused by arbitrary variations, in the streamwise direction, of the surface roughness length, z1(x). the linear changes to the flow are calculated as asymptotic sequences in the limit ϵ = u*/U0 → 0 (u* is the upwind friction velocity, and U0 is a typical value of the approach wind speed). the flow is divided into two regions, each of which is subdivided into two layers; the previous analyses may then be extended by calculating the second-order effects. Throughout the bulk of the inner region, of thickness l, the Reynolds shear-stress gradient balances the acceleration, but very close to the surface (in the inner surface layer), up to a height O (√lz0), the shear-stress gradient is constant and matches with its surface value. the outer region (where the leading-order perturbations are inviscid) also divides into two layers: the middle layer extending to a height hm, where the shear in the upwind profile determines the perturbations; and the upper layer, in which the perturbations decay in potential flow, and a weak perturbation pressure develops which produces second-order changes in the inner region. At second order the normal Reynolds stresses also accelerate the mean-flow perturbations, but their effect is numerically small. the solutions in the inner surface layer satisfy the full non-linear equations, and by matching prudently, the layers above also contain a non-linear correction. We show that this means that the theory is valid when Mu*/U0 ≪ 1 (so that it may be applied to atmospheric problems even when M = ln(z0/z1,) is of order one). the theory agrees well with experiments and numerical simulations (which use complex models for the turbulence closure) and improves on the previous analytic theories, especially in the prediction of the surface shear stress.
The changes imposed on mean velocities and turbulence statistics in the lower atmosphere by an abrupt change in surface roughness, from very rough to smooth, were modelled in a wind tunnel. The influence of a change in the effective surface level, which often accompanies such a variation in surface roughness, was also studied. A deep, turbulent flow was generated upstream of the change, which had a logarithmic mean velocity profile and constant shear-stress for approximately 200 mm above the floor, except for a region near the surface which was influenced by the three-dimensional nature of the random rough surface.When the surface roughness change coincided with a change in surface level, the downstream flow close to the surface was in the wake of the upstream roughness elements, and measured Reynolds shear-stress values were lower than those obtained when the downstream surface was raised. Otherwise, the influence of a change in surface level was small.In all cases, Reynolds shear-stress varied approximately linearly with height in the lower two-thirds of the internal layer and no constant stress region was apparent near the surface, even 2 m downstream of the roughness change. When the roughness change was not accompanied by a change in level, Reynolds shear-stress values extrapolated to the surface agreed well with surface shear-stress inferred from the law of the wall.Changes in mean squares of vertical and lateral velocity fluctuations and in integral time scales, as the flow passed downstream of the roughness change, were surprisingly small.
A review is given of relevant work on the internal boundary layer (IBL) associated with:(i)
Small-scale flow in neutral conditions across an abrupt change in surface roughness,
(ii)
Small-scale flow in non-neutral conditions across an abrupt change in surface roughness, temperature or heat/moisture flux,
(iii)
Mesoscale flow, with emphasis on flow across the coastline for both convective and stably stratified conditions.
The major theme in all cases is on the downstream, modified profile form (wind and temperature), and on the growth relations for IBL depth.
Modeling nonhydrostatic atmospheric flow requires the solution of the vertical equation of motion and a prognostic or diagnostic equation for pressure. If the nonhydrostatic components of the flow are relatively small, they can be approximated and incorporated into a purely hydrostatic model, which usually is conceptually simpler and computationally more efficient. A method to do this for a linear model of local thermally-induced circulations is further developed and adapted to a non-linear numerical model of the neutral atmospheric boundary layer. A hydrostatic model and the quasi-nonhydrostatic version were used to simulate neutral flow over simple terrain features. One set of observations taken over a simple change in roughness and another set taken over a change in both roughness and terrain were simulated by both models to assess the capabilities of the quasi-nonhydrostatic technique.
It is found that (as expected) the pressure deviation from the hydrostatic state is negligible for the roughness change, but it is an important aspect of neutral flow over terrain. Thus, for flow encountering a simple roughness change, the hydrostatic approximation is good, even for small horizontal scales. However, the quasi-nonhydrostatic model qualitatively produces the features in the observations for flow over a terrain change that the hydrostatic model cannot produce.
Thesis (Ph. D.)--University of Minnesota, 2006. Major: Civil engineering. Includes bibliographical reference (leaves 128-141)
Under moist conditions, the energy balance approach to determining evapotranspiration from plant communities can give good results, but the method may not be nearly so accurate under very dry conditions, or with considerable advection of energy in moist conditions.In the former case, error analysis shows that the relative error in evapotranspiration can only be kept small provided that the relative error in the Bowen ratio is likewise small. In dry conditions, however, the absolute error in evapotranspiration is always fairly small, because of the small value of evapotranspiration itself. Analysis of the effect on the Bowen ratio of errors in the dry- and wet-bulb temperature gradients shows that in very dry conditions the required accuracy in the measurement of these gradients is an order of magnitude greater than could reasonaly be expected for most Bowen ratio equipment.In the latter case, experimental results show that Bowen ratio measurements considered to be made within the boundary layer, can give by day too small a value of evapotranspiration, and by night a latent heat flux direction which is inconsistent with the direction of the vapour pressure gradient. This raises the question as to what exactly is meant by adjustment of atmospheric properties to those of a new underlying surface when air passes over a boundary between two types of surface.
This work describes the major available techniques to simulate the time andspace evolution of the planetary boundary layer. For homogeneous andequilibrium conditions the structure of the planetary boundary layer can bediagnosed from the Monin-Obukhov, Free Convection, Local and MixedLayer Similarity theories. For the other atmospheric conditions theplanetary boundary layer can be numerically simulated using first andsecond order closure models and large eddy models. The closure modelstake into consideration the traditional statistical approach. Large eddysimulation models are based on the filtered equations of motion and requirethe statistical approach to estimate subgrid turbulence.
Wind profiles have been measured over the marshes of southern New Jersey, where the natural vegetation has been uniformly cut over a large area. Observations have been made with the wind at right angles to the roughness discontinuity, both in near‐neutral and in unstable air. Preliminary results from the analysis of near‐neutral cases are the following: (1) Over the cut grass the friction velocity is essentially a linear function of height. (2) The statement kz∕u* (∂V∕∂z) = 1 seems to hold in the transition zone. (3) The error in the function ϕ = kz∕u* (∂V∕∂z) made when assuming u* constant is about 5% at one‐tenth the height of the interface between the air influenced by rough and smooth terrain, and is nearly a linear function of height.
This report describes the research methods and data processing for basic research in the energy and mass transfers near the ground in plants and soil. Fundamental measurements of diurnal cycles of energy and moisture flux rates are reported. These include preliminary measure ments of air drag on a sod surface of 6-meter dia which indicate that von Karman's constant varies from less than 0.4 to more than 0.5. Concurrent hourly profiles of airspeed, tempera ture and moisture are reported and these cover a range of Richardson No. from 0.5 to -2 and show curvatures in the stable case opposite to those reported by Best and by Deacon. They reveal dissimilarities between velocity and temperature profiles which indicate that the eddy transfers processes are more complex than usually assumed. A square-root function of z/L is used to represent the curvature of semilog profiles ranging from strong thermal convection in the daytime to strong stable conditions at night.
If a thick, turbulent boundary layer is disturbed near the rigid boundary, the flow changes are confined initially to a thin layer adjacent to the boundary. Elliott (1958) and Panofsky & Townsend (1964) have attempted to calculate the flow disturbance caused by an abrupt change in surface roughness by assuming special velocity distributions which are consistent with a logarithmic velocity variation near the boundary. Inspection of their distributions shows that the deviations from the upstream distribution are self-preserving in form, and it is shown that self-preserving development is dynamically possible if log l0/z0 (l0 being depth of modified flow, z0 roughness length) is fairly large and if l0 is small compared with the total thickness of the layer. Other kinds of surface disturbance may lead to self-preserving changes of the original flow and the theory is developed also for flow downstream of a line roughness, for the temperature distribution downstream of a boundary separating an upstream region of uniform roughness and heat-flux from a region of different or possibly varying roughness and heat-flux, and for the return of a complete boundary layer to self-preserving development after a disturbance. The requirement that the distributions of velocity and temperature should conform to the logarithmic, equilibrium forms near the surface makes the predictions of surface stress and surface flux nearly independent of the exact nature of the turbulent transfer process, and the profiles of velocity and temperature are determined within narrow limits by the surface fluxes. To provide explicit profiles, the mixing-length transfer relation is used. Its validity for the self-preserving flows is discussed in an appendix.
In a previous paper, it was shown that abrupt changes in the surface conditions under a very deep boundary layer cause changes of mean velocity and temperature that satisfy the dynamical conditions for self-preserving development. Here the theory is extended to predict the development of the modified flow in the moderately deep layers that occur in nature and the laboratory. The problems considered are the changes in the velocity profile produced by an abrupt change of surface roughness and also by a line of concentrated roughness such as a fence, the changes in temperature produced by change of roughness combined with changes of heat flux at the surface, and diffusion of heat or a scalar pollutant from a line source at or near ground level. The predictions are compared with observations by Rider (1952) of the flow downwind of a hedge, by Rider, Philip & Bradley (1963) of temperature and humidity downwind of a change in surface, and of vertical diffusion from a line-source at ground level.
An experimental study of the structure of the internal layer which grows down-stream from a rough-to-smooth surface change shows it to be essentially different from that studied by Antonia & Luxton (1971 b) for the case of a smooth-to-rough perturbation. The rate of growth of the internal layer is less than that for the smooth-to-rough step and it appears that the more intense initial rough-wall flow dictates the rate of diffusion of the disturbance for a considerable distance. Inside the internal layer the mixing length I is increased relative to the equilibrium distribution I = KY. A turbulent energy budget shows that the advection is comparable with the production or dissipation, whilst there seems to be some diffusion of energy into the internal-layer region close to the wall. The boundary layer, as a whole, recovers much more slowly following a rough-to-smooth change than following a smooth-to-rough change, and at the last measuring station (16 boundary-layer thicknesses from the start of the smooth surface) the distributions of mean velocity and Reynolds shear stress are far from self-preserving.
The structure and growth of the internal boundary layer which forms downstream of a sudden change from a smooth to a rough surface under zero pressure gradient conditions has been studied experimentally. To keep pressure disturbances due to the roughness change small, the level of the rough surface was depressed, so that the crest of the roughness was aligned with the level of the smooth surface. It has been found that, in the region near the change, the structure of the internal layer is largely independent of that in the almost undisturbed outer layer, whilst both the zero time delay and the moving axis integral length scales in the internal layer are significantly reduced below those on the smooth wall. The growth-rate of the internal layer is similar to that of the zero pressure gradient boundary layer, whilst the level of turbulence inside the internal layer is high because of the large turbulent energy production near the rough wall. From the mixing length results, and an analysis of the turbulent energy equation, it is deduced that the internal layer flow near the wall is not in energy equilibrium, and hence the concept of inner layer similarity breaks down. From an initially self-preserving state on the smooth wall, the turbulent boundary layer approaches a second self-preserving state on the rough wall well downstream of the roughness step.
The changes of surface stress in a deep boundary layer passing from a surface of one roughness to another of different roughness are described fairly accurately by theories that assume self-preserving development of the flow modifications. It has been shown that the dynamical conditions for self-preserving flow can be satisfied if the change in friction velocity is small and if log l0/z0 is large (l0 is the depth of the modified flow and z0 is the roughness length of the surface). In this paper it is shown that, if the change of friction velocity is not small, the dynamical conditions can be satisfied to a good approximation over considerable fetches if log l0/z0 is large. The flow modification is then locally self-preserving, that is, the fields of mean velocity and turbulence are in a moving equilibrium but one which changes very slowly with fetch and depends on the ratio of the initial to the current friction velocity. In the limit of a very large increase in friction velocity, the moving equilibrium is essentially that of a boundary layer developing in a non-turbulent free stream. Equations describing the flow development are derived for all changes of friction velocity, and the form of the velocity changes is discussed. For large increases of friction velocity, the depth of the modified layer is substantially less than would be expected from the theories of Elliott and of Panofsky & Townsend.
Much micrometeorological work to date has assumed, or tried to ensure, that conditions of horizontal homogeneity exist at and near the earth's surface. The present paper reports an observational study of the variation in the meteorological elements with distance and height downwind of a pronounced discontinuity from dry to wet surface conditions. In particular the temperature and humidity fields were observed together with the changes in the radiative-balance components and in the wind structure. It was found that temperature and humidity changes at a height of 5 cm within 16 m of the discontinuity were commonly as much as 5$C and 5 g m−3 respectively. Theoretical treatments of the problem are outlined, and a slight modification of Philip's (1959) analysis is used to compare observed and predicted changes in temperature and humidity with distance downwind up to a height of 150 cm. It is found that the observed humidity changes are in good agreement with expectations, but that the measured temperature changes are about half those predicted. Changes in the evaporation rate in various distance intervals downwind from the leading edge have been computed. These are compared with an estimate of the rate which would have occurred under the same conditions from a wet area of infinite extent.
The discrepancies between theory and observation are attributed to the fact that the available theory fails to take into account the (demonstrable) differences in the aerodynamic properties of the adjacent surfaces. There is scope for further theoretical and experimental work on this matter.
This paper describes experiments in the lower atmosphere in which the wind passes from one surface to another with different roughness. Observations were made of the variation of surface stress, and of the development of velocity profiles in the region of flow modification over the downwind surface. Measurements are compared with the theories of Taylor, Elliot, and Panofsky and Townsend, and with the growth of a boundary layer on a flat plate. A large proportion of the surface stress adjustment occurs rapidly after the transition in agreement with Taylor's assumption. Velocity changes agree fairly well with the Panofsky and Townsend theory in the smooth-rough direction, but not so well in the reverse. Growth of the modified region follows the 4/5 power law of boundary layer growth. It is concluded that the height/fetch criterion for a good micrometeorological site is about 1/200.
Temperature profiles observed over a heavily irrigated grass field in the midst of dry surroundings show continuous modification up to the maximum height of measurement (5 m) even at a distance of 200 m from the leading edge.
Considerable variation of eddy fluxes in the vertical is demonstrated. The surface fluxes are found to undergo gradual adjustment.
These observations illustrate that a site of considerable extent is required for micrometeorological and agricultural studies before horizontal uniformity can be assumed.
Using the model and methods developed in Part I of this study, it is shown that steady-state evaporation, downwind of a sharp boundary separating uniform regions with constant but different surface resistances and available energies, can be written as
where ϕx is a dimensionless ‘exchange function’ that decreases from unity to zero as distance increases downwind of the boundary. The symbols have their conventional meanings and the primes signify upwind values. The form of ϕx depends on the profiles of wind speed and effective diffusivity, and on the downwind surface resistance and temperature via the parameter γrs/(s+γ).
Empirical expressions for ϕx are obtained from a known solution of the atmospheric diffusion equations assuming power law forms of the wind speed and effective diffusivity profiles and from a simple model assuming perfect vertical mixing and constant wind speed beneath an impermeable inversion base. These may give some indication of the form and magnitude of ϕx at small and at large distances respectively.
Handbook of mathematical functions
- M. Abromowitz
- I. A. Segun
A.1973Numerical modelling of the planetary boundary layer Workshop in micrometeorology ed
- M Estoque