Andrey A. Grachev

Andrey A. Grachev
Army Research Laboratory | ALC · Computational and Information Sciences Directorate (CISD)

PhD

About

109
Publications
31,315
Reads
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6,082
Citations
Introduction
I am a research scientist and my interest focuses on the atmospheric boundary layers over land/sea/ice, unraveling the intricacies of the atmospheric & oceanic turbulence. My work is devoted to making in-situ measurements of surface fluxes & meteorology for understanding and proper parameterization of the turbulent fluxes for climate modeling, weather forecasting, and other important applications. I participated in numerous research field campaigns and sea cruises from the Tropics to the Arctic.
Additional affiliations
February 1999 - October 2020
University of Colorado Boulder
Position
  • Researcher
February 1999 - October 2020
National Oceanic and Atmospheric Administration
Position
  • Researcher
November 1997 - January 1999
Arizona State University
Position
  • Researcher
Education
September 1980 - June 1983
Moscow Institute of Physics and Technology
Field of study
  • Geophysics and Atmospheric Physics
September 1974 - June 1980
Moscow Institute of Physics and Technology
Field of study
  • Oceanography and Atmospheric Physics

Publications

Publications (109)
Article
The universal velocity log law proposed by von Kármán in wall-bounded turbulent flows is one of the cornerstones of turbulence theory. When buoyancy effects are important, the universal velocity log law is typically believed to break down according to Monin-Obukhov similarity theory (MOST), which has been used in almost all global weather and clima...
Article
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The Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) was a yearlong expedition supported by the icebreaker R/V Polarstern, following the Transpolar Drift from October 2019 to October 2020. The campaign documented an annual cycle of physical, biological, and chemical processes impacting the atmosphere-ice-ocean system....
Article
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This paper reports analysis of eddy-covariance data collected during the WFIP2 field campaign in the complex-terrain of the US Pacific Northwest. A 31-day period representative of the region’s dry season was used to address the following questions: (1) To what extent does the Constant-Flux Layer (CFL) assumption hold? (2) What is the spatial variab...
Article
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Despite the importance of high-latitude surface energy budgets (SEBs) for land-climate interactions in the rapidly changing Arctic, uncertainties in their prediction persist. Here, we harmonize SEB observations across a network of vegetated and glaciated sites at circumpolar scale (1994–2021). Our variance-partitioning analysis identifies vegetatio...
Preprint
The universal velocity log law first proposed by von K\'arm\'an in the near-wall region of turbulent shear flows is one of the cornerstones of turbulence theory. When buoyancy effects are important, the universal velocity log law is typically believed to break down according to Monin-Obukhov similarity theory (MOST), which has been used in almost a...
Article
Full-text available
Measurements made in the Columbia River basin (Oregon) in an area of irregular terrain during the second Wind Forecast Improvement Project (WFIP2) field campaign are used to develop an optimized hybrid bulk algorithm to predict the surface turbulent fluxes from readily measured or modeled quantities over dry and wet bare or lightly vegetated soil s...
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An interesting mixing-fog event was identified during the C-FOG field campaign, where a cold-frontal airmass arriving from the north-east collided with The Downs peninsula in Ferryland, Newfoundland, Canada, to produce misty/foggy conditions. A comprehensive set of field observations suggests that this collision caused turbulent mixing of nearly sa...
Article
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Measurements of atmospheric turbulence at a site in Ferryland (Newfoundland) during the C-FOG (Coastal-Fog) field campaign in September–October 2018 are used to study meteorological parameters, turbulence statistics, internal boundary layers, and scaling laws for turbulent mixing in the coastal zone. We observe stable/unstable shallow internal boun...
Article
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Plain Language Summary Results of weather forecast, present‐day climate simulations, and future climate projections depend among other factors on the interaction between the atmosphere and the underlying sea‐ice, the land, and the ocean. In numerical weather prediction and climate models, some of these interactions are accounted for by transport co...
Conference Paper
The New Arctic has more open water in late summer and autumn than previously. However, during autumn, new ice freezes over open water areas, reaching the Arctic coastline by December. Hence, the autumn sea ice, over a large portion of the Arctic Ocean, consists of new ice that is thin, initially smooth, and quite different than sea ice later in the...
Article
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Surface turbulent fluxes provide a key boundary condition for the prediction of weather, hydrology, and atmospheric carbon dioxide. The turbulence cospectrum is assumed to typically follow a −7/3 power-law scaling, which is used for the high-frequency spectral correction of eddy-covariance data. The derivation of this scaling is mostly grounded on...
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C-FOG is a comprehensive bi-national project dealing with the formation, persistence, and dissipation (life cycle) of fog in coastal areas (coastal fog) controlled by land, marine, and atmospheric processes. Given its inherent complexity, coastal-fog literature has mainly focused on case studies, and there is a continuing need for research that int...
Article
Full-text available
C-FOG is a comprehensive bi-national project dealing with the formation, persistence, and dissipation (life cycle) of fog in coastal areas (coastal fog) controlled by land, marine, and atmospheric processes. Given its inherent complexity, coastal-fog literature has mainly focused on case studies, and there is a continuing need for research that int...
Article
Climate models still have deficits in reproducing the surface energy and momentum budgets in Arctic regions. One of the reasons is that currently used transfer coefficients occurring in parametrizations of the turbulent fluxes are based on stability functions derived from measurements over land and not over sea ice. An improved parametrization is d...
Article
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Measurements of the surface energy fluxes (turbulent and radiative) and other ancillary atmospheric/soil parameters made in the Columbia River Basin (Oregon) in an area of complex terrain during a 10-month long portion of the second Wind Forecast Improvement Project (WFIP 2) field campaign are used to study the surface energy budget (SEB) and surfa...
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Flow in the stable boundary layer is examined at four contrasting sites with greater upwind surface roughness. The surface heterogeneity is disorganized and in some cases weak as commonly occurs. With low wind speeds, the vertical divergence (or convergence) of the momentum and heat fluxes can be large near the surface in what is normally assumed t...
Preprint
Full-text available
Turbulent fluxes in the atmospheric surface layer are key input for the prediction of weather, hydrology, and carbon dioxide concentration. In numerical modelling of turbulent fluxes, a -7/3 power-law scaling in turbulence cospectra is usually assumed at high wavenumbers. In eddy-covariance (EC) measurements of turbulent fluxes, an assumed shape of...
Article
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This observational study compares seasonal variations of surface fluxes (turbulent, radiative, and soil heat) and other ancillary atmospheric/surface/permafrost data based on in-situ measurements made at terrestrial research observatories located near the coast of the Arctic Ocean. Hourly-averaged multiyear data sets collected at Eureka (Nunavut, C...
Article
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Atmospheric turbulence measurements made at the U.S. Army Corps of Engineers Field Research Facility (FRF) located on the Atlantic coast near the town of Duck, North Carolina during the CASPER-East Program (October–November 2015) are used to study air–sea/land coupling in the FRF coastal zone. Turbulence and mean meteorological data were collected...
Article
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CASPER objective is to improve our capability to characterize the propagation of radio frequency (RF) signals through the marine atmosphere with coordinated efforts in data collection, data analyses, and modeling of the air-sea interaction processes, refractive environment, and RF propagation. The Coupled Air-Sea Processes and Electromagnetic duct...
Article
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International Arctic Systems for Observing the Atmosphere (IASOA) activities and partnerships were initiated as a part of the 2007-09 International Polar Year (IPY) and are expected to continue for many decades as a legacy program. The IASOA focus is on coordinating intensive measurements of the Arctic atmosphere collected in the United States, Can...
Article
Science education can build a bridge between research carried out by scientists and relevant learning opportunities for students. The Broader Impact requirements for scientists by funding agencies facilitate this connection. We propose and test a model curriculum development process in which scientists, curriculum developers, and classroom educator...
Article
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Flow in a stably-stratified environment is characterized by anisotropic and intermittent turbulence, and wavelike motions of varying amplitudes and periods. Understanding turbulence intermittency and wave-turbulence interactions in a stably-stratified flow remains a challenging issue in geosciences including planetary atmospheres and oceans. The st...
Article
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Emerging application areas such as air pollution in megacities, wind energy, urban security, and operation of unmanned aerial vehicles have intensified scientific and societal interest in mountain meteorology. To address scientific needs and help improve the prediction of mountain weather, the U.S. Department of Defense has funded a research effort...
Article
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Measurements of small-scale turbulence made over the complex-terrain atmospheric boundary layer during the MATERHORN Program are used to describe the structure of turbulence in katabatic flows. Turbulent and mean meteorological data were continuously measured at multiple levels at four towers deployed along the East lower slope (2-4 deg) of Granite...
Article
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Local similarity theory is suggested based on the Brunt-Vaisala frequency and the dissipation rate of turbulent kinetic energy instead the turbulent fluxes used in the traditional Monin-Obukhov similarity theory. Based on dimensional analysis (Pi theorem), it is shown that any properly scaled statistics of the small-scale turbulence are universal f...
Conference Paper
The Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program is a Multidisciplinary University Research Initiative (MURI) designed to improve weather predictability in mountain terrain. Here we present some results from the first MATERHORN field experiment, a 30-day intense field campaign conducted during September 25-October 25,...
Article
Based on meteorological measurements collected at the Russian drifting stations "North Pole" for the 2007 - 2011 field seasons, estimates have been made of Central Arctic surface heat balances. A number of methods which utilize different parameterizations and measured long-wave and short-wave radiation fluxes are utilized and compared. A descriptio...
Article
Full-text available
The gradient-based similarity approach removes turbulent fluxes as governing parameters and replaces them with vertical gradients of mean wind speed and potential temperature. As a result, the gradient Richardson number, Ri, appears as a stability parameter instead of the Monin–Obukhov stability parameter z/L (L is the Obukhov length). The gradient...
Article
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This study focuses on variability of turbulent surface fluxes based on measurements made at two different sites located near the coast of the Arctic Ocean at Eureka (Canadian territory of Nunavut) and Tiksi (East Siberia). Turbulent fluxes and mean meteorological data are measured continuously and reported hourly at various levels on 10-m (Eureka)...
Article
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The applicability of the classical Monin-Obukhov similarity theory (1954) has been limited by constant flux assumption, which is valid in a narrow range z/L < 0.1 in the stable boundary layer (SBL). Nieuwstadt (1984) extended the range of applicability of the original theory using the local scaling (height-dependent) in place of the surface scaling...
Article
Instrumentation at four Study of Environmental Arctic Change (SEARCH) sites (Barrow, Eureka, Alert, and Tiksi) have been enhanced in the past 6 years, including during the 2007-2008 IPY. Data from these sites are used to investigate the annual cycle of the surface energy budget (SEB), its coupling to atmospheric processes, and for Alert, its intera...
Article
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Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin-Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on the spectral analysis of wind velocity a...
Article
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Air-sea/land turbulent fluxes of momentum, sensible heat, water vapor, carbon dioxide, and ozone are discussed on the basis of eddy covariance measurements made aboard the NOAA R/V Ronald H. Brown during the Texas Air Quality Study (TexAQS) in August-September 2006. The TexAQS 2006 field campaign focused on air pollution meteorology associated prim...
Article
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Data collected during the SHEBA and CASES-99 field programs are employed to examine the flux–gradient relationship for wind speed and temperature in the stably stratified boundary layer. The gradient-based and flux-based similarity functions are assessed in terms of the Richardson number Ri and the stability parameter z/Λ*, z being height and Λ* th...
Conference Paper
Full-text available
Analysis of Surface Fluxes at Eureka Climate Observatory in Arctic A. A. Grachev (1, 2), R. Albee (2), C. W. Fairall (1), J. E. Hare (1, 2), P. O. G. Persson (1, 2), and T. Uttal (2) (1) University of Colorado CIRES, Boulder, CO United States (andrey.grachev@noaa.gov) (2) NOAA Earth System Research Laboratory, Boulder CO, United States The Arcti...
Article
The surface of the Arctic Ocean in summer is a mix of sea ice and water in both leads and melt ponds. Here we use data collected at multiple sites during the year-long experiment to study the Surface Heat Budget of the Arctic Ocean (SHEBA) to develop a bulk turbulent flux algorithm for predicting the surface fluxes of momentum and sensible and late...
Article
Full-text available
The Surface Heat Budget of the Arctic Ocean (SHEBA) experiment produced 18 000 h of turbulence data from the atmospheric surface layer over sea ice while the ice camp drifted for a year in the Beaufort Gyre. Multiple sites instrumented during SHEBA suggest only two aerodynamic seasons over sea ice. In "winter" (October 1997 through 14 May 1998 and...
Article
Full-text available
The Surface Heat Budget of the Arctic Ocean (SHEBA) experiment produced 18 000 h of turbulence data from the atmospheric surface layer over sea ice while the ice camp drifted for a year in the Beaufort Gyre. Multiple sites instrumented during SHEBA suggest only two aerodynamic seasons over sea ice. In ''winter'' ice was compact and snow covered, an...
Article
Full-text available
1] Continuous surface-layer ozone flux measurements over the polar, year-round snowpack at Summit, Greenland, resulted in deposition velocities (v d) that were smaller than most previous assumptions and model inputs. Substantial seasonal differences were seen in the ozone v d behavior. Spring, daytime ozone v d values showed low variability and wer...
Article
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Eureka site (80.0 N, 85.9 W) is a long-term research observatory near the coast of the Arctic Ocean (Canadian territory of Nunavut). Eureka was established in 1947 as part of Arctic weather stations network and currently has been identified for enhanced instrumentation to monitor the changing Arctic climate. Beginning in 2004, remote sensors and in...
Article
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This paper documents the development of nocturnal flows in the wide open Phoenix, Arizona (U.S.A) valley (30 km × 100 km) that is bordered by a large nearly flat plain to the west and high mountains to the north and east. Local thermally driven winds concomitant with the absence of significant synoptic pressure gradients dominate typical winter con...
Article
Several long-term research observatories near the coast of the Arctic Ocean have been identified for enhanced instrumentation to monitor the changing Arctic climate. Eureka site (80.0 N, 85.9 W) is a small research base on Slidre Fjord on Ellesmere Island in the Canadian territory of Nunavut established in 1947 as part of Arctic weather stations ne...
Article
This paper focuses on the use of an acoustic sounder, or sodar, during the 2003 Antarctic Tropospheric Chemistry Investigation (ANTCI), to document the behavior of very shallow (<50 m) stable boundary layers thought to be one of the critical factors for explaining the very high levels of nitric oxide (NO) found in past field experiments at the Sout...
Article
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This paper surveys results of the comprehensive turbulent measurements in the stable boundary layer (SBL) made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) in the Beaufort Gyre from October 1997 through September 1998. Turbulent fluxes and mean meteorological data were continuously measured and repo...
Article
Full-text available
During the experiment to study the Surface Heat Budget of the Arctic Ocean (SHEBA), our multiple micrometeorological sites yielded over 10,000 hours of turbulent surface flux measurements during the polar winter. These measurements are relevant to the Eastern Snow Conference because polar sea ice is an ideal site for observing the fundamental proce...
Article
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This study focuses on the behaviour of the turbulent Prandtl number, Pr t , in the stable atmospheric boundary layer (SBL) based on measurements made during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA). It is found that Pr t increases with increasing stability if Pr t is plotted vs. gradient Richardson number, Ri; but at the same...
Article
Full-text available
Measurements of atmospheric turbulence made during the Surface Heat Budget of the Arctic Ocean Experiment (SHEBA) are used to examine the profile stability functions of momentum, φ m , and sensible heat, φ h , in the stably stratified boundary layer over the Arctic pack ice. Turbulent fluxes and mean meteorological data that cover different surface...
Article
Sonic anemometer turbulence measurements were made at Summit, Greenland during summer 2004 and spring 2005. These measurements allow for the characterization of the variability of the atmospheric boundary layer at this site by describing seasonal and diurnal changes in sensible heat flux and boundary layer stability as well as providing estimates o...
Article
modern atmosphere-hydrosphere-biosphere model chains, convective boundary-layer models and parameterization packages represent the most important coupling agents, which essentially control the overall quality of predictions from coupled models. This paper focuses on the enhancement of turbulent mixing due to large-scale semi-organized eddies and in...
Article
Full-text available
Turbulence-resolving modelling technique, widely known as large-eddy simulation (LES), becomes a popular tool to investigate environmental turbulence and to aggregate the impact of the turbulent mixing on larger, meteorologically important scales. Although the LES are proved to be useful, the technique still needs careful validation against availab...
Article
This study focuses on the behaviour of the turbulent Prandtl number, Pr t, in the stable atmospheric boundary layer (SBL) based on measurements made during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA). It is found that Pr t increases with increasing stability if Pr t is plotted vs. gradient Richardson number, Ri; but at the same t...
Article
Full-text available
1] In this paper, we examine observations of shallow, stable boundary layers in the cool waters of the Gulf of Maine between Cape Cod, Massachusetts, and Nova Scotia, obtained in the 2004 New England Air Quality Study (NEAQS-04), which was part of the International Consortium for Atmospheric Research into Transport and Transformation (ICARTT). The...
Article
Our group has used eddy correlation to make over 10,000 hours of measurements of the turbulent momentum and heat fluxes over snow-covered sea ice in both the Arctic and the Antarctic. Polar sea ice is an ideal site for studying fundamental processes for turbulent exchange over snow. Both our Arctic and Antarctic sites---in the Beaufort Gyre and dee...
Article
Full-text available
The von Kármán constant $k$ relates the flow speed profile in a wall-bounded shear flow to the stress at the surface. Recent laboratory studies in aerodynamically smooth flow report $k$ values that cluster around 0.420.39. Recent data from the atmospheric boundary layer, where the flow is usually aerodynamically rough, are similarly ambiguous: $k$...
Article
Close to the surface large coherent eddies consisting of plumes and downdraughts cause convergent winds blowing towards the plume axes, which in turn cause wind shears and generation of turbulence. This mechanism strongly enhances the convective heat/mass transfer at the surface and, in contrast to the classical formulation, implies an important ro...
Article
Full-text available
Turbulent and mean meteorological data collected at five levels on a 20-m tower over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are analyzed to examine different regimes of the stable boundary layer (SBL). Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the w...
Article
Full-text available
This paper presents a new theory of the convective heat/mass transfer. It focuses on (i) advanced treatment of turbulent mixing caused by large-scale semi-organised eddies overlooked in the classical theory and (ii) interactions between large eddies and surface roughness elements up to very high obstacles such as buildings, rocks and hills. Large-s...
Article
The Antarctic Tropospheric Chemistry Investigation (ANTCI) field program, during November and December 2003 at the South Pole, deployed a number of measurement systems to document the behavior of the atmospheric boundary layer (ABL) and the associated chemical processes that lead to high values of NO. These measurements included an acoustic sounder...
Article
Full-text available
Previous investigations of the wind stress in the marine surface layer have primarily focused on determining the stress magnitude (momentum flux) and other scalar variables (e.g., friction velocity, drag coefficient, roughness length). However, the stress vector is often aligned with a direction different from that of the mean wind flow. In this pa...
Article
In this study, directional characteristics of the wind stress in different wind-wave regimes are considered. We discuss results based on measurements made during three field campaigns onboard the R/P FLIP in the Pacific in 1993 and 1995 (SCOPE, MBL II, and COPE). We find a strong influence of the surface waves on the wind stress direction especiall...
Conference Paper
Full-text available
Data collected during several marine expeditions are used to investigate synoptic-scale disturbances in the Tropical Western Pacific. Measurements made on board the NOAA ship Ron Brown reveal westward propagating organized structures moving parallel to the equator. It is found that the true wind direction oscillates between about 60 and 120 deg wit...
Article
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In 1996, version 2.5 of the Coupled Ocean-Atmosphere Response Experiment (COARE) bulk algorithm was published, and it has become one of the most frequently used algorithms in the air-sea interaction community. This paper describes steps taken to improve the algorithm in several ways. The number of iterations to solve for stability has been shortene...
Article
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This paper focuses on the study of momentum flux between ocean and atmosphere in light winds and is based on the data collected during several field campaigns, the Atlantic Stratocumulus Transition Experiment, the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment, and the San Clemente Ocean Probing Experiment. Weak wind...
Article
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The heat and mass transfer over the sea is considered in terms of the sea surface roughness lengths for scalars, z0T for potential temperature , and z0q for specific humidity q, or alternatively, in terms of the roughness-layer scalar increments, and q. A new scaling reasoning is proposed in support of the familiar square root dependence of the abo...
Article
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This paper examines the interpolation betweenBusinger–Dyer (Kansas-type) formulae,u = (1 -1 6 )-1/4 andt = (1 - 16 )-1/2, and free convection forms. Based on matching constraints, the constants, au and at, in the convective flux-gradient relations, u = (1 - au )-1/3 and t = (1 - at )-1/3, are determined. It isshown that au and at cannot be complete...
Article
Air pollution in urban areas of the Southwestern United States reaches high levels during clear winter nights when atmospheric mixing is limited by stable temperature stratification near the ground. In order to develop a fundamental understanding of vertical structure of the atmosphere very close to the surface, we made wind, temperature and partic...
Article
The data obtained from the measurements of turbulent. fluxes and standard meteorological parameters during the TOGA COARE and SCOPE experiments are used to determine the relationship between the dimensionless height zeta = z/L of the Monin-Oboukhov similarity theory and the bulk Richardson number Ri(b) determined through the mean wind velocity and...
Article
Full-text available
Based on the idea that free convection can be considered as a particular case of forced convection, where the gusts driven by the large-scale eddies are scaled with the Deardorff convective velocity scale, a new formulation for the neutral drag coefficient, CDn, in the convective boundary layer (CBL) is derived. It is shown that (i) a concept of CD...
Chapter
During the last several decades the surface frictional processes in the shear-free convective boundary layer (CBL) are considered conceptually in the spirit of the Prandtl (1932) theory of free convection, implying the ideas of (i) universal chaotic turbulence and (ii) local correspondence between turbulent fluxes and mean gradients. Accordingly th...
Article
Full-text available
The Prandtl, Obukhov, and Monin andObukhov similarity theories are widely used todescribe the structure of turbulence in theatmospheric surface layer. Currently it isunderstood that in strong convection with no or veryweak mean wind the traditional theory breaks down.In particular, the traditional theory implies asingle-valued correspondence betwee...
Article
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Recent measurements made onboard the R/P FLIP in the San Clemente Ocean Probing Experiment in September 1993 and onboard the R/V Moana Wave during Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment are used to evaluate the direct dependence between the Monin-Obukhov stability parameter (ratio of height to Obukhov length)...
Article
The behavior of Eulerian frequency spectra of sensible and latent heat fluxes, as well as of tg-cospectrum, is considered in the inertial subrange above a water surface in calm conditions. This work is based on theoretical and experimental data of previous work [1,2] and extends an approach that has been developed for frequency autospectra in the l...
Article
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The aerodynamic classification of the resistance laws above solid surfaces is based on the use of a so-called Reynolds roughness number Re s =h s u */, whereh s is the effective roughness height, -viscosity,u *-friction velocity. The recent experimental studies reported by Toba and Ebuchi (1991), demonstrated that the observed variability of the se...
Article
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Frequency spectra of atmospheric turbulenceS (f) in the inertial subrange are considered in the free convection regime over the sea surface in a case of motionless instrument measurements (Eulerian frequency spectra). The frequency spectra formulaef * S (f)/ 2 =c (f */f)5/3 for wind velocity (=1–3), temperature (=t) and humidity (=e) fluctuations...
Article
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The problem of turbulent thermohaline convection in a horizontal slab of liquid in the case Sc ≫ Pr ≥ 1, i.e., when the sublayer of molecular diffusion of impurity lies deep within the sublayer of molecular thermal conductivity, is solved. This situation is observed in the surface layer of sea water (Sc/Pr ≃ 88), when thermohaline convection is cau...
Article
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Turbulent heat, salt and contaminant fluxes are considered in seawater in a horizontally uniform and statistically stationary case. By analogy with moist air, it is shown that the presence of buoyancy flux brought about by a heat flux and/or a mass flux leads to the fact that the value for the mean vertical velocity <>ob.\w is different from zero....
Article
The results of Golitsyn and Grachev (1980) for a two-component medium (moist air and sea water) are extended to a multicomponent medium and are verified for a three-component gas medium. The results are confirmed experimentally for different concentrations of ethyl alcohol in distilled water.
Article
The approximate formula K n a-2R(N-1), where a is a constant near 9 and R and N are the Rayleigh and Nusselt numbers, was proposed in [1] for the dimensionless kinetic energy K of convection in a horizontal layer of liquid. It is shown in the present paper that this expression is exact in linear and weakly nonlinear convection theory when the veloc...

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