doi:10.1007/s00376-016-5208-x

Arya S. P. S., J. C. Wyngaard, 1975: Effect of baroclinicity on wind profiles and the geostrophic drag law for the convective planetary boundary layer. J. Atmos. Sci., 32, 767- 778.10.1175/1520-0469(1975)032<0767:EOBOWP>2.0.CO;2

cafee80efe2adbeb012c25cd57a6cc6e

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1975jats...32..767a

http://adsabs.harvard.edu/abs/1975jats...32..767aBy using a simple physical model of the baroclinic convective planetary boundary layer, the similarity functions of the geostrophic drag law are expressed as sums of a barotropic part, dependent only on the stability and boundary layer height parameters, and a baroclinicity dependent part. The latter are predicted to he sinusoidal functions of the angle between surface wind and geostrophic shear, their amplitudes being proportional to the normalized magnitude of geostrophic shear. These drag laws are confirmed by the results of a more sophisticated higher-order closure model, which also predict the magnitude of actual wind shears in the bulk of the mixed layer remaining much smaller than the magnitude of imposed geostrophic shear. The results are shown to be supported by some observations from the recent Wangara and ATFX experiments. The surface cross-isobar angle is predicted to increase toward the equator, a trend well confirmed by observations, but in obvious conflict with the drag laws proposed by others who have ignored the height of the lowest inversion base from their similarity considerations.

Batchvarova E., S.-E. Gryning, 1994: An applied model for the height of the daytime mixed layer and the entrainment zone. Bound.-Layer Meteor., 71, 311- 323.10.1007/BF00713744

8d58ec7b7321fe88a676d495107746cc

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1994bolme..71..311b

http://adsabs.harvard.edu/abs/1994bolme..71..311bA model is presented for the height of the mixed layer and the depth of the entrainment zone under near-neutral and unstable atmospheric conditions. It is based on the zero-order mixed-layer height model of Batchvarova and Gryning (1991) and the parameterization of the entrainment zone depth proposed by Gryning and Batchvarova (1994). However, most zero-order slab type models of mixed-layer height may be applied. The use of the model requires only information on those meteorological parameters that are needed in operational applications of ordinary zero-order slab type models of mixed-layer height: friction velocity, kinematic heat flux near the ground and potential temperature gradient in the free atmosphere above the entrainment zone. When information is available on the horizontal divergence of the large-scale flow field, the model also takes into account the effect of subsidence, although this is usually neglected in operational models of mixed-layer height owing to lack of data. Model performance is tested using data from the CIRCE experiment.

Betts A. K., 1974: Reply to comment on the paper "Non-precipitating cumulus convection and its parameterization". Quart. J. Roy. Meteor. Soc., 100, 469- 471.10.1002/qj.49710042517

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http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2Fqj.49710042517%2Fcitedby

http://onlinelibrary.wiley.com/doi/10.1002/qj.49710042517/citedbyNot Available

Boers R., E. W. Eloranta, and R. L. Coulter, 1984: Lidar observations of mixed layer dynamics: Tests of parameterized entrainment models of mixed layer growth rate. J. Climate Appl. Meteor., 23, 247- 266.10.1175/1520-0450(1984)0232.0.CO;2

1d4cb8c1ab531612a8bf9f0cb22fb47d

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1984JApMe..23..247B

http://adsabs.harvard.edu/abs/1984JApMe..23..247BGround based lidar measurements of the atmospheric mixed layer depth, the entrainment zone depth and the wind speed and wind direction were used to test various parameterized entrainment models of mixed layer growth rate. Six case studies under clear air convective conditions over flat terrain in central Illinois are presented. It is shown that surface heating alone accounts for a major portion of the rise of the mixed layer on all days. A new set of entrainment model constants was determined which optimized height predictions for the dataset. Under convective conditions, the shape of the mixed layer height prediction curves closely resembled the observed shapes. Under conditions when significant wind shear was present, the shape of the height prediction curve departed from the data suggesting deficiencies in the parameterization of shear production. Development of small cumulus clouds on top of the layer is shown to affect mixed layer depths in the afternoon growth phase.

Conzemius R. J., E. Fedorovich, 2006a: Dynamics of sheared convective boundary layer entrainment. Part I: Methodological background and large-eddy simulations. J. Atmos. Sci., 63, 1151- 1178.10.1175/JAS3691.1

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http%3A%2F%2Fwww.ams.org%2Fmathscinet-getitem%3Fmr%3D2216927

http://www.ams.org/mathscinet-getitem?mr=2216927Abstract The reported study examines the dynamics of entrainment and its effects on the evolution of the dry atmospheric convective boundary layer (CBL) when wind shear is present. The sheared CBL can be studied by means of direct measurements in the atmosphere, laboratory studies, and numerical techniques. The advantages and disadvantages of each technique are discussed in the present paper, which also describes the methodological background for studying the dynamics of entrainment in sheared CBLs. For the reported study, large-eddy simulation (LES) was chosen as the primary method of convective entrainment investigation. Twenty-four LES runs were conducted for CBLs growing under varying conditions of surface buoyancy flux, free-atmospheric stratification, and wind shear. The simulations were divided into three categories: CBL with no mean wind (NS), CBL with a height-constant geostrophic wind of 20 m s鈭1 (GC), and CBL with geostrophic wind shear (GS). In the simulated cases, the sheared CBLs grew fastes...

Conzemius R. J., E. Fedorovich, 2006b: Dynamics of sheared convective boundary layer entrainment. Part II: Evaluation of bulk model predictions of entrainment flux. J. Atmos. Sci., 63, 1179- 1199.10.1175/JAS3696.1

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refpaperuri:(39f545aff06888e3d4a6d9c0cb9971b8)

http://www.ams.org/mathscinet-getitem?mr=2216928Abstract Several bulk model–based entrainment parameterizations for the atmospheric convective boundary layer (CBL) with wind shear are reviewed and tested against large-eddy simulation (LES) data to evaluate their ability to model one of the basic integral parameters of convective entrainment—the entrainment flux ratio. Test results indicate that many of these parameterizations fail to correctly reproduce entrainment flux in the presence of strong shear because they underestimate the dissipation of turbulence kinetic energy (TKE) produced by shear in the entrainment zone. It is also found that surface shear generation of TKE may be neglected in the entrainment parameterization because it is largely balanced by dissipation. However, the surface friction has an indirect effect on the entrainment through the modification of momentum distribution in the mixed layer and regulation of shear across the entrainment zone. Because of this effect, parameterizations that take into account the surface friction veloci...

Conzemius R. J., E. Fedorovich, 2007: Bulk models of the sheared convective boundary layer: Evaluation through large eddy simulations. J. Atmos. Sci., 64, 786- 807.10.1175/JAS3870.1

5f2cb93756df7f36d1efd427378c30c7

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2007JAtS...64..786C

http://adsabs.harvard.edu/abs/2007JAtS...64..786CAbstract A set of first-order model (FOM) equations, describing the sheared convective boundary layer (CBL) evolution, is derived. The model output is compared with predictions of the zero-order bulk model (ZOM) for the same CBL type. Large eddy simulation (LES) data are employed to test both models. The results show an advantage of the FOM over the ZOM in the prediction of entrainment, but in many CBL cases, the predictions by the two models are fairly close. Despite its relative simplicity, the ZOM is able to quantify the effects of shear production and dissipation in an integral sense鈥攁s long as the constants describing the integral dissipation of shear- and buoyancy-produced turbulence kinetic energy (TKE) are prescribed appropriately and the shear is weak enough that the denominator of the ZOM entrainment equation does not approach zero, causing a numerical instability in the solutions. Overall, the FOM better predicts the entrainment rate due to its ability to avoid this instability. Also, the FOM in a more physically consistent manner reproduces the sheared CBL entrainment zone, whose depth is controlled by a balance among shear generation, buoyancy consumption, and dissipation of TKE. Such balance is manifested by nearly constant values of Richardson numbers observed in the entrainment zone of simulated sheared CBLs. Conducted model tests support the conclusion that the surface shear generation of TKE and its corresponding dissipation, as well as the nonstationary terms, can be omitted from the integral TKE balance equation.

Deardorff J. W., 1979: Prediction of convective mixed-layer entrainment for realistic capping inversion structure. J. Atmos. Sci., 36, 424- 436.10.1175/1520-0469(1979)0362.0.CO;2

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http%3A%2F%2Fonlinelibrary.wiley.com%2Fresolve%2Freference%2FADS%3Fid%3D1979JAtS...36..424D

http://onlinelibrary.wiley.com/resolve/reference/ADS?id=1979JAtS...36..424DThe 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 Δand 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 (Δ)/in order to obtain the entrainment rates at both the outer and inner edges of the interfacial layer. A particular closure assumption for (Δ)/is tested against five laboratory experiments and found to yield favorable results for both Δand the mixed-layer thickness if the initial value of Δis known. It is also compared against predictions from two zero-order jump models which do not attempt prediction of Δand one first-order jump model.

Deardorff J. W., 1980: Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound.-Layer Meteor., 18, 495- 527.6618e7dc0e5515dbf5ac81d7f5e9eb65

http%3A%2F%2Fwww.nrcresearchpress.com%2Fservlet%2Flinkout%3Fsuffix%3Drefg4%2Fref4%26dbid%3D16%26doi%3D10.1139%252Fcjfr-2014-0184%26key%3D10.1007%252FBF00119502

http://xueshu.baidu.com/s?wd=paperuri%3A%282cb7d26b0f739a344dfcfa43abf9f3ee%29&filter=sc_long_sign&tn=SE_xueshusource_2kduw22v&sc_vurl=http%3A%2F%2Fwww.nrcresearchpress.com%2Fservlet%2Flinkout%3Fsuffix%3Drefg4%2Fref4%26dbid%3D16%26doi%3D10.1139%252Fcjfr-2014-0184%26key%3D10.1007%252FBF00119502&ie=utf-8&sc_us=9920505749051549919

Deardorff J. W., G. E. Willis, and B. H. Stockton, 1980: Laboratory studies of the entrainment zone of a convectively mixed layer. J. Fluid Mech., 100, 41- 64.10.1017/S0022112080001000

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http%3A%2F%2Fjournals.cambridge.org%2Farticle_S0022112080001000

http://journals.cambridge.org/article_S0022112080001000Not Available

Driedonks A. G. M., 1982: Models and observations of the growth of the atmospheric boundary layer. Bound.-Layer Meteor., 23, 283- 306.10.1007/BF00121117

9b1feedd63d1e4c5ad37dca0b80d9b13

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1982BoLMe..23..283D

http://adsabs.harvard.edu/abs/1982BoLMe..23..283DThe evolution of the mixed layer during a clear day can be described with a slab model. The model equations have to be closed by a parameterization of the turbulent kinetic energy budget. Several possibilities for this parameterization have been proposed. In order to assess the practical applicability of these models for the atmosphere, field experiments were carried out on ten clear days in 1977 and 1978. Within the accuracy of the measurements the mixed-layer height in fully convective conditions (at noon on clear days) is well predicted taking a constant heat flux ratio [ - overline {θ w_h } = 0.2overline {θ w_s } ]. In the early morning hours mechanical entrainment is also important. Good overall results are obtained with the entrainment formulation [ - overline {θ w_h } = 0.2overline {θ w_s } + 5u_ * ^3 T/gh]. Only large differences in the entrainment coefficients lead to significantly different results. Making the entrainment model more complex does not lead to substantial improvement. The mean potential temperature in the mixed layer is reproduced within 0.5 °C. This temperature is insensitive to the choice of a particular entrainment formulation and depends more on the surface heat input and the temperature gradient in the stable air aloft.

Fedorovich E., 1995: Modeling the atmospheric convective boundary layer within a zero-order jump approach: An extended theoretical framework. J. Appl. Meteor., 34, 1916- 1928.10.1175/1520-0450(1995)0342.0.CO;2

960bb803447a2f112425d5b5e9e2fdfb

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1995JApMe..34.1916F

http://adsabs.harvard.edu/abs/1995JApMe..34.1916FThe paper presents an extended theoretical background for applied modeling of the atmospheric convective boundary layer within the so-called zero-order jump approach, which implies vertical homogeneity of meteorological fields in the bulk of convective boundary layer (CBL) and zero-order discontinuities of variables at the interface of the layer.The zero-order jump model equations for the most typical cases of CBL are derived. The models of nonsteady, horizontally homogeneous CBL with and without shear, extensively studied in the past with the aid of zero-order jump models, are shown to be particular cases of the general zero-order jump theoretical framework. The integral budgets of momentum and heat are considered for different types of dry CBL. The profiles of vertical turbulent fluxes are presented and analyzed. The general version of the equation of CBL depth growth rate (entrainment rate equation) is obtained by the integration of the turbulence kinetic energy balance equation, invoking basic assumptions of the zero-order parameterizations of the CBL vertical structure. The problems of parameterizing the turbulence vertical structure and closure of the entrainment rate equation for specific cases of CBL are discussed. A parameterization scheme for the horizontal turbulent exchange in zero-order jump models of CBL is proposed. The developed theory is generalized for the case of CBL over irregular terrain.

Fedorovich E. E., D. V. Mironov, 1995: A model for a shear-free convective boundary layer with parameterized capping inversion structure. J. Atmos. Sci., 52, 83- 95.10.1175/1520-0469(1995)0522.0.CO;2

8486a60388d6003b2f04f303266a9cc2

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1995JAtS...52...83F

http://adsabs.harvard.edu/abs/1995JAtS...52...83FThe paper extends Deardorff's general structure parameterization for a shear-free convective boundary layer. The model suggested employs the mixed layer hypothesis that the buoyancy (which is defined as b = g(rho(sub 0) - rho/rho(sub 0) where rho is the density, rho(sub 0) is the reference density, and g is the acceleration due to gravity) is constant with height within the mixed layer. The buoyancy flux zero-crossing height is taken as the mixed layer. The buoyancy flux zero-crossing height is taken as the mixed layer depth. The vertical buoyancy profile within the capping inversion, where the buoyancy flux is negative due to entrainment, is made dimensionless, using the buoyancy difference across the inversion and its thickness as appropiate scales. The auhtors examine the idea against the data from atmospheric measurements, laboratory experiments with buoyancy-agitated turbulence, and large-eddy simulations. The rate equations for the mixed layer and inversion layer depths are derived using the turbulent kinetic energy equation and Deardorff's scaling hypothesis refined to account for the inversion layer structure. The constants of the model are evaluated from the data of atmospheric, oceanic, and laboratory measurements, and large-eddy simulations. The causes of divergence of the estimates based on data of different origin are discussed. The model is applied to simulate convective entrainment in laboratory experiments. A reasonable explanation for ambiguous behavior of the entrainment zone in the experiments with a two-layer fluid is suggested. The model simulates transition regimes of convective entrainment in multilayer fluid strongly affected by the nonstationary of the entrainment zone.

Fedorovich E., R. Conzemius, and D. Mironov, 2004a: Convective entrainment into a shear-free, linearly stratified atmosphere: bulk models reevaluated through large eddy simulations. J. Atmos. Sci., 61, 281- 295.10.1175/1520-0469(2004)0612.0.CO;2

62a794565bb20787780f79ab6f52e61b

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2004JAtS...61..281F

http://adsabs.harvard.edu/abs/2004JAtS...61..281FRelationships between parameters of convective entrainment into a shear-free, linearly stratified atmosphere predicted by the zero-order jump and general-structure bulk models of entrainment are reexamined using data from large eddy simulations (LESs). Relevant data from other numerical simulations, water tank experiments, and atmospheric measurements are also incorporated in the analysis. Simulations have been performed for 10 values of the buoyancy gradient in the free atmosphere covering a typical atmospheric stability range. The entrainment parameters derived from LES and relationships between them are found to be sensitive to the model framework employed for their interpretation. Methods of determining bulk model entrainment parameters from the LES output are proposed and discussed. Within the range of investigated free-atmosphere stratifications, the LES predictions of the inversion height and buoyancy increment across the inversion are found to be close to the analytical solutions for the equilibrium entrainment regime, which is realized when the rate of time change of the CBL-mean turbulence kinetic energy and the energy drain from the CBL top are both negligibly small. The zero-order model entrainment ratio of about 0.2 for this regime is generally supported by the LES data. However, the zero-order parameterization of the entrainment layer thickness is found insufficient. A set of relationships between the general-structure entrainment parameters for typical atmospheric stability conditions is retrieved from the LES. Dimensionless constants in these relationships are estimated from the LES and laboratory data. Power-law approximations for relationships between the entrainment parameters in the zero-order jump and general-structure bulk models are evaluated based on the conducted LES. In the regime of equilibrium entrainment, the stratification parameter of the entrainment layer, which is the ratio of the buoyancy gradient in the free atmosphere to the overall buoyancy gradient across the entrainment layer, appears to be a constant of about 1.2.

Fedorovich E., Coauthors, 2004b: Entrainment into sheared convective boundary layers as predicted by different large eddy simulation codes. 16th Symposium on Boundary Layers and Turbulence, Portland, ME, Amer. Meteor. Soc.

6b1aea7f319dfadcff87c4cd5d77141f

http%3A%2F%2Fwww.researchgate.net%2Fpublication%2F40124905_Entrainment_into_sheared_convective_boundary_layers_as_predicted_by_different_large_eddy_simulation_codes

http://www.researchgate.net/publication/40124905_Entrainment_into_sheared_convective_boundary_layers_as_predicted_by_different_large_eddy_simulation_codesEntrainment is a complex physical process that is a driving mechanism of convective boundary-layer (CBL) development. There is no consensus in the boundarylayer research community regarding the role played by wind shears in the entrainment dynamics.

Flamant C., J. Pelon, B. Brashers, and R. Brown, 1999: Evidence of a mixed-layer dynamics contribution to the entrainment process. Bound.-Layer Meteor., 93, 47- 73.10.1023/A:1002083425811

d4c51794fdb300ea7d1a8b1f54b3b816

http%3A%2F%2Fwww.ingentaconnect.com%2Fcontent%2Fklu%2Fboun%2F1999%2F00000093%2F00000001%2F00237681

http://www.ingentaconnect.com/content/klu/boun/1999/00000093/00000001/00237681The internal thermal boundary layer developing over the Mediterranean during a cold-air outbreak associated with a Tramontane event has been studied by means of airborne lidar, in situ sensors, and a modelling approach that consisted of nesting the University of Washington (UW) planetary boundary-layer (PBL) model in an advective zero-order jump model. This approach bypasses some of the deficiencies associated with each model: the absence of the dynamics in the mixed layer for the zero-order jump model and the lack of an inversion at the PBL top for the UW PBL model. Particular attention is given to the parameterization of the entrainment flux at the PBL top. Values of the entrainment closure parameter derived with the model when matching PBL structure observations are much lower than those derived with standard zero-order jump models. They also are in good agreement with values measured in different meteorological situations by other studies. This improvement is a result of the introduction of turbulent kinetic energy production in the mixed layer.

Garcia J. R., J. P. Mellado, 2014: The two-layer structure of the entrainment zone in the convective boundary layer. J. Atmos. Sci., 71, 1935- 1955.10.1175/JAS-D-13-0148.1

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http%3A%2F%2Fconnection.ebscohost.com%2Fc%2Farticles%2F96286975%2Ftwo-layer-structure-entrainment-zone-convective-boundary-layer

refpaperuri:(9fb41f6ea2ee89986da2641c687297c9)

http://connection.ebscohost.com/c/articles/96286975/two-layer-structure-entrainment-zone-convective-boundary-layerAbstract The entrainment zone (EZ) of a dry, shear-free convective boundary layer growing into a linearly stratified fluid is studied by means of direct numerical simulation. The scale separation between the boundary layer thickness and the Kolmogorov length scale is shown to be sufficient to observe Reynolds number similarity in the statistics of interest during the equilibrium entrainment regime. Contrary to previous considerations, the vertical structure of the entrainment zone is found to be better described by the superposition of two sublayers: 1) an upper EZ sublayer that is dominated by overshooting thermals and is characterized by a penetration depth that scales with the ratio of the convective velocity and the buoyancy frequency of the free troposphere and 2) a lower EZ sublayer that is dominated by troughs of mixed fluid and is characterized by the integral length scale of the mixed layer. Correspondingly, different buoyancy scales are identified. The consequences of this multiplicity of scales on the entrainment rate parameters are evaluated directly, without resorting to any bulk model, through an exact relation among the mean entrainment rate, the local buoyancy increment, and both the turbulent and the finite-thickness contributions to the entrainment ratio A measured at the height of minimum buoyancy flux. The smaller turbulent contribution to A that is usually observed for relatively thick EZs is found to be compensated by the smaller local buoyancy increment instead of by the finite-thickness contribution. The two-layer structure of the entrainment zone is found to affect the exponent of the power-law relation between the normalized mean entrainment rate and the convective Richardson number such that the exponent deviates from 鈭1 for typical atmospheric conditions, although it asymptotically approaches 1 for higher Richardson numbers.

Gentine P., G. Bellon, and C. C. van Heerwaarden, 2015: A closer look at boundary layer inversion in large-eddy simulations and bulk models: Buoyancy-driven case. J. Atmos. Sci., 72, 728- 749.10.1175/JAS-D-13-0377.1

12c584dede0768688d18df132f541dc6

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2015JAtS...72..728G

http://adsabs.harvard.edu/abs/2015JAtS...72..728GNot Available

Heus T., Coauthors, 2010: Formulation of the dutch atmospheric large-eddy simulation (DALES) and overview of its applications. Geoscientific Model Development, 3, 415- 444.10.5194/gmd-3-415-2010

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http%3A%2F%2Fwww.oalib.com%2Fpaper%2F1377513

http://www.oalib.com/paper/1377513The current version of the Dutch Atmospheric Large-Eddy Simulation (DALES) is presented. DALES is a large-eddy simulation code designed for studies of the physics of the atmospheric boundary layer, including convective and stable boundary layers as well as cloudy boundary layers. In addition, DALES can be used for studies of more specific cases, such as flow over sloping or heterogeneous terrain, and dispersion of inert and chemically active species. This paper contains an extensive description of the physical and numerical formulation of the code, and gives an overview of its applications and accomplishments in recent years.

Hoxit L. R., 1974: Planetary boundary layer winds in baroclinic conditions. J. Atmos. Sci., 31, 1003- 1020.10.1175/1520-0469(1974)0312.0.CO;2

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1974JAtS...31.1003H

http://adsabs.harvard.edu/abs/1974JAtS...31.1003HSystematic stratifications and analyses of low-level radiosonde data are performed for portions of the eastern half of the United States. The procedures are designed to specify changes in the planetary boundary layer wind profile resulting from variations in baroclinicity. The angle between the winds and isobars, the ageostrophic wind components, the surface stress, and the surface wind speeds are all shown to be functions of the orientation of the thermal wind vector relative to the surface geostrophic wind. These variations are consistent with a mixing-length model of the additional turbulent momentum transport initiated by the vertical shear of the geostrophic wind.

Huang J. P., X. H. Lee, and E. G. Patton, 2011: Entrainment and budgets of heat, water vapor, and carbon dioxide in a convective boundary layer driven by time-varying forcing. J.Geophys. Res., 116, D06308.10.1029/2010JD014938

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http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1029%2F2010JD014938%2Fpdf

http://onlinelibrary.wiley.com/doi/10.1029/2010JD014938/pdfA large-eddy simulation (LES) code is coupled with a land surface model to investigate the diurnal variation of the atmospheric boundary layer (ABL). The diurnal evolution of the ABL is driven by a time-varying incoming solar radiation. The results show that the domain average surface fluxes of sensible heat, water vapor, and carbon dioxide are smooth functions of time but the fluxes at any given surface grid point show random variations, especially the sensible heat flux. At the ABL top, the LES-resolved entrainment fluxes of these scalars also evolve with time and are not fixed fractions of their respective surface fluxes. Entrainment efficiency (the ratio of entrainment flux at zto w, where zis the ABL height, wis entrainment velocity, and is the jump of scalar across the entrainment zone) is highest for COand lowest for sensible heat. The first-order jump condition model is very good approximation to simulated entrainment fluxes which are largely controlled by the vertical gradients of the scalars across the capping inversion. Our results suggest that over the range of geostrophic winds considered (0-5 m s), neither the surface nor the entrainment flux reveals sensitivity to the geostrophic wind speed variations.

Kim S.-W., S.-U. Park, and C.-H. Moeng, 2003: Entrainment processes in the convective boundary layer with varying wind shear. Bound.-Layer Meteor., 108, 221- 245.10.1023/A:1024170229293

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http%3A%2F%2Fwww.ingentaconnect.com%2Fcontent%2Fklu%2Fboun%2F2003%2F00000108%2F00000002%2F05111563

http://www.ingentaconnect.com/content/klu/boun/2003/00000108/00000002/05111563Large-eddy simulations (LES) are performed to investigate the entrainment and the structure of the inversion layer of the convective boundary layer (CBL) with varying wind shears. Three CBLs are generated with the constant surface kinematic heat flux of 0.05 K m sand varying geostrophic wind speeds from 5 to 15 m s. Heat flux profiles show that the maximum entrainment heat flux as a fraction of the surface heat flux increases from 0.13 to 0.30 in magnitude with increasing wind shear. The thickness of the entrainment layer, relative to the depth of the well-mixed layer, increases substantially from 0.36 to 0.73 with increasing wind shear. The identification of vortices and extensive flow visualizations near the entrainment layer show that concentrated vortices perpendicular to the mean boundary-layer wind direction are identified in the capping inversion layer for the case of strong wind shear. These vortices are found to develop along the mean wind directions over strong updrafts, which are generated by convective rolls and to appear as large-scale wavy motions similar to billows generated by the Kelvin Helmholtz instability. Quadrant analysis of the heat flux shows that in the case of strong wind shear, large fluctuations of temperature and vertical velocity generated by large amplitude wavy motions result in greater heat flux at each quadrant than that in the weak wind shear case.

Kim S.-W., S.-U. Park, D. Pino, and J. V.-G. de Arellano, 2006: Parameterization of entrainment in a sheared convective boundary layer using a first-order jump model. Bound.-Layer Meteor., 120, 455- 475.10.1007/s10546-006-9067-3

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http%3A%2F%2Fwww.ingentaconnect.com%2Fcontent%2Fklu%2Fboun%2F2006%2F00000120%2F00000003%2F00009067

http://www.ingentaconnect.com/content/klu/boun/2006/00000120/00000003/00009067Basic entrainment equations applicable to the sheared convective boundary layer (CBL) are derived by assuming an inversion layer with a finite depth, i.e., the first-order jump model. Large-eddy simulation data are used to determine the constants involved in the parameterizations of the entrainment equations. Based on the integrated turbulent kinetic energy budget from surface to the top of the CBL, the resulting entrainment heat flux normalized by surface heat flux is a function of the inversion layer depth, the velocity jumps across the inversion layer, the friction velocity, and the convection velocity. The developed first-order jump model is tested against large-eddy simulation data of two independent cases with different inversion strengths. In both cases, the model reproduces quite reasonably the evolution of the CBL height, virtual potential temperature, and velocity components in the mixed layer and in the inversion layer.

Lemone M. A., M. Y. Zhou, C.-H. Moeng, D. H. Lenschow, L. J. Miller, and R. L. Grossman, 1999: An observational study of wind profiles in the baroclinic convective mixed layer. Bound.-Layer Meteor., 90, 47- 82.10.1023/A:1001703303697

1745ef0cf1760def501daf72a3e86786

http%3A%2F%2Fwww.ingentaconnect.com%2Fcontent%2Fklu%2Fboun%2F1999%2F00000090%2F00000001%2F00187684

http://www.ingentaconnect.com/content/klu/boun/1999/00000090/00000001/00187684A comprehensive planetary boundary-layer (PBL) and synoptic data set is used to isolate the mechanisms that determine the vertical shear of the horizontal wind in the convective mixed layer. To do this, we compare a fair-weather convective PBL with no vertical shear through the mixed layer (10 March 1992), with a day with substantial vertical shear in the north-south wind component (27 February). The approach involves evaluating the terms of the budget equations for the two components of the vertical shear of the horizontal wind; namely: the time-rate-of-change or time-tendency term, differential advection, the Coriolis terms (a thermal wind term and a shear term), and the second derivative of the vertical transport of horizontal momentum with respect to height (turbulent-transport term). The data, gathered during the 1992 STorm-scale Operational and Research Meteorology (STORM) Fronts Experiments Systems Test (FEST) field experiment, are from gust-probe aircraft horizontal legs and soundings, 915-MHz wind profilers, a 5-cm Doppler radar, radiosondes, and surface Portable Automated Mesonet (PAM) stations in a roughly 50 脳 50 km boundary-layer array in north-eastern Kansas, nested in a mesoscale-to-synoptic array of radiosondes and surface data. We present evidence that the shear on 27 February is related to the rapid growth of the convective boundary layer. Computing the shear budget over a fixed depth (the final depth of the mixed layer), we find that the time-tendency term dominates, reflecting entrainment of high-shear air from above the boundary layer. We suggest that shear within the mixed layer occurs when the time-tendency term is sufficiently large that the shear-reduction terms namely the turbulent-transport term and differential advection terms 鈥 cannot compensate. In contrast, the tendency term is small for the slowly-growing PBL of 10 March, resulting in a balance between the Coriolis terms and the turbulent-transport term. Thus, the thermal wind appears to influence mixed-layer shear only indirectly, through its role in determining the entrained shear.

Lewellen D. C., W. S. Lewellen, 1998: Large-eddy boundary layer entrainment. J. Atmos. Sci., 55, 2645- 2665.10.1175/1520-0469(1998)0552.0.CO;2

611229986f11e8dd13d1165d4e08a028

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1998JAtS...55.2645L

http://adsabs.harvard.edu/abs/1998JAtS...55.2645LA series of large-eddy simulations have been performed to explore boundary layer entrainment under conditions of a strongly capped inversion layer with the boundary layer dynamics driven dominantly by buoyant forcing. Different conditions explored include cloud-top cooling versus surface heating, smoke clouds versus water clouds, variations in cooling height and optical depth of longwave radiation, degree of cloud-top evaporative instability, and modest wind shear. Boundary layer entrainment involves transport and mixing over a full range of length scales, as warm fluid from the region of the capping inversion is first transported into the boundary layer and then mixed throughout. While entrainment is often viewed as the small-scale process of capturing warm fluid from the inversion into the top of the boundary layer, this need not be the physics that ultimately determines the entrainment rate. In these simulations the authors find instead that the entrainment rate is often limited by the boundary layercale eddy transport and is therefore surprisingly insensitive to the smaller scales of mixing near the inversion. The fraction of buoyant energy production available to drive large eddies that is lost to entrainment rather than dissipation was found to be nearly constant over a wide range of simulation conditions, with no apparent fundamental difference between top- versus bottom-driven or cloudy versus clear boundary layers. In addition, it is found that for quasi-steady boundary layers with dynamics driven by cloud-top cooling there is an effective upper limit on the entrainment rate for which the boundary layer dynamics just remains coupled, which is often approached when the cloud top is evaporatively unstable.

Mahrt L., D. H. Lenschow, 1976: Growth dynamics of the convectively mixed layer. J. Atmos. Sci., 33, 41- 51.10.1175/1520-0469(1976)0332.0.CO;2

18401ed2aba14c08432c3296d4eaad19

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1976JAtS...33...41M

http://adsabs.harvard.edu/abs/1976JAtS...33...41MA model for the growth of a convectively mixed layer is derived by layer integrating the basic equations and parameterizing unknown terms in the mixed layer turbulence kinetic energy equation by means of free convection similarity theory. When shear generation of turbulence energy is neglected in the turbulent inversion layer capping the mixed layer, the model essentially reduces to that of Tennekes. This shear generation is found to be important only in cases of significant baroclinicity and shallow mixed layer depth or small free flow stratification.

Moeng C.-H., P. P. Sullivan, 1994: A comparison of shear- and buoyancy-driven planetary boundary layer flows. J. Atmos. Sci., 51, 999- 1022.10.1175/1520-0469(1994)051<0999:ACOSAB>2.0.CO;2

a945d6409e2832addc2a5902eabf8f89

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1994JAtS...51..999M

http://adsabs.harvard.edu/abs/1994JAtS...51..999MPlanetary boundary layer (PBL) flows are known to exhibit fundamental differences depending on the relative combination of wind shear and buoyancy forces. These differences are not unexpected in that shear instabilities occur locally, while buoyancy force sets up vigorous thermals, which result in nonlocal transport of heat and momentum. At the same time, these two forces can act together to modify the flow field. In this study, four large-eddy simulations (LESs) spanning the shear and buoyancy flow regimes were generated; two correspond to the extreme cases of shear and buoyancy-driven PBLs, while the other two represent intermediate PBLs where both forces are important. The extreme cases are used to highlight and quantify the basic differences between shear and convective PBLs in 1) flow structures, 2) overall statistics, and 3) turbulent kinetic energy (TKE) budget distributions. Results from the two intermediate LES cases are used to develop and verify a velocity scaling and a TKE budget model, which are proposed for the intermediate PBL. The velocity variances and the variance fluxes (i.e., third moments) normalized by this velocity scaling are shown to become quantities on the order of one, and to lie mostly between those of the two extreme PBL cases. The proposed TKE budget model is shown to adequately reproduce the profiles of the TKE budget terms and the TKE.

Nieuwstadt F. T. M., R. A. Brost, 1986: The decay of convective turbulence. J. Atmos. Sci., 43, 532- 546.10.1175/1520-0469(1986)0432.0.CO;2

fbf50b319f50c812ee9c599a8adae4fe

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1986JAtS...43..532N

http://adsabs.harvard.edu/abs/1986JAtS...43..532NAbstract Using simulations with a large-eddy model we have studied the decay of convective turbulence in the atmospheric boundary layer when the upward surface sensible heat flux is suddenly stopped. The decay of turbulent kinetic energy and temperature variance scales with the dimensionless time tw * / h . The temperature fluctuations start to decrease almost immediately after the forcing has been removed, whereas the turbulent kinetic energy stays constant for a time t 鈮 h / w * . Vertical velocity fluctuations decay faster than horizontal fluctuations. Entrainment persists well into the decay process and may explain departures from similarity. Some evidence suggests a decoupling of large and small scales during the decay.

Otte M. J., J. C. Wyngaard, 2001: Stably stratified interfacial-layer turbulence from large-eddy simulation. J. Atmos. Sci., 58, 3424- 3442.10.1175/1520-0469(2001)0582.0.CO;2

38321ecbd1227f8b6186b1e8a7a85cbb

http%3A%2F%2Fonlinelibrary.wiley.com%2Fresolve%2Freference%2FADS%3Fid%3D2001JAtS...58.3424O

http://onlinelibrary.wiley.com/resolve/reference/ADS?id=2001JAtS...58.3424OThe structure of the interfacial layer capping the atmospheric boundary layer is not well understood. The dominant influence on turbulence within the interfacial layer is the stable stratification induced by the capping inversion. A series of 26 high-resolution large eddy simulation runs ranging from neutral, inversion-capped to free-convection cases are used to study interfacial layer turbulence. The interfacial layer is found to be similar in many aspects to a classic stable boundary layer. For example, the shapes of interfacial layer spectra and cospectra, including the locations of the spectral peaks, agree with previous observations from nocturnal PBLs. The eddy diffusivities, variances, structure-function parameters, and dissipation rates within the interfacial layer, suitably nondimensionalized using local scaling, also agree with observations from nocturnal PBLs. These results may lead to improved models of the interfacial layer and entrainment, and may also have implications for remote sensing of the interfacial layer.

Pino D., J. Vilà-Guerau De Arellano, 2008: Effects of shear in the convective boundary layer: analysis of the turbulent kinetic energy budget. Acta Geophysica, 56, 167- 193.10.2478/s11600-007-0037-z

c39b39c1caf994827e9c06a3f877266c

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2008AcGeo..56..167P

http://adsabs.harvard.edu/abs/2008AcGeo..56..167PEffects of convective and mechanical turbulence at the entrainment zone are studied through the use of systematic Large-Eddy Simulation (LES) experiments. Five LES experiments with different shear characteristics in the quasi-steady barotropic boundary layer were conducted by increasing the value of the constant geostrophic wind by 5 m s-1 until the geostrophic wind was equal to 20 m s-1. The main result of this sensitivity analysis is that the convective boundary layer deepens with increasing wind speed due to the enhancement of the entrainment heat flux by the presence of shear. Regarding the evolution of the turbulence kinetic energy (TKE) budget for the studied cases, the following conclusions are drawn: (i) dissipation increases with shear, (ii) the transport and pressure terms decrease with increasing shear and can become a destruction term at the entrainment zone, and (iii) the time tendency of TKE remains small in all analyzed cases. Convective and local scaling arguments are applied to parameterize the TKE budget terms. Depending on the physical properties of each TKE budget contribution, two types of scaling parameters have been identified. For the processes influenced by mixed-layer properties, boundary layer depth and convective velocity have been used as scaling variables. On the contrary, if the physical processes are restricted to the entrainment zone, the inversion layer depth, the modulus of the horizontal velocity jump and the momentum fluxes at the inversion appear to be the natural choices for scaling these processes. A good fit of the TKE budget terms is obtained with the scaling, especially for shear contribution.

Pino D., J. Vilà-Guerau de Arellano, and P. G. Duynkerke, 2003: The contribution of shear to the evolution of a convective boundary layer. J. Atmos. Sci., 60, 1913- 1926.10.1175/1520-0469(2003)0602.0.CO;2

f9ad67c5412a6698d8b062a40a6a36fd

http%3A%2F%2Fonlinelibrary.wiley.com%2Fresolve%2Freference%2FADS%3Fid%3D2003JAtS...60.1913P

http://onlinelibrary.wiley.com/resolve/reference/ADS?id=2003JAtS...60.1913PStudies the role of shear in the development and maintenance of a convective boundary layer. Results of applying large eddy simulations (LES); Emphasis given to the growth of the boundary layer; Analysis of the processes that drive the mechanism.

Pino D., J. Vilà-Guerau de Arellano, and S.-W. Kim, 2006: Representing sheared convective boundary layer by zeroth- and first-order-jump mixed-layer models: Large-eddy simulation verification. Journal of Applied Meteorology and Climatology, 45, 1224- 1243.10.1175/JAM2396.1

b2517681b9dc4f23f2ca4524e246d307

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2006JApMC..45.1224P

http://adsabs.harvard.edu/abs/2006JApMC..45.1224PDry convective boundary layers characterized by a significant wind shear on the surface and at the inversion are studied by means of the mixed-layer theory. Two different representations of the entrainment zone, each of which has a different closure of the entrainment heat flux, are considered. The simpler of the two is based on a sharp discontinuity at the inversion (zeroth-order jump), whereas the second one prescribes a finite depth of the inversion zone (first-order jump). Large-eddy simulation data are used to provide the initial conditions for the mixed-layer models, and to verify their results. Two different atmospheric boundary layers with different stratification in the free atmosphere are analyzed. It is shown that, despite the simplicity of the zeroth-order-jump model, it provides similar results to the first-order-jump model and can reproduce the evolution of the mixed-layer variables obtained by the large-eddy simulations in sheared convective boundary layers. The mixed-layer model with both closures compares better with the large-eddy simulation results in the atmospheric boundary layer characterized by a moderate wind shear and a weak temperature inversion. These results can be used to represent the flux of momentum, heat, and other scalars at the entrainment zone in general circulation or chemistry transport models.

Rand all, D. A., 1984: Buoyant production and consumption of turbulence kinetic energy in cloud-topped mixed layers. J. Atmos. Sci., 41, 402- 413.10.1175/1520-0469(1984)0412.0.CO;2

ab20bc3447559bd3fb02305590d90590

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1984JAtS...41..402R

http://adsabs.harvard.edu/abs/1984JAtS...41..402RNot Available

Sorbjan Z., 1996a: Numerical study of penetrative and "solid lid" nonpenetrative convective boundary layers. J. Atmos. Sci., 53, 101- 112.10.1175/1520-0469(1996)0532.0.CO;2

ef7e57b4408044b367364bbbe865b991

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1996JAtS...53..101S

http://adsabs.harvard.edu/abs/1996JAtS...53..101SA large eddy simulation model was used to generate and compare statistics of turbulence during nonpenetrative and penetrative dry convection. In penetrative convection dimensionless vertical velocities in updrafts were found to have almost the same values as in the nonpenetrative case. The countergradient transport of heat and moisture was found to be present during nonpenetrative convection at /> 0.6. For penetrative convection the countergradient transport of heat occurred only in a layer 0.5 < /< 0.75, while the countergradient transport of humidity was not present. During nonpenetrative convection, temperature and humidity were perfectly correlated. In penetrative convection the correlation coefficient was found to be less than unity, varying from about 0.9 near the surface to about 0.7 at the top of the mixed layer.

Sorbjan Z., 1996b: Effects caused by varying the strength of the capping inversion based on a large eddy simulation model of the shear-free convective boundary layer. J. Atmos. Sci., 53, 2015- 2024.10.1175/1520-0469(1996)0532.0.CO;2

7d830c87022924a07e018810456a5559

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1996JAtS...53.2015S

http://adsabs.harvard.edu/abs/1996JAtS...53.2015SEffects caused by variation of the potential temperature lapse rate Γ in the free atmosphere are examined based on a “large eddy simulation” model of the shear-free convective atmospheric boundary layer. The obtained results show that only near the top of the boundary layer are the statistical moments involving temperature strongly sensitive to changes of the parameter Γ. Furthermore, the moments involving only the vertical velocity are practically independent of Γ. The ratio of the heat fluxes at the top and the bottom of the mixed layer increases when Γ increases. For the values of Γ from 1 to 10 K/km, typically observed in the atmosphere, the heat flux ratio varies in the range 610.2 to 610.3. When Γ increases by an order of magnitude to 100 K/km, increases only slightly to about 610.4. When Γ decreases to zero, the heat flux , at the top of the mixed layer also decreases to zero. In this case, the thermal structure of the atmospheric boundary layer is found to be similar to nonpenetrative “solid lid” convection in a tank.

Sorbjan Z., 2004: Large-eddy simulations of the baroclinic mixed layer. Bound.-Layer Meteor., 112, 57- 80.10.1023/B:BOUN.0000020161.99887.b3

134cfd0dc15c9cd6b29d3c0b7251e76b

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2004BoLMe.112...57S

http://adsabs.harvard.edu/abs/2004BoLMe.112...57SThe effects of baroclinicity, imposed on the dry mixed layer by the presenceof large-scale, horizontal temperature gradients, have been investigated basedon a large-eddy simulation model. The purpose of this investigation is to examinesimultaneous impacts of thermal stratification and shear in the atmospheric boundarylayer. For this purpose, five cases are considered - one barotropic, and four baroclinic.Based on the performed simulations, a new parametrization of the interfacial layer isproposed. The parameterization employs new interfacial scaling, which is valid at thetop of the mixed layer. In terms of new scales, dimensionless moments characterizingturbulence at the top of the shearless mixed layer are universal constants. In the shearedcase, dimensionless statistics of turbulence are shown to be functions of the interfacialRichardson number.

Stull R. B., 1973: Inversion rise model based on penetrative convection. J. Atmos. Sci., 30, 1092- 1099.10.1175/1520-0469(1973)0302.0.CO;2

696749287e25aaae500acbc2ac322284

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1973JAtS...30.1092S

http://adsabs.harvard.edu/abs/1973JAtS...30.1092SA mathematical model to describe the height changes and other characteristics of an inversion base under the influence of surface convection and general subsidence is developed. Inversion interface dynamics and entrainment rates are formulated based on an unstable boundary layer environment of well-organized, plume-like, penetrative convection. The use of unstable boundary layer scaling velocities in describing the convection leads to a natural inclusion of the relevant parameters associated with inversions into this model. It is found that the model does accurately predict realistic rates of inversion rise and of temperature changes for conditions where organized free convection is prevalent.

Stull R. B., 1976: The energetics of entrainment across a density interface. J. Atmos. Sci., 33, 1260- 1267.10.1175/1520-0469(1976)0332.0.CO;2

8e96c8c924d9f9c04481cecb8ca3e04e

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1976JAtS...33.1260S

http://adsabs.harvard.edu/abs/1976JAtS...33.1260Sversion interface; and 4) energy losses due to internal gravity waves. It is shown that most previously published theories are just special cases of this more general energetics theory.

Sullivan P. P., E. G. Patton, 2011: The effect of mesh resolution on convective boundary layer statistics and structures generated by large-eddy simulation. J. Atmos. Sci., 68, 2395- 2415.10.1175/JAS-D-10-05010.1

1d827eb869815f83ac35cb669fdf0e44

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2011JAtS...68.2395S

http://adsabs.harvard.edu/abs/2011JAtS...68.2395SNot Available

Sullivan P. P., C.-H. Moeng, B. Stevens, D. H. Lenschow, and S. D. Mayor, 1998: Structure of the entrainment zone capping the convective atmospheric boundary layer. J. Atmos. Sci., 55, 3042- 3064.10.1175/1520-0469(1998)0552.0.CO;2

0512918a15664cbeb9e3b0d7f365e95f

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1998JAtS...55.3042S

http://adsabs.harvard.edu/abs/1998JAtS...55.3042SAbstract The authors use large-eddy simulation (LES) to investigate entrainment and structure of the inversion layer of a clear convectively driven planetary boundary layer (PBL) over a range of bulk Richardson numbers, Ri. The LES code uses a nested grid technique to achieve fine resolution in all three directions in the inversion layer. Extensive flow visualization is used to examine the structure of the inversion layer and to illustrate the temporal and spatial interaction of a thermal plume and the overlying inversion. It is found that coherent structures in the convective PBL, that is, thermal plumes, are primary instigators of entrainment in the Ri range 13.6 81 Ri 81 43.8. At Ri = 13.6, strong horizontal and downward velocities are generated near the inversion layer because of the plume–interface interaction. This leads to folding of the interface and hence entrainment of warm inversion air at the plume’s edge. At Ri = 34.5, the inversion’s strong stability prevents folding of the interface but stron...

Sun J. N., Y. Wang, 2008: Effect of the entrainment flux ratio on the relationship between entrainment rate and convective Richardson number. Bound.-Layer Meteor., 126, 237- 247.10.1007/s10546-007-9231-4

d93eceb40e9fe4602180137214e7aab4

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2008BoLMe.126..237S

http://adsabs.harvard.edu/abs/2008BoLMe.126..237SThe parameterization of the dimensionless entrainment rate ( w / w ) versus the convective Richardson number ( Ri ) is discussed in the framework of a first-order jump model (FOM). A theoretical estimation for the proportionality coefficient in this parameterization, namely, the total entrainment flux ratio, is derived. This states that the total entrainment flux ratio in FOM can be estimated as the ratio of the entrainment zone thickness to the mixed-layer depth, a relationship that is supported by earlier tank experiments, and suggesting that the total entrainment flux ratio should be treated as a variable. Analyses show that the variability of the total entrainment flux ratio is actually the effect of stratification in the free atmosphere on the entrainment process, which should be taken into account in the parameterization. Further examination of data from tank experiments and large-eddy simulations demonstrate that the different power laws for w / w versus Ri can be interpreted as the variability of the total entrainment flux ratio. These results indicate that the dimensionless entrainment rate depends not only on the convective Richardson number but also upon the total entrainment flux ratio.

Sun J. N., Q. J. Xu, 2009: Parameterization of sheared convective entrainment in the first-order jump model: Evaluation through large-eddy simulation. Bound.-Layer Meteor., 132, 279- 288.10.1007/s10546-009-9394-2

f1d08ffc61b9b800ffe263dc42d01c1c

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2009BoLMe.132..279S

http://adsabs.harvard.edu/abs/2009BoLMe.132..279SIn this note, two different approaches are used to estimate the entrainment-flux to surface-flux ratio for a sheared convective boundary layer (CBL); both are derived under the framework of the first-order jump model (FOM). That suggested by Sun and Wang (SW approach) has the advantage that there is no empirical constant included, though the dynamics are described in an implicit manner. The second, which was proposed by Kim et al. and Pino et al. (KP approach), explicitly characterizes the dynamics of the sheared entrainment, but uncertainties are induced through the empirical constants. Their performances in parameterizing the CBL growth rate are compared and discussed, and a new value of the parameter A in the KP approach is suggested. Large-eddy simulation (LES) data are employed to test both approaches: simulations are conducted for the CBL growing under varying conditions of surface roughness, free-atmospheric stratification, and wind shear, and data used when the turbulence is in steady state. The predicted entrainment rates in each case are tested against the LES data. The results show that the SW approach describes the evolution of the sheared CBL quite well, and the KP approach also reproduces the growth of the CBL reasonably, so long as the value of A is modified to 0.6.

Sun J. N., W. M. Jiang, Z. Y. Chen, and R. M. Yuan, 2005: A laboratory study of the turbulent velocity characteristics in the convective boundary layer. Adv. Atmos. Sci.,22, 770-780, doi: 10.1007/BF02918721.10.1007/BF02918721

90ebd1c2b7ffcd3757fe75ce4271a554

http%3A%2F%2Fwww.cnki.com.cn%2FArticle%2FCJFDTotal-DQJZ200505016.htm

http://d.wanfangdata.com.cn/Periodical_dqkxjz-e200505017.aspxBased on the measurement of the velocity field in the convective boundary layer (CBL) in a convection water tank with the particle image velocimetry (PIV) technique, this paper studies the characteristics of the CBL turbulent velocity in a modified convection tank. The experiment results show that the velocity distribution in the mixed layer clearly possesses the characteristics of the CBL thermals, and the turbulent eddies can be seen obviously. The comparison of the vertical distribution of the turbulent velocity variables indicates that the modeling in the new tank is better than in the old one. The experiment data show that the thermal鈥檚 motion in the entrainment zone sometimes fluctuates obviously due to the intermittence of turbulence. Analyses show that this fluctuation can influence the agreement of the measurement data with the parameterization scheme, in which the convective Richardson number is used to characterize the entrainment zone depth. The normalized square velocity w i 2 / w * 2 at the top of the mixed layer seems to be time-dependent, and has a decreasing trend during the experiments. This implies that the vertical turbulent velocity at the top of the mixed layer may not be proportional to the convective velocity ( w * ).

Tennekes H., 1973: A model for the dynamics of the inversion above a convective boundary layer. J. Atmos. Sci., 30, 558- 567.10.1175/1520-0469(1973)0302.0.CO;2

a376200825a73affbad785ca0da5bea8

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1973JAtS...30..558T

http://adsabs.harvard.edu/abs/1973JAtS...30..558TThe differential equations governing the strength Δ (a potential temperature difference) and the height of inversions associated with dry penetrative convection are considered. No assumptions on the magnitude of the downward heat flux at the inversion base are needed to obtain an algebraic equation that relates and Δ to the heating history of the boundary layer and to the initial conditions. After the nocturnal inversion has been filled in by heating, the inversion base generally grows linearly with time in the morning, but is proportional to the square root of time in the afternoon. The variation of Δ with time differs greatly from case to case.

Tennekes H., A. G. M. Driedonks, 1981: Basic entrainment equations for the atmospheric boundary layer. Bound.-Layer Meteor., 20, 515- 531.10.1007/BF00122299

82b7f52ef9fb22b14aae508e9f58bf5c

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1981BoLMe..20..515T

http://adsabs.harvard.edu/abs/1981BoLMe..20..515TThe parameterization of penetrative convection and other cases of turbulent entrainment by the atmospheric boundary layer is reviewed in this paper. The conservation equations for a one-layer model of entrainment are straightforward; all modeling problems arise in the context of the parameterization of various terms in the budget of turbulent kinetic energy. There is no consensus in the literature on the parameterization of shear production and of dissipation. Unfortunately, field experiments are not sufficiently accurate to guide the selection of suitable hypotheses. Carefully designed laboratory experiments are needed to settle the problems that remain.

vanZanten, M. C., P. G. Duynkerke, J. W. M. Cuijpers, 1999: Entrainment parameterization in convective boundary layers. J. Atmos. Sci., 56, 813- 828.10.1175/1520-0469(1999)0562.0.CO;2

fe9cc0b716154193f79ef27ea1304a58

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1999JAtS...56..813V

http://adsabs.harvard.edu/abs/1999JAtS...56..813VVarious runs were performed with a large eddy simulation (LES) model to evaluate different types of entrainment parametrizations. For this evaluation, three types of boundary layers were simulated: a clear convective boundary layer (CBL), a boundary layer containing a smoke concentration, and a cloud-topped boundary layer. It is shown that the assumption that the entrainment flux equals the product of the entrainment rate and the jump over a discontinuous inversion is not valid in CBLs simulated by an LES model. A finite inversion thickness (i.e., a first-order jump model) is needed to define an entrainment flux for which this approximation of the flux is valid. This entrainment flux includes not only the buoyancy flux at the inversion, but also the surface heat flux. The parameterization of the buoyancy flux at the inversion is evaluated for different closures, as suggested in the literature (i.e., Eulerian partitioning, process partitioning, and a closure developed by Deardorff), and where needed is extended for use in a first-order jump model. The closure based on process partitioning is found to yield consistent results in all types of convective boundary layers and shows the best agreement with the limit found in LES results if the longwave radiative flux divergence takes place in a much shallower layer than the mixed layer.

Zeman O., H. Tennekes, 1977: Parameterization of the turbulent energy budget at the top of the daytime atmospheric boundary layer. J. Atmos. Sci., 34, 111- 123.10.1175/1520-0469(1977)034<0111:POTTEB>2.0.CO;2

9f35074020f33de9586710888b97b82c

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http://adsabs.harvard.edu/abs/1977jats...34..111zAbstract The budget of turbulent kinetic energy at the base of the inversion which caps the daytime atmospheric boundary layer depends on the lapse rate of potential temperature in the air aloft. The principal gain term in the energy budget is turbulent transport of kinetic energy, the principal loss term is buoyant conversion of kinetic energy into potential energy. The contributions made by these and other terms in the energy budget need to be parameterized for applications to inversion-rise prediction schemes. This paper contains a detailed analysis of the effects of dissipation near the inversion base, which leads to reduced entrainment if the air aloft is very stable. The parameterized energy budget also includes the Zilitinkevich correction, the influence of mechanical energy production near the inversion base, and modifications needed to incorporate cases in which the surface heat flux is negligible. Extensive comparisons of the theoretical model with experimental data indicate that a simplified treatment of the energy budget is adequate for forecasts of the development of convective mixed layers. The parameterization scheme is also applicable to thermocline erosion in the ocean; in that case, however, some of the minor terms in the energy budget often play a major role.