• Anderson, P. S., 2009: Measurement of Prandtl number as a function of Richardson number avoiding self-correlation. Bound.-Layer Meteor., 131, 345362, doi:10.1007/s10546-009-9376-4.

    • Search Google Scholar
    • Export Citation
  • Andren, A., 1995: The structure of stably stratified atmospheric boundary layers: A large-eddy simulation study. Quart. J. Roy. Meteor. Soc., 121, 961985, doi:10.1002/qj.49712152502.

    • Search Google Scholar
    • Export Citation
  • Basu, S., , F. Porté-Agel, , E. Foufoula-Georgiou, , J.-F. Vinuesa, , and M. Pahlow, 2006: Revisiting the local scaling hypothesis in stably stratified atmospheric boundary-layer turbulence: An integration of field and laboratory measurements with large-eddy simulations. Bound.-Layer Meteor., 119, 473500, doi:10.1007/s10546-005-9036-2.

    • Search Google Scholar
    • Export Citation
  • Basu, S., , A. Ruiz-Columbié, , J. Phillipson, , and S. Harshan, 2010: Local scaling characteristics of Antarctic surface layer turbulence. Cryosphere, 4, 325331, doi:10.5194/tc-4-325-2010.

    • Search Google Scholar
    • Export Citation
  • Canuto, V. M., , Y. Cheng, , A. Howard, , and I. Isau, 2008: Stably stratified flows: A model with no Ri(cr). J. Atmos. Sci., 65, 24372447, doi:10.1175/2007JAS2470.1.

    • Search Google Scholar
    • Export Citation
  • Cava, D., , U. Giostra, , M. Siqueira, , and G. Katul, 2004: Organised motion and radiative perturbations in the nocturnal canopy sublayer above an even-aged pine forest. Bound.-Layer Meteor., 112, 129157, doi:10.1023/B:BOUN.0000020160.28184.a0.

    • Search Google Scholar
    • Export Citation
  • Cava, D., , U. Giostra, , and G. Katul, 2015: Characteristics of gravity waves over an Antarctic ice sheet during an austral summer. Atmosphere, 6, 12711289, doi:10.3390/atmos6091271.

    • Search Google Scholar
    • Export Citation
  • Cheng, Y., , V. Canuto, , and A. Howard, 2002: An improved model for the turbulent PBL. J. Atmos. Sci., 59, 15501565, doi:10.1175/1520-0469(2002)059<1550:AIMFTT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chung, D., , and G. Matheou, 2012: Direct numerical simulation of stationary homogeneous stratified sheared turbulence. J. Fluid Mech., 696, 434467, doi:10.1017/jfm.2012.59.

    • Search Google Scholar
    • Export Citation
  • Corrsin, S., 1951: On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys., 22, 469473, doi:10.1063/1.1699986.

    • Search Google Scholar
    • Export Citation
  • Derbyshire, S., 1999: Stable boundary-layer modeling: Established approaches and beyond. Bound.-Layer Meteor., 90, 423446, doi:10.1023/A:1001749007836.

    • Search Google Scholar
    • Export Citation
  • Esau, I., , and A. A. Grachev, 2007: Turbulent Prandtl number in stably stratified atmospheric boundary layer: Intercomparison between LES and SHEBA data. e-WindEng, 005, 1–17.

    • Search Google Scholar
    • Export Citation
  • Fernando, H., 1991: Turbulent mixing in stratified fluids. Annu. Rev. Fluid Mech., 23, 455493, doi:10.1146/annurev.fl.23.010191.002323.

    • Search Google Scholar
    • Export Citation
  • Fernando, H., , and J. Weil, 2010: Whither the stable boundary layer? A shift in the research agenda. Bull. Amer. Meteor. Soc., 91, 14751484, doi:10.1175/2010BAMS2770.1.

    • Search Google Scholar
    • Export Citation
  • Ferrero, E., , L. Quan, , and D. Massone, 2011: Turbulence in the stable boundary layer at higher Richardson numbers. Bound.-Layer Meteor., 139, 225240, doi:10.1007/s10546-010-9581-1.

    • Search Google Scholar
    • Export Citation
  • Galperin, B., , L. Kantha, , S. Hassid, , and A. Rosati, 1988: A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci., 45, 5562, doi:10.1175/1520-0469(1988)045<0055:AQETEM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Galperin, B., , S. Sukoriansky, , and P. S. Anderson, 2007: On the critical Richardson number in stably stratified turbulence. Atmos. Sci. Lett., 8, 6569, doi:10.1002/asl.153.

    • Search Google Scholar
    • Export Citation
  • Gerz, T., , U. Schumann, , and S. Elghobashi, 1989: Direct numerical simulation of stratified homogeneous turbulent shear flows. J. Fluid Mech., 200, 563594, doi:10.1017/S0022112089000765.

    • Search Google Scholar
    • Export Citation
  • Grachev, A., , E. L Andreas, , C. Fairall, , P. Guest, , and P. G. Persson, 2007: On the turbulent Prandtl number in the stable atmospheric boundary layer. Bound.-Layer Meteor., 125, 329341, doi:10.1007/s10546-007-9192-7.

    • Search Google Scholar
    • Export Citation
  • Grachev, A., , E. L Andreas, , C. Fairall, , P. Guest, , and P. G. Persson, 2012: Outlier problem in evaluating similarity functions in the stable atmospheric boundary layer. Bound.-Layer Meteor., 144, 137155, doi:10.1007/s10546-012-9714-9.

    • Search Google Scholar
    • Export Citation
  • Grachev, A., , E. L Andreas, , C. Fairall, , P. Guest, , and P. G. Persson, 2013: The critical Richardson number and limits of applicability of local similarity theory in the stable boundary layer. Bound.-Layer Meteor., 147, 5182, doi:10.1007/s10546-012-9771-0.

    • Search Google Scholar
    • Export Citation
  • He, P., , and S. Basu, 2015: Direct numerical simulation of intermittent turbulence under stably stratified conditions. Nonlinear Processes Geophys., 22, 447471, doi:10.5194/npg-22-447-2015.

    • Search Google Scholar
    • Export Citation
  • Holtslag, A. A. M., and et al. , 2013: Stable atmospheric boundary layers and diurnal cycles: Challenges for weather and climate models. Bull. Amer. Meteor. Soc., 94, 16911706, doi:10.1175/BAMS-D-11-00187.1.

    • Search Google Scholar
    • Export Citation
  • Huang, J., , E. Bou-Zeid, , and J.-C. Golaz, 2013: Turbulence and vertical fluxes in the stable atmospheric boundary layer. Part 2: A novel mixing-length model. J. Atmos. Sci., 70, 15281542, doi:10.1175/JAS-D-12-0168.1.

    • Search Google Scholar
    • Export Citation
  • Ishihara, T., , K. Yoshida, , and Y. Kaneda, 2002: Anisotropic velocity correlation spectrum at small scales in a homogeneous turbulent shear flow. Phys. Rev. Lett., 88, 154501, doi:10.1103/PhysRevLett.88.154501.

    • Search Google Scholar
    • Export Citation
  • Juang, J.-Y., , G. G. Katul, , M. B. Siqueira, , P. C. Stoy, , and H. R. McCarthy, 2008: Investigating a hierarchy of Eulerian closure models for scalar transfer inside forested canopies. Bound.-Layer Meteor., 128, 132, doi:10.1007/s10546-008-9273-2.

    • Search Google Scholar
    • Export Citation
  • Kaimal, J. C., 1973: Turbulence spectra, length scales and structure parameters in the stable surface layer. Bound.-Layer Meteor., 4, 289309, doi:10.1007/BF02265239.

    • Search Google Scholar
    • Export Citation
  • Kaimal, J. C., , and J. Finnigan, 1994: Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, 304 pp.

  • Karimpour, F., , and S. Venayagamoorthy, 2014: A simple turbulence model for stably stratified wall-bounded flows. J. Geophys. Res. Oceans, 119, 870880, doi:10.1002/2013JC009332.

    • Search Google Scholar
    • Export Citation
  • Katul, G. G., , D. Li, , M. Chamecki, , and E. Bou-Zeid, 2013a: Mean scalar concentration profile in a sheared and thermally stratified atmospheric surface layer. Phys. Rev., 87, 023004, doi:10.1103/PhysRevE.87.023004.

    • Search Google Scholar
    • Export Citation
  • Katul, G. G., , A. Porporato, , C. Manes, , and C. Meneveau, 2013b: Co-spectrum and mean velocity in turbulent boundary layers. Phys. Fluids, 25, 091702, doi:10.1063/1.4821997.

    • Search Google Scholar
    • Export Citation
  • Katul, G. G., , A. Porporato, , S. Shah, , and E. Bou-Zeid, 2014: Two phenomenological constants explain similarity laws in stably stratified turbulence. Phys. Rev., 89, 023007, doi:10.1103/PhysRevE.89.023007.

    • Search Google Scholar
    • Export Citation
  • Katul, G. G., , C. Manes, , A. Porporato, , E. Bou-Zeid, , and M. Chamecki, 2015: Bottlenecks in turbulent kinetic energy spectra predicted from structure function inflections using the Von Kármán–Howarth equation. Phys. Rev., 92, 033009, doi:10.1103/PhysRevE.92.033009.

    • Search Google Scholar
    • Export Citation
  • Klipp, C. L., , and L. Mahrt, 2004: Flux-gradient relationship, self-correlation and intermittency in the stable boundary layer. Quart. J. Roy. Meteor. Soc., 130, 20872103, doi:10.1256/qj.03.161.

    • Search Google Scholar
    • Export Citation
  • Kolmogorov, A., 1941a: Dissipation of energy under locally isotropic turbulence. Dokl. Akad. Nauk SSSR, 32, 1618.

  • Kolmogorov, A., 1941b: The local structure of turbulence in imcompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR, 30, 299303.

    • Search Google Scholar
    • Export Citation
  • Kosovic, B., , and J. A. Curry, 2000: A large-eddy simulation study of a quasi-steady, stably stratified atmospheric boundary layer. J. Atmos. Sci., 57, 10521068, doi:10.1175/1520-0469(2000)057<1052:ALESSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Li, D., , G. G. Katul, , and E. Bou-Zeid, 2015a: Turbulent energy spectra and cospectra of momentum and heat fluxes in the stable atmospheric surface layer. Bound.-Layer Meteor., 157, 121, doi:10.1007/s10546-015-0048-2.

    • Search Google Scholar
    • Export Citation
  • Li, D., , G. G. Katul, , and S. S. Zilitinkevich, 2015b: Revisiting the turbulent Prandtl number in an idealized atmospheric surface layer. J. Atmos. Sci., 72, 2394–2410, doi:10.1175/JAS-D-14-0335.1.

    • Search Google Scholar
    • Export Citation
  • Li, D., , S. Salesky, , and T. Banerjee, 2016: Connections between the Ozmidov scale and mean velocity profile in stably stratified atmospheric surface layers. J. Fluid Mech., 797, R3, doi:10.1017/jfm.2016.311.

    • Search Google Scholar
    • Export Citation
  • Mahrt, L., 1999: Stratified atmospheric boundary layers. Bound.-Layer Meteor., 90, 375396, doi:10.1023/A:1001765727956.

  • Mahrt, L., 2009: Characteristics of submeso winds in the stable boundary layer. Bound.-Layer Meteor., 130, 114, doi:10.1007/s10546-008-9336-4.

    • Search Google Scholar
    • Export Citation
  • Mahrt, L., 2014: Stably stratified atmospheric boundary layers. Annu. Rev. Fluid Mech., 46, 2345, doi:10.1146/annurev-fluid-010313-141354.

    • Search Google Scholar
    • Export Citation
  • Mahrt, L., , and D. Vickers, 2005: Boundary-layer adjustment over small-scale changes of surface heat flux. Bound.-Layer Meteor., 116, 313330, doi:10.1007/s10546-004-1669-z.

    • Search Google Scholar
    • Export Citation
  • Mauritsen, T., , and G. Svensson, 2007: Observations of stably stratified shear-driven atmospheric turbulence at low and high Richardson numbers. J. Atmos. Sci., 64, 645655, doi:10.1175/JAS3856.1.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., 1973: Analytic prediction of the properties of stratified planetary surface layers. J. Atmos. Sci., 30, 10611069, doi:10.1175/1520-0469(1973)030<1061:APOTPO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., , and T. Yamada, 1974: A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci., 31, 17911806, doi:10.1175/1520-0469(1974)031<1791:AHOTCM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., , and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys., 20, 851875, doi:10.1029/RG020i004p00851.

    • Search Google Scholar
    • Export Citation
  • Miller, N. E., , and R. Stoll, 2013: Surface heterogeneity effects on regional-scale fluxes in the stable boundary layer: Aerodynamic roughness length transitions. Bound.-Layer Meteor., 149, 277301, doi:10.1007/s10546-013-9839-5.

    • Search Google Scholar
    • Export Citation
  • Nakanish, M., 2001: Improvement of the Mellor–Yamada turbulence closure model based on large-eddy simulation data. Bound.-Layer Meteor., 99, 349378, doi:10.1023/A:1018915827400.

    • Search Google Scholar
    • Export Citation
  • Obukhov, A., 1968: Structure of the temperature field in turbulent flow. Defense Technical Information Center Tech. Rep. 683016, 14 pp.

  • Ohya, Y., 2001: Wind-tunnel study of atmospheric stable boundary layers over a rough surface. Bound.-Layer Meteor., 98, 5782, doi:10.1023/A:1018767829067.

    • Search Google Scholar
    • Export Citation
  • Ohya, Y., , R. Nakamura, , and T. Uchida, 2008: Intermittent bursting of turbulence in a stable boundary layer with low-level jet. Bound.-Layer Meteor., 126, 349363, doi:10.1007/s10546-007-9245-y.

    • Search Google Scholar
    • Export Citation
  • Pardyjak, E., , P. Monti, , and H. Fernando, 2002: Flux Richardson number measurements in stable atmospheric shear flows. J. Fluid Mech., 459, 307316, doi:10.1017/S0022112002008406.

    • Search Google Scholar
    • Export Citation
  • Pope, S., 2000: Turbulent Flows. Cambridge University Press, 771 pp.

  • Poulos, G. S., and et al. , 2002: CASES-99: A comprehensive investigation of the stable nocturnal boundary layer. Bull. Amer. Meteor. Soc., 83, 555558, doi:10.1175/1520-0477(2002)083<0555:CACIOT>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rodrigo, J. S., , and P. S. Anderson, 2013: Investigation of the stable atmospheric boundary layer at Halley Antarctica. Bound.-Layer Meteor., 148, 517539, doi:10.1007/s10546-013-9831-0.

    • Search Google Scholar
    • Export Citation
  • Rohr, J. J., , E. C. Itsweire, , K. N. Helland, , and C. W. V. Atta, 1988: Growth and decay of turbulence in a stably stratified shear flow. J. Fluid Mech., 195, 77111, doi:10.1017/S0022112088002332.

    • Search Google Scholar
    • Export Citation
  • Rotta, J., 1951a: Statistical theory of nonhomogeneous turbulence—Part 1. Z. Phys., 129, 257–572.

  • Rotta, J., 1951b: Statistical theory of nonhomogeneous turbulence—Part 2. Z. Phys., 131, 51–77.

  • Sandu, I., , A. Beljaars, , P. Bechtold, , T. Mauritsen, , and G. Balsamo, 2013: Why is it so difficult to represent stably stratified conditions in numerical weather prediction (NWP) models? J. Adv. Model. Earth Syst., 5, 117133, doi:10.1002/jame.20013.

    • Search Google Scholar
    • Export Citation
  • Schumann, U., , and T. Gerz, 1995: Turbulent mixing in stably stratified shear flows. J. Appl. Meteor., 34, 3348, doi:10.1175/1520-0450-34.1.33.

    • Search Google Scholar
    • Export Citation
  • Shih, L., , J. Koseff, , J. Ferziger, , and C. Rehmann, 2000: Scaling and parameterization of stratified homogeneous turbulent shear flow. J. Fluid Mech., 412, 120, doi:10.1017/S0022112000008405.

    • Search Google Scholar
    • Export Citation
  • Sorbjan, Z., 2006: Local structure of turbulence in stably stratified boundary layers. J. Atmos. Sci., 63, 15261537, doi:10.1175/JAS3704.1.

    • Search Google Scholar
    • Export Citation
  • Sorbjan, Z., 2010: Gradient-based scales and similarity laws in the stable boundary layer. Quart. J. Roy. Meteor. Soc., 136, 12431254, doi:10.1002/qj.638.

    • Search Google Scholar
    • Export Citation
  • Sorbjan, Z., 2014: Modelling of the evolving stable boundary layer. Bound.-Layer Meteor., 151, 407428, doi:10.1007/s10546-013-9893-z.

    • Search Google Scholar
    • Export Citation
  • Stoll, R., , and F. Porté-Agel, 2009: Surface heterogeneity effects on regional-scale fluxes in stable boundary layers: Surface temperature transitions. J. Atmos. Sci., 66, 412431, doi:10.1175/2008JAS2668.1.

    • Search Google Scholar
    • Export Citation
  • Strang, E., , and H. Fernando, 2001: Entrainment and mixing in stratified shear flows. J. Fluid Mech., 428, 349386, doi:10.1017/S0022112000002706.

    • Search Google Scholar
    • Export Citation
  • Stretch, D., , J. Rottman, , S. Venayagamoorthy, , K. K. Nomura, , and C. R. Rehmann, 2010: Mixing efficiency in decaying stably stratified turbulence. Dyn. Atmos. Oceans, 49, 2536, doi:10.1016/j.dynatmoce.2008.11.002.

    • Search Google Scholar
    • Export Citation
  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 666 pp.

  • Sun, J., and et al. , 2002: Intermittent turbulence associated with a density current passage in the stable boundary layer. Bound.-Layer Meteor., 105, 199219, doi:10.1023/A:1019969131774.

    • Search Google Scholar
    • Export Citation
  • Sun, J., and et al. , 2004: Atmospheric disturbances that generate intermittent turbulence in nocturnal boundary layers. Bound.-Layer Meteor., 110, 255279, doi:10.1023/A:1026097926169.

    • Search Google Scholar
    • Export Citation
  • Sun, J., and et al. , 2015: Review of wave–turbulence interactions in the stable atmospheric boundary layer. Rev. Geophys., 53, 956993, doi:10.1002/2015RG000487.

    • Search Google Scholar
    • Export Citation
  • Venayagamoorthy, S., , and D. Stretch, 2010: On the turbulent Prandtl number in homogeneous stably stratified turbulence. J. Fluid Mech., 644, 359369, doi:10.1017/S002211200999293X.

    • Search Google Scholar
    • Export Citation
  • Webster, C., 1964: An experimental study of turbulence in a density-stratified shear flow. Dyn. Atmos. Oceans, 19, 221245, doi:10.1017/S0022112064000672.

    • Search Google Scholar
    • Export Citation
  • Yamada, T., 1975: The critical Richardson number and the ratio of the eddy transport coefficients obtained from a turbulence closure model. J. Atmos. Sci., 32, 926933, doi:10.1175/1520-0469(1975)032<0926:TCRNAT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S., , T. Elperin, , N. Kleeorin, , and I. Rogachevskii, 2007: Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: Steady-state, homogeneous regimes. Bound.-Layer Meteor., 125, 167192, doi:10.1007/s10546-007-9189-2.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S., , T. Elperin, , N. Kleeorin, , I. Rogachevskii, , I. Esau, , T. Mauritsen, , and M. Miles, 2008: Turbulence energetics in stably stratified geophysical flows: Strong and weak mixing regimes. Quart. J. Roy. Meteor. Soc., 134, 793799, doi:10.1002/qj.264.

    • Search Google Scholar
    • Export Citation
  • Zilitinkevich, S., , T. Elperin, , N. Kleeorin, , I. Rogachevskii, , and I. Esau, 2013: A hierarchy of energy- and flux-budget (EFB) turbulence closure models for stably-stratified geophysical flows. Bound.-Layer Meteor., 146, 341373, doi:10.1007/s10546-012-9768-8.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 26 26 7
PDF Downloads 18 18 8

Closure Schemes for Stably Stratified Atmospheric Flows without Turbulence Cutoff

View More View Less
  • 1 Department of Earth and Environment, Boston University, Boston, Massachusetts
  • | 2 Nicholas School of the Environment, and Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina
  • | 3 Finnish Meteorological Institute, and Division of Atmospheric Sciences, University of Helsinki, Helsinki, Finland, and Department of Radio Physics, N.I. Lobachevski State University of Nizhniy Novgorod, Nizhniy Novgorod, and Faculty of Geography, Moscow University, and Institute of Geography, Russian Academy of Sciences, Moscow, Russia, and Nansen Environmental and Remote Sensing Center/Bjerknes Centre for Climate Research, Bergen, Norway
© Get Permissions
Restricted access

Abstract

Two recently proposed turbulence closure schemes are compared against the conventional Mellor–Yamada (MY) model for stably stratified atmospheric flows. The Energy- and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a “critical gradient Richardson number,” both EFB and CSB models allow turbulence to exist at any gradient Richardson number and predict a saturation of flux Richardson number () at sufficiently large . The CSB approach further predicts the value of and reveals a unique expression linking the Rotta and von Kármán constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing . However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.

Corresponding author address: Dan Li, Department of Earth and Environment, Boston University, 685 Commonwealth Ave., Boston, MA 02215. E-mail: lidan@bu.edu

Abstract

Two recently proposed turbulence closure schemes are compared against the conventional Mellor–Yamada (MY) model for stably stratified atmospheric flows. The Energy- and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a “critical gradient Richardson number,” both EFB and CSB models allow turbulence to exist at any gradient Richardson number and predict a saturation of flux Richardson number () at sufficiently large . The CSB approach further predicts the value of and reveals a unique expression linking the Rotta and von Kármán constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing . However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.

Corresponding author address: Dan Li, Department of Earth and Environment, Boston University, 685 Commonwealth Ave., Boston, MA 02215. E-mail: lidan@bu.edu
Save