Abstract
We give a new derivation of the familiar linear relation for the dimensionless velocity gradient in the stably stratified surface layer and provide physical and empirical grounds for its universal applicability in stationary homogeneous turbulence over the whole range of static stabilities from Ri = 0 to very large Ri. Combining this relation with the budget equation for the turbulent kinetic energy we obtain the “equilibrium formulation” of the turbulent dissipation length scale, and recommend it for use in turbulence closure models.
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References
Barenblatt GI (1996) Scaling, self-similarity, and intermediate asymptotics. Series: Cambridge texts in applied mathematics, vol 14. Cambridge University Press, Cambridge, 386 pp. ISBN 05214-35226
Basu S, Porté-Agel F, Foufoula-Georgiou E, Vinuesa JF, Pahlow M (2006) Revisiting the local scaling hypothesis in stably stratified atmospheric boundary-layer turbulence: an integtration of field and laboratory measurements with Large-Eddy simulations. Boundary-Layer Meteorol 119:473–500. doi:10.1007/s10546-005-9036-2
Dyer AJ (1974) A review of flux-profile relationships. Boundary-Layer Meteorol 7: 363–372
Esau IN, Zilitinkevich SS (2006) Universal dependences between turbulent and mean flow parameters in stably and neutrally stratified planetary boundary layers. Nonlinear Processes Geophys 13: 135–144
Garratt JR (1992) The atmospheric boundary layer. Cambridge atmospheric and space science series. Cambridge University Press, Cambridge, 316 pp
Heinemann G (2004) Local similarity properties of the continuously turbulent stable boundary layer over Greenland. Boundary-Layer Meteorol 112: 283–305
Högström U (1996) Review of some basic characteristics of the atmospheric surface layer. Boundary-Layer Meteorol 78: 215–246
Kolmogorov AN (1941) Energy dissipation in locally isotropic turbulence. Dokl Akad Nauk SSSR 32(1): 19–21
Kouznetsov RD, Zilitinkevich SS (2010) On the velocity gradient in the stably stratified sheared flows. Part 2: observations and models. Boundary-Layer Meteorol. doi:10.1007/s10546-010-9487-y
Lo TS, L’vov VS, Pomyalov A, Procaccia I (2005) Estimating von-Karman’s constant from homogeneous turbulence. http://arxiv.org/abs/nlin/0506044v1
Mahalov A, Nicolaenko B, Tse KL, Joseph B (2004) Eddy mixing in jet-stream turbulence under stronger stratification. Geophys Res Lett 31:L23111. doi:10.1029/2004GL021055
Mann J (1994) The special structure of neutral atmospheric surface layer turbulence. J Fluid Mech 273: 141–168
Mauritsen T, Svensson G (2007) Observations of stably stratified shear-driven atmospheric turbulence at low and high Richardson numbers. J Atmos Sci 64: 645–655
Mauritsen T, Svensson G, Zilitinkevich SS, Esau I, Enger L, Grisogono B (2007) A total turbulent energy closure model for neutrally and stably stratified atmospheric boundary layers. J Atmos Sci 64: 4117–4130
Stretch DD, Rottman JW, Venayagamoorthy SK, Nomura KK, Rehmann CR (2009) Mixung efficiency in decaying stably stratified turbulence. Dyn Atmos Oceans. doi:10.1016/j.dynatmoce.2008.11.002
Stroscio MA (1982) Enhancement of turbulence in a stratified fluid by the presence of a shear field. J Stat Phys 28(3): 607–612
van de Wiel BJH, Moene AF, De Ronde WH, Jonker HJJ (2008) Local similarity in the stable boundary layer and mixing-length approaches: consistency of concepts. Boundary-Layer Meteorol 128: 103–116
Venayagamoorthy SK, Stretch DD (2010) On the turbulent Prandtl number in homogeneous stably stratified turbulence. J Fluid Mech 644: 359–369
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: 926–933
Zilitinkevich S, Esau I (2007) Similarity theory and calculation of turbulent fluxes at the surface for the stably stratified atmospheric boundary layers. Boundary-Layer Meteorol 125: 193–296
Zilitinkevich SS, Elperin T, Kleeorin N, Rogachevskii I (2007) Energy- and flux-budget (EFB) turbulence closure model for the stably stratified flows. Part I: Steady-state, homogeneous regimes. Boundary-Layer Meteorol 125: 167–192
Zilitinkevich SS, Elperin T, Kleeorin N, Rogachevskii I, Esau I, Mauritsen T, Miles MW (2008) Turbulence energetics in stably stratified geophysical flows: strong and weak mixing regimes. Q J R Meterol Soc 134: 793–799
Zilitinkevich SS, Elperin T, Kleeorin N, L’vov V, Rogachevskii I (2009) Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part II: The role of internal gravity waves. Boundary-Layer Meteorol 133: 139–164
Acknowledgements
This work has been supported by the EC FP7 projects ERC PBL-PMES (No. 227915) and MEGAPOLI (No. 212520); and the Norwegian Research Council project 191516/V30 Planetary Boundary Layer Feedback in the Earth’s Climate System.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Zilitinkevich, S.S., Esau, I., Kleeorin, N. et al. On the Velocity Gradient in Stably Stratified Sheared Flows. Part 1: Asymptotic Analysis and Applications. Boundary-Layer Meteorol 135, 505–511 (2010). https://doi.org/10.1007/s10546-010-9488-x
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DOI: https://doi.org/10.1007/s10546-010-9488-x