TY - JOUR
T1 - A Hierarchy of Energy- and Flux-Budget (EFB) Turbulence Closure Models for Stably-Stratified Geophysical Flows
AU - Zilitinkevich, S. S.
AU - Elperin, T.
AU - Kleeorin, N.
AU - Rogachevskii, I.
AU - Esau, I.
N1 - Funding Information:
Acknowledgments This work has been supported by the EC FP7 ERC Grant No. 227915 “Atmospheric planetary boundary layers—physics, modelling and role in Earth system”; the Russian Federation Government Grant No. 11.G34.31.0048 “Air-sea/land interaction: physics and observation of planetary boundary layers and quality of environment”; the Israel Science Foundation governed by the Israeli Academy of Sciences, Grants No. 259/07 and No. 1037/11; and the Norwegian Research Council Grant No. 191516/V30 “Planetary Boundary Layer Feedback in the Earth’s Climate System”. Our thanks to Rostislav Kouznetsov (A.M. Obuk-hov Institute of Atmospheric Physics, Moscow/Finnish Meteorological Institute, Helsinki) for his contribution to Figs. 1, 2, 3 and 6; and to Frank Beyrich (German Weather Service) for providing us with the Lindenberg data shown in Fig. 6.
PY - 2013/3/1
Y1 - 2013/3/1
N2 - Here we advance the physical background of the energy- and flux-budget turbulence closures based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, and a new relaxation equation for the turbulent dissipation time scale. The closure is designed for stratified geophysical flows from neutral to very stable and accounts for the Earth's rotation. In accordance with modern experimental evidence, the closure implies the maintaining of turbulence by the velocity shear at any gradient Richardson number Ri, and distinguishes between the two principally different regimes: "strong turbulence" at ≪ typical of boundary-layer flows and characterized by the practically constant turbulent Prandtl number PrT; and "weak turbulence" at Ri > 1 typical of the free atmosphere or deep ocean, where PrT asymptotically linearly increases with increasing Ri (which implies very strong suppression of the heat transfer compared to the momentum transfer). For use in different applications, the closure is formulated at different levels of complexity, from the local algebraic model relevant to the steady-state regime of turbulence to a hierarchy of non-local closures including simpler down-gradient models, presented in terms of the eddy viscosity and eddy conductivity, and a general non-gradient model based on prognostic equations for all the basic parameters of turbulence including turbulent fluxes.
AB - Here we advance the physical background of the energy- and flux-budget turbulence closures based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, and a new relaxation equation for the turbulent dissipation time scale. The closure is designed for stratified geophysical flows from neutral to very stable and accounts for the Earth's rotation. In accordance with modern experimental evidence, the closure implies the maintaining of turbulence by the velocity shear at any gradient Richardson number Ri, and distinguishes between the two principally different regimes: "strong turbulence" at ≪ typical of boundary-layer flows and characterized by the practically constant turbulent Prandtl number PrT; and "weak turbulence" at Ri > 1 typical of the free atmosphere or deep ocean, where PrT asymptotically linearly increases with increasing Ri (which implies very strong suppression of the heat transfer compared to the momentum transfer). For use in different applications, the closure is formulated at different levels of complexity, from the local algebraic model relevant to the steady-state regime of turbulence to a hierarchy of non-local closures including simpler down-gradient models, presented in terms of the eddy viscosity and eddy conductivity, and a general non-gradient model based on prognostic equations for all the basic parameters of turbulence including turbulent fluxes.
KW - Boundary layers
KW - Conductivity
KW - Critical Richardson number
KW - Diffusivity
KW - Eddy viscosity
KW - Free atmosphere
KW - Inter-component kinetic energy exchange
KW - Kinetic potential and total turbulent energies Monin-Obukhov similarity theory
KW - Stability parameters
KW - Stable stratification
KW - Turbulence closure
KW - Turbulent dissipation time and length scales
KW - Turbulent fluxes
UR - http://www.scopus.com/inward/record.url?scp=84873569272&partnerID=8YFLogxK
U2 - 10.1007/s10546-012-9768-8
DO - 10.1007/s10546-012-9768-8
M3 - Article
AN - SCOPUS:84873569272
SN - 0006-8314
VL - 146
SP - 341
EP - 373
JO - Boundary-Layer Meteorology
JF - Boundary-Layer Meteorology
IS - 3
ER -