A Hierarchy of Energy- and Flux-Budget (EFB) Turbulence Closure Models for Stably-Stratified Geophysical Flows

S. S. Zilitinkevich, T. Elperin, N. Kleeorin, I. Rogachevskii, I. Esau

Research output: Contribution to journalArticlepeer-review

122 Scopus citations


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.

Original languageEnglish
Pages (from-to)341-373
Number of pages33
JournalBoundary-Layer Meteorology
Issue number3
StatePublished - 1 Mar 2013


  • Boundary layers
  • Conductivity
  • Critical Richardson number
  • Diffusivity
  • Eddy viscosity
  • Free atmosphere
  • Inter-component kinetic energy exchange
  • Kinetic potential and total turbulent energies Monin-Obukhov similarity theory
  • Stability parameters
  • Stable stratification
  • Turbulence closure
  • Turbulent dissipation time and length scales
  • Turbulent fluxes

ASJC Scopus subject areas

  • Atmospheric Science


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