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Energy- and flux-budget (EFB) turbulence-closure theory and a hierarchy of turbulence-closure models for stably stratified atmospheric flows

Speaker: Sergei Zilitinkevich, University of Helsinki, Finland
Series: CEE Departmental Seminars
Location: Bowen Hall Auditorium
Date/Time: Tuesday, February 25, 2014, 12:30 p.m. - 1:30 p.m.


The proposed theory opposes the widely recognised judgment that in sufficiently stable stratifications, at Richardson numbers (Ri) exceeding some critical value (Ric ~ 0.25), turbulence inevitably decays and the flow becomes laminar. We demonstrate that this judgement holds true only for the low-Reynolds-number (Re) turbulence (such as in lab experiments), disclose overlooked mechanisms of the turbulence self-preservation, and explain why and how the very-high-Re geophysical turbulence is maintained by the velocity shear up to very stable stratifications typical of the bulk of the atmosphere and ocean (where Ri approaches 102). The theory distinguishes between the two principally different regimes: the familiar “strong turbulence” at Ri < Ric typical of boundary-layer flows and characterised by the practically constant turbulent Prandtl number ~ 1 (corresponding to the so-called “Reynolds analogy”); and the newly recognised “weak turbulence” at Ri >> Ric typical of the free atmosphere or deep ocean. In this regime, asymptotically linearly increases with increasing Ri, so that the heat transfer can be orders of magnitude weaker than the momentum transfer. For use in different applications, we propose a hierarchy of turbulence closure models from the local algebraic model relevant to the steady-state turbulence to non-local models of different complexity including comparatively simple downgradient transport model (consistent with on the concept of eddy viscosity and eddy conductivity) and general model based on prognostic equations for turbulent kinetic and potential energies, turbulent fluxes, and the dissipation time scale.