Energy- and Flux-Budget (EFB) Turbulence-Closure Theory for Stably Stratified Geophysical Flows

It is widely recognised that in very stable stratifications, at Richardson numbers (Ri) exceeding the critical value (Ric ~ 0.25), turbulence inevitably decays and the flow becomes laminar. This statement is applicable to the low-Reynolds-number (Re) turbulence (such as in lab experiments) but does not hold true for the very-high-Re geophysical turbulence. We reveal principal mechanisms of the turbulence self-preservation, namely, the energy exchange between kinetic and potential turbulent energies and the self-restriction of the buoyancy forces due to the counter-gradient heat transfer. By this means, we explain why and how the very-high-Re turbulence is maintained by the velocity shear up to strongly supercritical stratifications typical of the bulk of the atmosphere and ocean (where Ri often exceeds 100). The proposed Energy- and Flux-Budget (EFB) turbulence-closure theory distinguishes between the two principally different regimes: the familiar “strong turbulence” at sub-critical stratifications (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 supercritical stratifications (Ri >> Ric) typical of the free atmosphere and deep ocean. In the latter regime, turbulent Prandtl number asymptotically behaves as ~ 4Ri, so that the heat transfer becomes orders of magnitude weaker than the momentum transfer. For use in different applications, we propose a hierarchy of turbulence closure models from comparatively simple local algebraic model relevant to the steady-state regime of turbulence to non-local models of different complexity designed for different research and operational-modelling applications.