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Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: steady-state,homogeneous regimes
Authors:S S Zilitinkevich  T Elperin  N Kleeorin  I Rogachevskii
Institution:(1) Division of Atmospheric Sciences, University of Helsinki, Helsinki, Finland;(2) Finnish Meteorological Institute, Helsinki, Finland;(3) Nansen Environmental and Remote Sensing Centre, Bjerknes Centre for Climate Research, Bergen, Norway;(4) Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Abstract:We propose a new turbulence closure model based on the budget equations for the key second moments: turbulent kinetic and potential energies: TKE and TPE (comprising the turbulent total energy: TTE = TKE + TPE) and vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature). Besides the concept of TTE, we take into account the non-gradient correction to the traditional buoyancy flux formulation. The proposed model permits the existence of turbulence at any gradient Richardson number, Ri. Instead of the critical value of Richardson number separating—as is usually assumed—the turbulent and the laminar regimes, the suggested model reveals a transitional interval, $$0.1 < {\rm Ri} < 1$$ , which separates two regimes of essentially different nature but both turbulent: strong turbulence at $${\rm Ri} \ll 1$$ ; and weak turbulence, capable of transporting momentum but much less efficient in transporting heat, at $${\rm Ri} > 1$$ . Predictions from this model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulation and large-eddy simulation.
Keywords:Anisotropy  Critical Richardson number  Eddy viscosity  Heat conductivity  Kinetic  potential and total turbulent energies  Stable stratification  Turbulence closure  Turbulent fluxes  Turbulent length scale
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