Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: steady-state, homogeneous regimes

By Sergej Zilitinkevich, T. Elperin, N. Kleeorin, I. Rogachevskii. 2006

210 citations recorded by the source corpus.

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.

Subfields: Atmospheric Science, Computational Mechanics, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/b388dba6ee401106654bf4eb06f2ee51cdc3df5f

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Citations in the corpus

Turbulence Regimes and Turbulence Intermittency in the Stable Boundary Layer during CASES-99 (2012, unknown): “Recent investigation demonstrates that the universal critical Richardson number varies between ﬂows (e.g., Canuto 2002) or may not exist at all (e.g., Galperin et al. 2007; Zilitinkevich et al. 2007; Mahrt 2010b).”
A Total Turbulent Energy Closure Model for Neutrally and Stably Stratified Atmospheric Boundary Layers (2007, background): “…production Recognizing that (A4) is equal to 1 , where R is the flux Richardson number, and taking the limit R (cid:1) 0.3 (cid:23) 0.1 at Ri → (cid:19) after Zilitinkevich et al. (2007) and Esau and Grachev (2007), we found an upper bound of (A4) for very stably stratified conditions as 0.3 ± 0.”
A Hierarchy of Energy- and Flux-Budget (EFB) Turbulence Closure Models for Stably-Stratified Geophysical Flows (2011, methodology): “In the energy- and flux-budget (EFB) closure (Zilitinkevich et al. 2007, 2008, 2009) we refined budget equations for the basic second moments: the two energies, the TKE EK and the turbulent potential energy (TPE) EP, and the vertical turbulent fluxes of momentum and potential temperature, τi (i =…”
Stably Stratified Atmospheric Boundary Layers (2014, background): “As an additional source of turbulence, available potential energy of the perturbation flow can be converted back to turbulent kinetic energy at any Richardson number (Zilitinkevich et al. 2007).”
THE MARTIAN ATMOSPHERIC BOUNDARY LAYER (2011, background): “Some models take into account the dependence of ‘ on the vertical Coriolis parameter, f, by adding another term to equation (51), ‘ 1 ¼ ‘ 1B þ f =Cf qþ ‘ 1s ; ð52Þ where Cf is a constant [see, e.g., Zilitinkevich et al., 2007, and references therein].”