Closure of the Reynolds equations for stably stratified turbulent flows in the atmosphere and the ocean

Authors: Zilitinkevich S.S., Elperin T., Kleeorin N., Rogachevsky I.

Year: 2009

Issue: 04

Pages: 75-102

Abstract

This paper presents 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 essentially use the non-gradient correction to the traditional
buoyancy flux formulation (disregarded in the traditional formulations for the eddy conductivity). In the
proposed model, turbulent motions exist at any values of the gradient Richardson number, Ri. Instead of its
critical value separating – as usually assumed – the turbulent and the laminar regimes, the model, as well as
experimental data, reveals a transition interval, 0.1<Ri<1, which separates two regimes of principally
different nature but both turbulent: strong turbulence at Ri«1; and weak turbulence, capable of transporting
momentum but much less efficient in transporting heat, at Ri>1. Predictions from the model are consistent with
available data from atmospheric and laboratory experiments, direct numerical simulation (DNS) and large-eddy
simulation (LES).

Tags: anisotropy; closure of turbulent motion equations; critical Richardson number; kinetic turbulent energy; mixing length; potential turbulent energy; stable stratification; total turbulent energy; turbulent transport; turbulent viscosity

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