**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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