On dissipation timescales of the basic second-order moments: the effect on the energy and flux budget (EFB) turbulence closure for stably stratified turbulence

Abstract

The dissipation rates of the basic second-order moments are the key parameters playing a vital role in turbulence modelling and controlling turbulence energetics and spectra and turbulent fluxes of momentum and heat. In this paper, we use the results of direct numerical simulations (DNSs) to evaluate dissipation rates of the basic second-order moments and revise the energy and flux budget (EFB) turbulence closure theory for stably stratified turbulence. We delve into the theoretical implications of this approach and substantiate our closure hypotheses through DNS data. We also show why the concept of down-gradient turbulent transport becomes incomplete when applied to the vertical turbulent flux of potential temperature under stable stratification. We reveal essential feedback between the turbulent kinetic energy (TKE), the vertical turbulent flux of buoyancy, and the turbulent potential energy (TPE), which is responsible for maintaining shear-produced stably stratified turbulence for any Richardson number.