Turbulence energetics in stably stratified geophysical flows: strong and weak mixing regimes

TL;DR

This paper revises the understanding of turbulence energetics in stratified flows by analyzing total energy budgets, revealing two distinct turbulent regimes separated by the Richardson number, which challenges the classical laminar-turbulent transition concept.

Contribution

It extends energy analysis to turbulent potential and total energies, showing TTE is conserved and identifying two turbulence regimes based on Ri, not a laminar-turbulent transition.

Findings

TTE is conserved and maintained by shear in all stratifications.

The interval 0.25<Ri<1 separates strong and weak turbulence regimes.

Turbulence can persist at Ri>>1, contrary to classical beliefs.

Abstract

Traditionally, turbulence energetics is characterized by turbulent kinetic energy (TKE) and modelled using solely the TKE budget equation. In stable stratification, TKE is generated by the velocity shear and expended through viscous dissipation and work against buoyancy forces. The effect of stratification is characterized by the ratio of the buoyancy gradient to squared shear, called Richardson number, Ri. It is widely believed that at Ri exceeding a critical value, Ric, local shear cannot maintain turbulence, and the flow becomes laminar. We revise this concept by extending the energy analysis to turbulent potential and total energies (TPE and TTE = TKE + TPE), consider their budget equations, and conclude that TTE is a conservative parameter maintained by shear in any stratification. Hence there is no "energetics Ric", in contrast to the hydrodynamic-instability threshold, Ric-instability, whose typical values vary from 0.25 to 1. We demonstrate that this interval, 0.25<Ri<1, separates two different turbulent regimes: strong mixing and weak mixing rather than the turbulent and the laminar regimes, as the classical concept states. This explains persistent occurrence of turbulence in the free atmosphere and deep ocean at Ri>>1, clarify principal difference between turbulent boundary layers and free flows, and provide basis for improving operational turbulence closure models.