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

Sergie S. Zilitinkevich, T. Elperin, N. Kleeorin, I. Rogachevskii, I. Esau, T. Mauritsen, M. V. Miles

Research output: Contribution to journalArticlepeer-review

146 Scopus citations


Traditionally, turbulence energetics is characterised 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 characterised by the ratio of the buoyancy gradient to squared shear, called the 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, clarifies the principal difference between turbulent boundary layers and free flows, and provides the basis for improving operational turbulence closure models.

Original languageEnglish
Pages (from-to)793-799
Number of pages7
JournalQuarterly Journal of the Royal Meteorological Society
Issue number633 B
StatePublished - 1 Apr 2008


  • Heat transfer
  • Momentum transfer
  • Richardson number
  • Stable and very stable stratification
  • Turbulent energies
  • Turbulent prandtl number

ASJC Scopus subject areas

  • Atmospheric Science


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