Mixing Coefficient in Stably Stratified Flows

Abstract

AbstractTurbulent mixing in the interior of the oceans is not as well understood as mixing in the oceanic boundary layers. Mixing in the generally stably stratified interior is primarily, although not exclusively, due to intermittent shear instabilities. Part of the energy extracted by the Reynolds stresses acting on the mean shear is expended in increasing the potential energy of the fluid column through a buoyancy flux, while most of it is dissipated. The mixing coefficient χm, the ratio of the buoyancy flux to the dissipation rate of turbulence kinetic energy ε, is an important parameter, since knowledge of χm enables turbulent diffusivities to be inferred. Theory indicates that χm must be a function of the gradient Richardson number. Yet, oceanic studies suggest that a value of around 0.2 for χm gives turbulent diffusivities that are in good agreement with those inferred from tracer studies. Studies by scientists working with atmospheric radars tend to reinforce these findings but are seldom referenced in oceanographic literature. The goal of this paper is to bring together oceanographic, atmospheric, and laboratory observations related to χm and to report on the values deduced from in situ data collected in the lower troposphere by unmanned aerial vehicles, equipped with turbulence sensors and flown in the vicinity of the Middle and Upper Atmosphere (MU) radar in Japan. These observations are consistent with past studies in the oceans, in that a value of around 0.16 for χm yields good agreement between ε derived from turbulent temperature fluctuations using this value and ε obtained directly from turbulence velocity fluctuations.