Direct numerical simulations of stably stratified decaying unforced turbulence

Abstract

In the present paper, the turbulent mixing and structure of decaying stably stratified flows are investigated using direct numerical simulations (DNS). A key quantity for estimating turbulent diapyncal mixing in stably stratified flows is the flux Richardson number Rf (also commonly referred to as the mixing efficiency) which is a measure of the amount of turbulent kinetic energy that is irreversibly converted to background potential energy. Using simulations with varying strengths of density stratification, it is found that when the buoyancy Reynolds number Reb=ϵ/(νN2) (where ϵ is the turbulent kinetic energy dissipation rate, ν is the kinematic viscosity, and N is the Brunt–Väisälä frequency), is less than 10, Rf becomes a property of the fluid as strong buoyancy effects inhibit turbulent mixing and hence Rf is influenced by (molecular) Prandtl number effects. On the other hand, for energetic flows at higher buoyancy Reynolds numbers (i.e. Reb > O(10)), Prandtl number effects diminish, indicating that Rf is a property of the flow. Flow visualization of enstrophy structures show the presence of elongated vortex tubes characteristic of classic isotropic turbulence for weakly stratified flows while ‘pancake-like’ structures emerge for strongly stratified flows.