Bolgiano-Obukhov spectrum and mixing efficiency in stably stratified turbulence.

Abstract

In this paper, using a shell model, we simulate highly turbulent stably stratified flow for weak to moderate stratification at unitary Prandtl number. We investigate the energy spectra and fluxes of velocity and density fields. We observe that for moderate stratification, in the inertial range, the kinetic energy spectrum E_{u}(k) and the potential energy spectrum E_{b}(k) show dual scaling-Bolgiano-Obukhov scaling [E_{u}(k)∼k^{-11/5} and E_{b}(k)∼k^{-7/5}] for k<k_{B}, where k_{B} is the Bolgiano wave number, and Kolmogorov scaling (∼k^{-5/3}) for k>k_{B}. In addition, we find that the mixing efficiency η_{mix} varies as η_{mix}∼Ri for weak stratification, whereas η_{mix}∼Ri^{1/3} for moderate stratification, where Ri is the Richardson number.