Decaying turbulence in a stratified fluid of high Prandtl number

Abstract

Decaying turbulence in a density-stratified fluid with a Prandtl number up to $Pr=70$ is investigated by direct numerical simulation. In turbulent flow with a Prandtl number larger than unity, it is well known that the passive scalar fluctuations cascade to scales smaller than the Kolmogorov scale, and show the $k^{-1}$ spectrum in the viscous–convective range, down to the Batchelor scale. In decaying stratified turbulence, the same phenomenon is initially observed for the buoyant scalar of high $Pr~(=70)$, until the Ozmidov scale becomes small and the buoyancy becomes effective even at the Kolmogorov scale. After that moment, however, the velocity components near the Kolmogorov scale begin to show strong anisotropy dominated by the vertically sheared horizontal flow, which reduces the vertical scale of density fluctuations. An analysis similar to that of Batchelor (J. Fluid Mech., vol. 5, 1959, pp. 113–133) indeed shows that the vertically sheared horizontal flow reduces the vertical scale of density fluctuations, without changing the horizontal scale.