Turbulence in a Fluid Stratified by a High Prandtl-Number Scalar

Abstract

Turbulence in the fluid stratified by a high Prandtl-number (P r) scalar such as heat (P r = 7) or salinity (P r = 700) has been simulated by direct numerical simulations, using 4096³ grid points. Computations have been performed using the 1024 nodes of NEC SX-ACE, which have enabled us to resolve the smallest scale of salinity fluctuations $\sqrt{ 700}(\sim 26)$ times smaller than the smallest eddy size. In our simulations, buoyancy initially affects only the large scale motions, and the k ⁻¹ spectrum predicted by Batchelor (J. Fluid Mech. 5:113–133, 1959) for a passive scalar could be observed in the spectrum of potential energy, i.e. the salinity fluctuations. However, as time proceeds, the buoyancy affects the smaller-scale motions, and the salinity fluctuations begin to show a unique spatially localised structure. At the same time, there appears a flat spectrum ( ∝ k ⁰) instead of the k ⁻¹ spectrum. The localised structure and the flat spectrum could be observed only for the salinity (P r = 700) and not for heat (P r = 7).