The effect of Prandtl number on decaying stratified turbulence

Abstract

The effects of the variation in the Prandtl number on turbulence in a stably-stratified fluid is investigated by direct numerical simulation. The results of simulations are presented of the homogeneous decay of turbulence for a given initial Froude number and three different initial Reynolds numbers of increasing values. For each of these cases results for two different Prandtl numbers, 1 and 7, are shown. Various statistics are put forward, including kinetic and potential energy decay rates, kinetic and potential energy dissipation rates, buoyancy fluxes, energy spectra, and statistics conditioned on the local value of the vertical density gradient. It is found that the effect of increasing the Prandtl number is to increase the kinetic energy dissipation rate, while decreasing the potential energy dissipation rate. There is a notable transfer of potential to kinetic energy for the higher Prandtl number case. Finally there is evidence, based upon the analysis of vertical planes and statistics conditional on the local density gradient, that most irreversible mixing of both density and momentum occurs in regions of stronger static stability.

Keywords:

• Stratified turbulence
• Prandtl number

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy [contract number DE-AC05-00OR22725]. JJR would like to acknowledge support from the U.S. Office of Naval Research [grant number N00014-19-1-2154]. SdeBK was supported under U.S. Office of Naval Research [grant number N00014-19-1-2152].