Turbulence in a stably stratified fluid: Onset of global anisotropy as a function of the Richardson number

TL;DR

This paper investigates how turbulence in a stably stratified fluid develops anisotropy, demonstrating analytically and numerically that anisotropy increases linearly with the Richardson number, with minor quadratic correction.

Contribution

It introduces an analytical and numerical analysis of the relationship between anisotropy and the Richardson number in stratified turbulence, using the Heisenberg eddy viscosity model.

Findings

Anisotropy increases linearly with Richardson number.

Numerical simulations confirm the analytical linear relationship.

Small quadratic correction to the anisotropy-Richardson number relation.

Abstract

It is necessary to introduce an external forcing to induce turbulence in a stably stratified fluid. The Heisenberg eddy viscosity technique should in this case suffice to calculate a space-time averaged quantity like the global anisotropy parameter as a function of the Richardson number. We find analytically that the anisotropy increases linearly with the Richardson number, with a small quadratic correction. A numerical simulation of the complete equations shows the linear behaviour.