Computational study of a weakly compressible mixing barrier in low Prandtl number, strongly stratified fluids

Abstract

The effects of weak compressibility in the evolution of a fluid governed by the anelastic fluid equations are explored computationally. The basis for this study is a careful determination of the role which the anelastic divergence constraint plays in the evolution of a periodic array of interacting vortices. Our numerical studies address a blocking phenomenon occurring in strongly stratified flows with small Prandtl numbers. Computationally, we first document this blocking event which strongly limits vertical mixing. This is achieved using idealized equations of fluid motion which do not excite a density perturbation and exhibits that the presence of a strong density transition layer, consistently modeled in the anelastic mass balance, may lead to a dramatic modification of vortex interactions when compared with the incompressible analog. These modifications are evidenced by the formation of a weakly compressible mixing barrier. We subsequently isolate this particular blocking phenomenon as emerging in the limit of small Prandtl number through a sequence of computational simulations of the complete anelastic fluid equations which retain a density perturbation. It is shown that a sequential reduction of the Prandtl number yields much weaker vertical mixing as evidenced by passive tracer statistics.