Computational Study of a Weakly Compressible Mixing Barrier in Low Prandtl Number, Strongly Stratified Fluids

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 Num∗Current address: Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA 95064 1 bers. 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 phenomena 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.