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 Num

A spectral anelastic Navier–Stokes solver for a stratified two-miscible-layer system in infinite horizontal channel

“…As a result, source terms due to the boundary conditions appear in equations (36), (39), (41) and (43). To show this, we first notice that if (X p ) is a vector with (N z + 1) components, then X p = N z j=0 D pj X j .…”

“…, ii) injecting these terms in equation (41) and finally iii) identifying the operator A P k and the r.h.s. F (q)(s) P k .…”

“…We are now able to construct the Uzawa operator A P k acting on the pressure, which allows equation (41) to be satisfied at the z-nodes. It writes…”

“…The velocity field is u and ρ(z) is a mean density profile. Such approximations appear in various domains, for example in the anelastic model for thermal convection [3,4,19,26,41,44] or the recently built anelastic approximation for Rayleigh-Taylor (RT) flows [29,51].…”