Incompressible Rayleigh-Taylor mixing in circular and spherical geometries

We present a numerical investigation of the turbulent evolution of the mixing layer developing from the Rayleigh-Taylor instability for miscible incompressible fluids in circular (in two dimensions) and in spherical (in three dimensions) geometries in the Boussinesq approximation. We show that the main difference caused by the convergent geometry with respect to the planar case is that the center of the mixing layer drifts toward the center of the domain during the evolution of the mixing layer. A similar effect is observed for the radial profile of the density flux. We derive a simple geometrical relation for this inward drift based on mass conservation. In the late stage of the evolution we observe also the appearance of an inward-outward asymmetry in the radial profiles.

Automated summary

In this study, a numerical investigation was conducted to examine the turbulent evolution of the mixing layer formed by the Rayleigh-Taylor instability in circular and spherical geometries. The results revealed that the convergent geometry caused the center of the mixing layer to drift towards the center of the domain, and a simple geometric relation based on mass conservation was derived to explain this inward drift. Furthermore, an inward-outward asymmetry in the radial profiles was observed in the late stage of the evolution.