Mixing induced by Rayleigh–Taylor instability in a vortex

Abstract

The direct numerical simulation (DNS) of a two-dimensional Lamb–Oseen vortex with a heavy internal core has been performed. Linear stability theory predicts the existence of Rayleigh–Taylor (RT) instabilities due to the destabilizing effect of the centrifugal force on the radial flow nonhomogeneities. The DNS first exhibits wavy azimuthal perturbations which are nonlinearly distorted into bubble-like patterns, characteristic of the standard development of the RT instabilities, i.e., instabilities obtained in a planar nonhomogeneous flow in the presence of gravity. Nevertheless, important differences may be observed in the late stage development of the instability: contrary to the standard case, the bubbles are then stretched in the azimuthal direction leading to a strong radial filamentation of the flow.