Rayleigh–Taylor modes in the presence of velocity shear and vortices

Abstract

Two-field models for Rayleigh–Taylor modes are investigated. The changes due to external velocity shear (without flow curvature) are reviewed, and the influences of the various terms in the models are discussed. It is shown that, in principle, velocity shear in combination with dissipation leads to the suppression of linear Rayleigh–Taylor modes in the long-time limit. The long-wavelength modes first seem to be damped; however, later they show an algebraic growth in time, before ultimately the exponential viscous damping wins. In general, the amplitudes become very large, and therefore the often-quoted stability of Rayleigh–Taylor modes in the presence of velocity shear is more a mathematical artefact than a real physical process. Vortices, on the other hand, can lead (together with velocity shear) to a quite different dynamical behaviour. Because of a locking of the wave vectors, pronounced oscillations appear. This effect is demonstrated by a simple model calculation. When vortices and velocity shear are generated from linear instability, the resulting oscillatory state finally becomes unstable with respect to Rayleigh–Taylor modes on a long time scale (‘secondary instability’).