The Rayleigh–Taylor instability of viscous fluid layers

Abstract

The effects of viscosity and surface tension on the nonlinear evolution of Rayleigh–Taylor instability of plane fluid layers are investigated. Full two-dimensional incompressible Navier–Stokes equations and exact boundary equations are solved simultaneously for a precise prediction of this phenomenon. An accurate flux line segment model (FLAIR) for fluid surface advection is employed for the interface reconstruction. The instability is characterized by three stages of development, which are defined based on the competition of the bubble and spike growth. This competition is responsible for the development of different spike and bubble morphologies and is decided based on geometrical factors, mainly the amplitude and wavelength of the initial perturbation, and on the fluid properties, mainly viscosity and surface tension. It is addressed and explained why the spike sometimes grows faster than the bubble, and vice versa. The cutoff and the most unstable wave numbers are identified numerically based on the Weber number. The effect of Weber and Reynolds numbers on the growth rate of instability and the role of viscosity in dragging the development of instability are also investigated.