Chapter 2 - Rayleigh–Taylor instability

Abstract

This chapter considers how a stratification of density can cause an instability under certain settings. For this purpose, we consider a simple fluid whose density does not change by any external conditions, but the fluid density is simply carried along as fluid moves around (or flows around). Of course, this is a very drastic simplification: with any realistic materials (even for solids), the density would change both by temperature and pressure. However, this drastic simplification can elucidate the essence of convection induced by unstable stratification. The concept of the basic force associated with convection, buoyancy, can also be easily introduced under this simplification. The instability that leads to this type of convection is called the Rayleigh–Taylor instability, thus the title of this chapter follows. In most part of this chapter, we adopt an even more drastic simplification: a system consisting of two layers of fluids with different constant densities, ρ1 and ρ2. Only after considering a problem with a discretized stratification, we only briefly consider the case with continuous stratification with a basic state of density given by ρ=ρ¯(z), where z is a height.