Temporal Stability of Complex Flows

Abstract

In previous chapters we developed a mathematical framework to analyze the stability characteristics of shear flows. We addressed instabilities of inviscid flows, and the effects of viscosity, transient behavior, and various effects of nonlinearities. The examples chosen have concentrated on the mathematical tools rather than an accurate modeling of realistic flow behavior. However, few applications of hydrodynamic stability theory deal with these idealized flow situations, and additional effects have to be taken into account. Varying pressure gradients, three-dimensionality of the mean flow, rotation and curvature, surface tension for free-surface flows and compressibility of the fluid medium are but a few of the effects that arise in realistic situations. Although the mathematical techniques introduced in previous chapters carry over to more complex flows, we will devote this chapter to the study of selected complications of the basic flow and their effect on the temporal growth of infinitesimal perturbations.