# Developments in Stability Theory

## Abstract

In these notes we describe some of the recent developments in the linear theory of hydrodynamic stability. We start by distinguishing between temporal and spatial stability, in the context of the very familiar model problem of the Kelvin-Helmholtz theory for a vortex sheet. The general prescription for determining the stability of causal solutions for initial-value problems is then described, which introduces the distinction between convective and absolute instabilities. These ideas have found very wide application, and we describe a number of different situations in which absolute instability in particular is seen to play an important role; this includes the response of an elastic fluid-loaded plate, the boundary-layer flow on a rotating disk, and the stability of a range of wake flows. All these situations apply very much to parallel flows, however, and in order to handle non-parallel flows one must find ways of connecting the local, quasi-parallel properties of the flow to the global dynamics.

## Keywords

Vortex Sheet Absolute Instability Pinch Point Plane Poiseuille Flow Lower Deck## Preview

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