Fluid Dynamics

Abstract This is Part 4 of a book series on fluid dynamics that comprises the following parts: Part 1. Classical Fluid Dynamics Part 2. Asymptotic Problems of Fluid Dynamics Part 3. Boundary Layers Part 4. Hydrodynamic Stability Theory The series is designed to give a comprehensive and coherent description of fluid dynamics, commencing with classical theory suitable for undergraduate lectures, and progressing through to more advanced material at the frontiers of modern research. Part 4 is devoted to hydrodynamic stability theory. In Chapter 1 we introduce the concept of the linear instability of fluid flows, and formulate the Orr–Sommerfeld and Rayleigh equations. We include discussions of Kelvin–Helmholtz, cross-flow, and centrifugal instabilities. In Chapter 2 we employ high Reynolds number analysis to analyse the behaviour of disturbances in the vicinity of the branches of the linear neutral curve. An internal structure that plays a vital role in this description is the critical layer and its properties are discussed in some detail. In Chapter 3 we introduce receptivity theory where the process of excitation of instability modes in the boundary layer by agencies such as free-stream turbulence, acoustic noise, and surface roughness is studied. In Chapter 4 we formulate the Landau-Stuart equation describing how weak nonlinearity of disturbances influences the critical Reynolds number. In addition, we present finite amplitude travelling wave solutions which lead to the concept of a neutral surface. Finally, in Chapter 5 we discuss self-sustaining processes in which large-scale coherent structures in the flow and finite-amplitude travelling waves exist in harmony.