This book begins with a basic introduction to three major areas of hydrodynamic stability: thermal convection, rotating and curved flows, and parallel shear flows. There follows a comprehensive account of the mathematical theory for parallel shear flows. A number of applications of the linear theory are discussed, including the effects of stratification and unsteadiness. The emphasis throughout is on the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, the theory is related to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems, for which hints and references are given, not only provide exercises for students but also provide many additional results in a concise form.
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Airy functions amplitude asymptotic asymptotic expansions basic flow Benard convection bifurcation Blasius Blasius boundary layer boundary conditions boundary layer coefficients consider constant critical value curve of marginal derived dimensionless discussed Drazin eigenfunctions eigenvalue relation equations of motion experimental exponentially finite flow is stable Fluid Mech given by equation gives group velocity Hence hydrodynamic stability initial-value problem inner expansions instability integral inviscid fluid Kelvin-Helmholtz instability laminar Landau equation linear theory marginal curve marginal stability Math method nonlinear normal modes obtain ordinary differential equations Orr-Sommerfeld equation oscillation outer expansions parallel flows perturbation plane Couette flow plane Poiseuille flow Rayleigh Rayleigh number Reid resonance satisfy shear layer shown in Fig solutions of equation spatial modes steady supercritical surface Taylor number Taylor vortices theoretical tion turbulence two-dimensional disturbances unstable mode viscous vortex wavenumber weakly nonlinear Wronskian zero