A detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. It presents analytical results and numerical simulations, linear and selected nonlinear stability methods. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It is equally of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Stability theory has seen a rapid development over the past decade, this book includes such new developments as direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem.

The question of the stability of steady state solutions in geophysical fluid flows is addressed through qualitative analysis and quantitative examples. The inviscid linear stability theory of stratified shear flows and the solution of the stability problem using normal modes and Fourier-Laplace transforms are discussed. Two numerical examples are used to illustrate the relationship of various physical parameters to the stability of the system and to trace the development of the instability of the instability for short, intermediate and long times. The examples are (1) two layer fluid of infinite extent with application to the air-sea interface and (2) a two-layer fluid having a free surface and finite depth with application to a salt wedge estuary. The initial-value problem is solved using a power series expansion for short times, superposition of modes for intermediate times and asymptotic analysis for long times. The asymptotic expansion applicable in non-conservative systems is compared with the approximate solution using ray techniques, which are valid in conservative systems, and analytic continuation of the eigenvalues into the complex wavenumber plane. (Author).

This book presents the fundamentals and advanced research on the global stability analysis of the shear flows. The contents investigate the results of global stability analysis for different configurations of internal and external shear flows. The topics covered are global stability analysis of converging-diverging channel flows, axisymmetric boundary layer developed on a circular cylinder, cone and inclined flat-plate boundary layer, and wall jets. It further explains the effect of divergence, convergence, transverse curvature, and pressure gradients on the global stability of the different configurations of shear flows. The book is a valuable reference for beginners, researchers, and professionals working in the field of aerodynamics and marine hydrodynamics.

Starting from fundamentals of classical stability theory, an overview is given of the transition phenomena in subsonic, wall-bounded shear flows. At first, the consideration focuses on elementary small-amplitude velocity perturbations of laminar shear layers, i.e. instability waves, in the simplest canonical configurations of a plane channel flow and a flat-plate boundary layer. Then the linear stability problem is expanded to include the effects of pressure gradients, flow curvature, boundary-layer separation, wall compliance, etc. related to applications. Beyond the amplification of instability waves is the non-modal growth of local stationary and non-stationary shear flow perturbations which are discussed as well. The volume continues with the key aspect of the transition process, that is, receptivity of convectively unstable shear layers to external perturbations, summarizing main paths of the excitation of laminar flow disturbances. The remainder of the book addresses the instability phenomena found at late stages of transition. These include secondary instabilities and nonlinear features of boundary-layer perturbations that lead to the final breakdown to turbulence. Thus, the reader is provided with a step-by-step approach that covers the milestones and recent advances in the laminar-turbulent transition. Special aspects of instability and transition are discussed through the book and are intended for research scientists, while the main target of the book is the student in the fundamentals of fluid mechanics. Computational guides, recommended exercises, and PowerPoint multimedia notes based on results of real scientific experiments supplement the monograph. These are especially helpful for the neophyte to obtain a solid foundation in hydrodynamic stability. To access the supplementary material go to extras.springer.com and type in the ISBN for this volume.

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