Propagation of waves in shear flows

Abstract

Present-day results in the theory of oscillatory and wave phenomena in hydrodynamic flows are presented. A unified approach is used for waves of different physical origins. A characteristic feature of this approach is that hydrodynamic phenomena are considered in terms of physics, which complements significantly the traditional formal mathematical approach. Some physical concepts such as wave energy and momentum in a moving fluid are analyzed taking into account induced mean flows. The physical mechanisms that are responsible for hydrodynamic instability of shear flows are considered within the concept of negative energy waves. The phenomenon of over-reflection for waves of different types is analysed. A number of well-known theorems of hydrodynamic theory of stability are interpreted in terms of the interaction of waves having different energy signs. Great attention is drawn to the plasma-hydrodynamic analogy which is a powerful tool for physical analyses of general mechanisms of wave amplification and absorption in flows. A lot of hydrodynamical, acoustical and geophysical phenomena may be classified on the basis of this analogy. Various wave-flow interaction problems are considered, for instance, wave generation in whistlers, wave scattering and amplification by vortices, methods of wave remote sounding, some nonlinear dynamical phenomena, etc. The book is intended for researchers specialized in wave theory, aero-acoustics, geophysical and astrophysical fluid dynamics, and related fields.