Propagation of waves in hydrodynamic shear flows

Abstract

A range of phenomena connected with the propagation of waves in hydrodynamic shear flows is studied. The problem of calculating the energy and momentum of a wave packet in a moving medium is discussed in detail. It is shown that in many cases the momentum of a body moving in a liquid can be correctly calculated only if the compressibility of the medium is taken into account. The phenomenon of super-reflection of waves from the interface between moving media—the fact that the amplitude of the reflected wave can be much greater than the amplitude of the incident wave—is described. An interpretation of this phenomenon is given based on the concept of waves with negative energy. It is also shown that the reflected wave can be amplified when the sign of the dissipation in the moving medium changes. The behavior of different types of waves on a tangential discontinuity of the velocity is described (surface and internal waves as well as Rossby waves are studied). A separate section is devoted to resonant interaction between waves and the flow. Here the plasma-hydrodynamic analogy and its generalization to the case of stratified media are discussed. Resonance amplification in shear flows is studied for sound waves, surface waves on water, and internal gravity waves. The interaction of waves with vortices is discussed briefly. An algebraic method for solving problems is described for cylindrical vortices. Different mechanisms of amplification of sound by vortices are examined.