Pulses in Shear Flows

Abstract

Wave motions in fluids may appear as a result of circumstances other than compressibility (acoustic waves) or stratification (internal waves). Waves in shear flows attract particular interest in hydrodynamics. They appear in the framework of the model of an incompressible fluid with constant density. Here we mention but a few of the large number of references concerned with the waves in jets, boundary layers, mixing layers and other shear flows (Landau and Lifshitz, 1989), (Lin, 1955), (Maslowe, 1981), (Timofeev, 1970), (Miles, 1961). Their study was initiated by Lord Rayleigh in connection with the problem of ‘singing flames’ described in his famous book (Rayleigh, 1894). Here he used model velocity profiles for the explicit calculation of dispersive curves. He initiated the interest to the problem of hydrodynamical stability, a problem continues to attract attention today. The core of the theory is the existence of unstable modes. Nevertheless the study of stable modes (decreasing or neutral) also is of interest for hydrodynamicists. In particular, it is relevant for a better understanding of non-linear wave interactions, the dynamics of turbulent boundary layer, etc.