Rayleigh Instability of Plane-parallel Liquid Flows

Studying in this paper the stability of plane-parallel flows of an ordinary liquid can be naturally translated into the language of the theory of hydrodynamic resonances. Thus, resonant absorption of oscillations induces stability of the flows of an ideal liquid having a velocity profile without inflection points (Rayleigh theorem), while resonant emission leads to Rayleigh instability in the presence of an inflection point. The flow velocity profile has an inflection point. Thus, the presence of inflection points is a necessary condition for instability. If, however, the velocity profile has inflection points, the flow is stable (Rayleigh's theorem). Note that the sign of the jump depends on whether the neutral oscillations are regarded as the limiting cases of growing or damped oscillations.