Theory of stability of rotating shear flows

The stability of rotating horizontal-shear flows is investigated within the framework of the linear approximation. The shear flow perturbations are divided into three classes (symmetric and two- and three-dimensional) and sufficient conditions of stability are obtained for each class. The perturbation dynamics in a flow with constant horizontal shear are described and the algebraic instability of the flow with respect to three-dimensional perturbations is detected. It is shown that the symmetric perturbations may be localized (trapped) inside the shear layer. The problem of finding the growth rates and frequencies of the trapped waves is reduced to a quantum-mechanical Schrödinger equation. Exact solutions are obtained for a “triangular” jet and hyperbolic shear.