Optimal Disturbances in the Development of the Instability of a Free Shear Layer and a System of Two Counter-Streaming Jet Flows

An analytical approach to the determination of optimal disturbances is developed. The approach, suitable for flows with piecewise-constant vorticity distributions, is based on the equation of disturbance energy balance and explicit expressions for the growth rate of the energy or the final-to-initial energy ratio. The corresponding expressions are functions of the initial parameters and the optimal disturbance parameters are determined from an extremization of these functions. Within the framework of the approach the classical Rayleigh problem of the free shear layer instability and the problem of the instability of a system consisting of two counter-streaming jet flows in a rotating shallow water layer are considered. The parameters of the optimal disturbances are compared with those of growing normal modes.