Abstract

The article received estimation of the imaginary and real parts of the eigenvalues of spectral problems of stationary plane-parallel flow of a viscous fluid between two infinite plane-parallel, moving relative to each other with constant speeds under any values of the Reynolds and wave numbers. It is shown that planar Couette flows are stable against small perturbations of the velocity of the main flow. Using the method of regularized traces, developed a new method for calculation of eigenvalues of a spectral problem Orr-Sommerfeld.

Keywords

Hydrodynamic stability theory, the Couette flow, spectral problem of Orr-Sommerfeld, eigenvalues and eigenfunctions of the operator, the corrections of the perturbation theory, method of regularized traces.