A special case of hydrodynamic stability (Q1185640)

The following dependence of the amplitude of the velocity perturbations on the supercriticality parameter: \(A\sim\delta^{1/2}\) is typical for the case of selfexcited oscillations which are generated when there is instability in the stationary flows of a viscous incompressible fluid. There is, however, a special case (it is investigated in this note) when this dependence is linear (as in the case of bifurcations in a stationary regime). A condition is obtained for the existence of such selfexcited oscillations together with an algorithm which enables one to find their frequency and amplitude.