The effect of stochastic modulations on the stability characteristics of hydrodynamic flows

The present study is concerned with the development of a model which can be employed to study the effect of temporal stochastic modulations of the boundary values on the stability of flows. The linearized equations of motion for the development of the disturbance of the basic flow have the form of stochastic differential equations with multiplicative 'external' noise. Equations for the first moment of the perturbation of the basic flow are derived for the formulation of an instability criterion. The Galerkin procedure is used for a calculation of the critical parameters. The considered method can be employed for all problems in which the basic flow can be calculated on the basis of the Navier-Stokes equations. An employment of the method to the Couette-Poiseuille flow is found to lead to equations which have to be evaluated numerically. On the other hand, in the case of convective instability, an approximate result can be obtained by means of an analytical calculation.