On unstable oscillations in a viscous-fluid flow through an infinite channel

Previous studies have developed an asymptotics for both the lower and upper branches of the neutral stability curve when the Reynolds number tends to infinity. The multilayer perturbation model, constituting the basis of the theory of the free interaction of the boundary layer with the outer potential flow, has made it possible to delineate the velocity-field structure and to simplify its mathematical analysis. Based on these studies, the present paper shows how it is possible to construct a solution in each of the regions arising in the case of a linear approach to the problem of the stability of a viscous incompressible fluid flow through an infinite plane channel.