Asymptotic solutions of the Navier-Stokes equations in regions with large local perturbations

Abstract

There are many problems of the dynamics of viscous flows of liquids and gases at high Reynolds numbers for the solution of which the classical theory of the boundary layer cannot be used. This applies, in particular, to all the problems with various sorts of local singularities in the stream-flows in the vicinity of corners, in regions of interaction of the boundary layer with an incident shock, flows near points of separation or attachment of the stream, etc. The purpose of the present paper is to attempt the theoretical investigation of problems of this type on the basis of the general analysis of the asymptotic behavior of the solutions of the Navier-Stokes equations. In order to do this, use is made of the familiar method of the construction and splicing of a combination of asymptotic expansions representing the solutions in the various characteristic regions of the stream with viscosity decreasing without bound [1].

As an example, detailed consideration is given to the problem of viscous supersonic flow near a wall with large local curvature of the surface.