Interaction of a simple Prandtl-Meyer wave with a weakly vortexed layer

The problem of interaction of a centered wave of rarefaction with a shear layer is solved in the case of a small flow vorticity in the shear layer. The solution is found in the form of an asymptotic series with respect to a small parameter of the problem. A system of equations derived in the zero approximation describes the flow in a simple wave. A uniformly applicable first-order expansion is constructed using the method of deformed coordinates.