Similarity solutions of the equations of a boundary layer in a nonuniform external flow

Similarity solutions of the equations of a laminar incompressible boundary layer, formed in a rotational external flow, are investigated. Such problems arise in the analysis of the flow in a boundary layer when there is an abrupt change in the boundary conditions (for example, in the case of a discrete inflation of the boundary layer, in hypersonic flow about blunt bodies, etc.). Various approaches to their solution have been proposed earlier in 1–4]. Solved below is the so-called inverse problem of boundary layer theory (see 3], p. 200), where the contour of the body that causes a given flow outside the boundary layer is unknown beforehand and is found during the course of solution of the problem in connection with the coupling of the longitudinal and transverse velocity components. The cases of a parabolic (u_e ~ y²) and a linear (u_e=a(x)+b(x)y) variation in the velocity of the external flow with distance along the transverse direction are considered in detail. The latter includes an investigation of the flow in the neighborhood of the critical point of a blunt body, taking account of the vorticity of the flow in the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 78–83, March–April, 1971.