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On similarity solutions of a boundary layer problem with an upstream moving wall. (English) Zbl 0634.76034

This work deals with the problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream. It has previously been shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream. In particular, it was proved that a solution exists only if this parameter does not exceed a certain critical value, and numerical evidence was adduced to show that this solution is nonunique. Using Crocco formulation the present work proves this nonuniqueness. Also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter.

MSC:

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
34D15 Singular perturbations of ordinary differential equations
76M99 Basic methods in fluid mechanics
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