IS TWO-DIMENSIONAL OBLIQUE strongSTAGNATIONstrong-POINT FLOW UNIQUE.pdfVIP

CANADIAN APPLIED MATHEMATICS QUARTERLY Volume 8, Number 1, Spring 2000 IS TWO-DIMENSIONAL OBLIQUE STAGNATION-POINT FLOW UNIQUE? J.M. DORREPAAL ABSTRACT. The problem of two-dimensional oblique stag- nation point flow is reviewed and the two solutions which exist in the literature are reconciled. It is found that a family of solutions exists for the problem, but that a unique solution can be obtained by examining the second order terms in the asymptotic expansions at infinity. The slope-ratio constant is verified to be independent of the incidence angle of the impinging stream. A second ratio involving the locations of maximum pressure along the wall and vanishing tangential stress is shown to share the same incident angle independence. 1. Introduction. Between 1959 and 1986, three authors [1], [2], [3] working independently gave solutions to the two-dimension problem of a viscous fluid impinging on a flat wall at an arbitrary angle of incidence. All three papers use a similarity approach to arrive at an exact solution to the full Navier-Stokes equations for an incompressible fluid. The procedure yields two ordinary differential equations, a nonlinear component describing the flow towards the wall and a linear equation corresponding to the shear flow parallel to the wall. The first two solutions by Stuart [1] and Tamada [2] are analytically equivalent, differing only in parameter definition and initial set-up. Tamada’s solution introduces a stream function while Stuart works with the two velocity components directly. Using Tamada’s notation, if the wall coincides with the plane y