On the Asymptotic Form of the Stream Function for the Flow of an Oseen-Like Fluid past a Parabolic Cylinder

摘要

The asymptotic behavior of the flow at a large distance from a parabolic cylindrical obstacle immersed in the uniform flow of an incompressible viscous fluid is considered on the basis of a successive approximation method, with the Oseen solution as the first step. Only dominant terms are retained in the expression for the stream function. Four steps in the approximation procedure yield a parabolic displacement surface which for the degenerate case; namely, the semi-infinite flat plate, approaches very closely the Blasius result and thus demonstrates the validity of the Oseen type of successive approximations in dealing with the Navier-Stokes equations. (Author)