Two-Dimensional Viscous Flow Accompanied by a Stagnation Point on a Plane Wall

Abstract

The two-dimensional flow, induced by a point source at a finite distance from an infinite plane wall, is analyzed on the basis of the Navier-Stokes equation in the following two cases. In the first case, the source strength is considered to oscillate sinusoidally with the vanishing Reynolds number (unsteady Stokes flow). The wall shear stress can then be evaluated for arbitrary values of the frequency \(\varOmega \) and is found to increase in proportion to \(\sqrt{\varOmega }\) as \(\varOmega \) becomes large. In the second case the steady flow with not-zero but small Reynolds number is dealt with by the perturbation method. It is found that the first-order perturbation to the steady Stokes solution is fairly small but that the back flow may occur far away from the stagnation point.