Unsteady Viscous Flow Due to the Impulsive Motion of a Flat Plate, with Special Reference to the Initial Period

Abstract

The basic flow structure due to the impulsive motion of a semi-infinite flat plate is established for a small parameter s(=(U²t⁄ν)^1⁄2). The asymptotic solution of the Navier-Stokes equations is obtained in the neighborhood of the leading edge of the plate by the Stokes-type successive approximation. It is shown that some of undetermined constants in the present solution can be determined by a matching procedure, if the unsteady Stokes solution for this problem, in particular the shear stress on the plate, is obtained asymptotically near the leading edge.