On the impulsive motion of a flat plate in a viscous fluid

Abstract

The unsteady laminar boundary-layer flow induced by the impulsive motion of a semi-infinite flat plate along its length is investigated. It is found that, unlike Stewartson's (1951, 1960) conclusion, a power-series solution is possible using the ‘correctly stretched’ variables in the analysis. The small-time solution, which is developed in powers of the time, shows a smooth transition from the initial Rayleigh flow to the final Blasius flow without an essential singularity and, furthermore, its validity extends to the whole time domain. The series solution developed for large times, however, seems divergent and merely asymptotic. No evidence is found for the existence of an essential singularity in the solution as described by Stewartson.