The unsteady laminar boundary layer on a semi-infinite flat plate due to small fluctuations in the magnitude of the free-stream velocity

Abstract

Asymptotic and numerical solutions of the unsteady boundary-layer equations are obtained for a main stream velocity given by equation (1.1). Far downstream the flow develops into a double boundary layer. The inside layer is a Stokes shear-wave motion, which oscillates with zero mean flow, while the outer layer is a modified Blasius motion, which convects the mean flow downstream. The numerical results indicate that most flow quantities approach their asymptotic values far downstream through damped oscillations. This behaviour is attributed to exponentially small oscillatory eigenfunctions, which account for different initial conditions upstream.