On the breakdown of the steady and unsteady interacting boundary-layer description

Abstract

It is known that the classical boundary-layer solution breaks down through the appearance of the Goldstein singularity in a steady solution or Van Dommelen's singularity in an unsteady solution. Interaction between the inviscid flow and the boundary layer removes the Goldstein singularity, until a new critical parameter is reached, corresponding to a marginal separation in the asymptotic triple-deck description. In earlier studies instabilities were encountered in interacting boundary-layer calculations of steady flow along an indented plate, which might be related to the breakdown of the marginal separation. The present study identifies them as numerical. Further, until now it was unknown whether the unsteady interacting boundary-layer approach would remove Van Dommelen's singularity in the classical boundary layer around an impulsively started cylinder. It is shown here that its appearance is at least delayed. The calculations show the experimentally known individualization of a vortex, after which the solution grows without reaching a steady limit; a process that is likely to be related to dynamic stall.