Application of a quasi-steady stability model to periodic boundary-layer flows.

A quasi-steady model has been used to investigate the stability of an unsteady, periodic boundary layer on a flat plate. The model combines the concepts of a disturbance wave packet propagating downstream with the generalization of the local effects of steady streamwise pressure gradients to the case of unsteady pressure gradients. Integration of the local amplification rates along the trajectory of the disturbance for several flow conditions has led to the following results which are consistent with previous experimental observations: 1) the disturbances form wave packets; 2) variations in the amplification histories of the disturbances can result in a sequential breakdown along the packet which gives the appearance of the nascent turbulent disturbance spreading upstream with time; 3) insufficient amplification of the packet over one cycle can result in a delayed transition occurring at higher Reynolds numbers.