Simulation of Nonlinear Tollmien-Schlichting Wave Growth Through a Laminar Separation Bubble

A two-dimensional simulation of the spatial growth of an initially small-amplitude Tollmien-Schlichting (T-S) wave through a thin laminar separation bubble is conducted. For this purpose, the unsteady incompressible Navier-Stokes equations in stream-function vorticity form are solved numerically using a direct matrix solver. A range of wave frequencies are considered. A strong nonlinear interaction between the T-S wave and the bubble is shown to occur especially for the higher frequencies resulting in periodic shedding of vorticity from the bubble. This interaction results in pronounced changes in the structure of the laminar separation bubble. It also leads to increasing discrepancy between the growth of the T-S wave predicted by linear stability theory and the growth observed in the present simulation.