The stability of two-phase flow over a swept wing

We use numerical and asymptotic techniques to study the stability of a two-phase air/water flow above a flat porous plate. This flow is a model of the boundary layer which forms on a yawed cylinder and can be used as a useful approximation to the air flow over swept wings. The air and water form an immiscible interface which can destabilize the flow, leading to travelling wave disturbances which move along the attachment line. This instability occurs for lower Reynolds numbers than is the case in the absence of a water layer. The two-fluid flow can be used as a crude model of the effect of heavy rain on the leading edge of a swept wing. We also investigate the instability of inviscid stationary modes. We calculate the effective wavenumber and orientation of the stationary disturbance when the fluids have identical physical properties. Using perturbation methods we obtain corrections due to a small stratification in viscosity, thus quantifying the interfacial effects. Our analytical results are in agreement with the numerical solution which we obtain for arbitrary fluid properties.