Linear stability of a gas boundary layer flowing past a thin liquid film over a flat plate (Q2731228)

The study of aircraft behaviour under conditions of heavy rain and high wind shear leads to the problem of a gas stream past a flat plate under the influence of rainfall. As raindrops deposit on the flat plate, they coalesce to form a water film that flows under the action of shear from the surrounding gas stream. In the limit of large Reynolds number of gas phase, small rainfall rate and small film thickness compared to gas boundary rainfall rate and to the thickness of gas boundary layer, the authors obtain a similarity solution that predicts growth of the liquid film like \(x^{3/4}\). The flow in the gas stream closely resembles Blasius solution, whereas viscous dissipation dominates inside the film. Local linear stability analysis leads to Tollmien-Schlichting waves in the gas phase, and to an interfacial instability.