Thin water films driven by air shear stress through roughness

A model of thin water film transport over small scale surface roughness is developed in the context of a high Reynolds number boundary layer theory. The surface water is found to be described by a lubrication equation. It is shown that small scale surface roughness can first effect the water flow at roughness heights which are much less than those of first nonlinear response in the air. A number of well known phenomenon are encountered when using this model, such as pooling of water between roughness elements and rivulet formation. A linearized subsonic heat transfer analysis is also presented, and water protuberances and roughness are found to enhance the ambient heat flux. Solitons are calculated for two-dimensional films, and a linear stability analysis shows that two-dimensional film fronts can become unstable and develop into rivulets.