Abstract
We study the flow of an incompressible liquid film down a wavy incline. Applying a Galerkin method with only one ansatz function to the Navier–Stokes equations, we derive a second-order weighted residual integral boundary layer equation, which, in particular, may be used to describe eddies in the troughs of the wavy bottom. We present numerical results which show that our model is qualitatively and quantitatively accurate in wide ranges of parameters, and we use the model to study some new phenomena, for instance, the occurrence of a short wave instability (at least in a phenomenological sense) for laminar flows which does not exist over a flat bottom.
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