An integral boundary layer equation for film flow over inclined wavy bottoms

Details An integral boundary layer equation for film flow over inclined wavy bottoms An integral boundary layer equation for film flow over inclined wavy bottoms

2008-11-20

arxiv.org/abs/0811.3436v3

Mathematics

Analysis of PDEs

23 pages, 12 figures. We added a new Section "Regularization" in which we additionally apply a Pade-like regularization to the

Scientific paper

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 for laminar flows which does not exist over flat bottom.

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