  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.
