Abstract
AbstractWe study the flow of an incompressible liquid film down a wavy incline. Starting from the Navier–Stokes equations we derive an integral boundary layer equation (IBLe) by applying a Galerkin method with a single test and ansatz function. In comparison with older models this approach has several advantages. First, a linear stability analysis for stationary solutions yields a critical Reynolds number which corresponds in the limit of a flat incline with results directly obtained by the Navier–Stokes equations. Second, the IBLe is consistent with the pertinent Benney equation. Finally, the velocity profile is not assumed to be parabolic, so that also parameter regimes with recirculations can be modelled. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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