Circulation cells in flow past a periodic wall

We present a long wavelength model in order to derive a simple formula for the amplitude at the onset of circulation cells in flow past a wavy wall. The flow takes place between a wavy wall and a plane wall and is driven by moving the plane wall. There is no amplitude restriction but the Reynolds number is small and the wavelength is long. We find recirculation cells at an amplitude of about 3/103/10 the average gap width. This is confirmed by a Stokes flow calculation which can be done for all wavelengths.At long wavelengths the circulation cells can be eliminated if, in addition to the moving wall, the flow is driven by gravity.