Steady streaming in an oscillatory flow over a periodic wavy surface

Oscillating flow over a periodic wavy surfaces is numerically investigated by solving the 2-D time-dependent incompressible Navier-Stokes equations in curvilinear coordinates. When the amplitude and the frequency of ambient oscillations are sufficiently small, solutions which are periodic in time and space exist and steady circulation cells due to the streaming effect form. The structure of the streaming pattern becomes great important since the steady circulation can help to redistribute the suspended sediments. Based on the present calculated results, the steady streaming patterns with either two cells or four cells over one period of the wavy surface are observed. The number of circulation cells is found to depend only on a and Re, but not on ka.