Effective Boundary Conditions for Stokes Flow
over a Rough Surface

K. Sarkar* and A. Prosperetti

Department of Mechanical Engineering
The Johns Hopkins University
Baltimore MD 21218

*Present address: Dynaflow Inc., 7210 Pindell School Road, Fulton MD 20759



ABSTRACT: Ensemble averaging combined with multiple scattering ideas is applied to the Stokes flow over a stochastic rough surface. The surface roughness is modeled by compact protrusions on an underlying smooth surface. It is established that the effect of the roughness on the flow far from the boundary may be represented by replacing the no-slip condition on the exact boundary by a partial slip condition on the smooth surface. An approximate analysis is presented for a sparse distribution of arbitrarily-shaped protrusions and explicit numerical results are given for hemispheres. Analogous conclusions for the two-dimensional case are obtained. It is shown that in certain cases a traction force develops on the surface at an angle with the direction of the flow.

J. Fluid Mech. 316, 223-240, 1996


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