Abstract
It is widely accepted that for bodies in turbulent flows a reduction of skin friction can be reached if the surface of the body is provided with small ridges aligned in the local flow direction. This surprising and counterintuitive phenomenon is called the shark-skin effect, motivated from the dermal surface morphology of sharks. In the present article we examine the possibility of resistance reduction due to a rippled surface topography in Stokes flow. We especially analyse the influence of wall riblets perpendicular to the flow direction on the mean transport velocity in gravity-driven creeping film flows following the idea that eddies generated in the valleys of the riblets act like fluid roller bearings and hence may reduce drag. Using a theoretical treatment of the Stokes equations with complex function theory, parameter studies with varying flow rate, bottom amplitude and bottom shape are presented. For the given bottom shapes the maximum enhancement of transport velocity is found by optimising the film thickness.
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Scholle, M., Rund, A. & Aksel, N. Drag reduction and improvement of material transport in creeping films. Arch Appl Mech 75, 93–112 (2006). https://doi.org/10.1007/s00419-005-0414-5
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DOI: https://doi.org/10.1007/s00419-005-0414-5