Effect of Wavy Roughness on Wall Turbulence Damping

Abstract

The present paper describes an analysis on the hydrodynamic effect of a fixed or oscillating wavy wall on the wall turbulence damping of the flow near the wall, and then on the velocity defect of the turbulent boundary layer of the plate. The turbulence damping is assumed to be represented by an eddy viscosity model proposed by Chapman and Kuhn. Then the model is applied to a wavy plate in which the boundary shape has a sinusoidal undulation, fixed in space or oscillating in time. The extention is made by assuming unsteady Oseen flow in the viscous sublayer of the turbulent boundary layer along the wavy wall. An analytical solution is obtained in terms of the geometrical parameters of the wavy wall, like height and wave length of the wall. The results show that the roughness function of the wavy wall, consequently the wall friction, becomes larger in most cases than that of a flat plate. However a little reduction of the friction is obtained in case when the amplitude of the wavy wall is small compared to the sublayer thickness and the ratio of the amplitude to the wave length is finite.