Shear flow over a protuberance on a plane wall

Abstract

Simple shear flow over a protuberance with an axisymmetric shape projecting from a plane wall with its axis normal to the wall is studied by means of a boundary-integral method that is suitable for computing three-dimensional Stokes flow in axisymmetric domains. The problem is formulated in terms of a system of three scalar Fredholm integral equations of the first kind for the distribution of traction over the surface of the protuberance and the wall, and is solved by means of a boundary-element method. Numerical computations are performed for a family of protuberances whose exposed surface is a section of a sphere or of an oblate spheroid with its minor axis normal to the wall, and the results are in agreement with those of previous analytical computations for hemi-spherical and spherical shapes. The numerical computations provide accurate information on the hydrodynamic force and torque exerted on the protuberances due to the shear flow, and the distribution of shear stresses, and illustrate the kinematical structure of the flow with reference to the development of stagnation points and flow reversal.