Modelling flow past a rough sphere via stream functions and solution through Galerkin’s method

We study the flow past a rough sphere considering the rugosity as a parameter and its effect on the drag coefficient. The numerical implementation is carried out via a novel approach using Galerkin’s method combined with an asymptotic expansion for the stream function. The amplitude of the spatial fluctuation is used as the perturbation parameter. The numerical results for the size of the vortex ring and streamlines in the smooth case are compared with experimental data found in the literature. In addition, when the surface is rough, we compare the numerical results with the smooth case and the implications of the rugosity in the separation point and other features of the flow are discussed.