Oscillatory flow around a sphere resting on a rough bottom: Direct numerical simulations

Oscillatory flow around a large sphere resting on a plane and rough bottom is simulated by means of direct numerical simulations of continuity and Navier-Stokes equations. The bottom roughness is provided by a layer of spherical particles, the size of which is much smaller than the radius of the large sphere, arranged in a hexagonal pattern. To investigate the conditions at the bottom of a propagating sea wave, the flow is forced by a spatially uniform and temporally oscillating pressure gradient. The numerical approach will determine the magnitude and spatial distributions of vorticity and bottom stress, which are difficult to measure in an experimental apparatus. Attention is focused on the dynamics of the vortex structures originated by the free shear layer shed by the surface of the large sphere and on the interaction of the vortex structures with the bottom roughness. In particular, the bottom shear stress in the region close to the large sphere was evaluated suggesting the tendency of the small spheres to be moved and transported by the flow. The results show that peaks of the bed stress originate in the lateral regions as an effect of the flow acceleration around the spherical object.