Inviscid dipole-vortex rebound from a wall or coast

Abstract

A vortex approaching a no-slip wall ‘rebounds’ due to the creation of vorticity at the wall in a viscous boundary layer. Here it is demonstrated that a purely inviscid mechanism can also produce vortex rebound from a slip wall. In inviscid vortex rebound, vortex tube stretching generates the necessary vorticity to allow rebound, eliminating the need for viscous vorticity generation. This vortex stretching mechanism is demonstrated through numerical simulations and laboratory experiments on dipole-vortex rebound from a boundary. In an application to oceanography, numerical simulations of both quasi-geostrophic and shallow water dynamics are used to show that the β-effect at an eastern boundary can produce this inviscid rebound. Through a series of numerical experiments in which the strength of the β-effect is varied, a formula for predicting the point of separation of the vortices from the boundary in a dipole–coast collision is deduced. Through simulations, the flux of vorticity and fluid away from the boundary is measured as a function of β and initial angle of incidence. It is found that, in contrast to viscous vortex rebound, which typically does not produce a flux of material away from the boundary farther than a distance comparable to the initial vortex radius, the β-induced rebound does carry fluid far from the coast. Laboratory experiments in a rotating tank are used to show that a sloping bottom can also provide an inviscid mechanism for dipole-vortex rebound from the wall of the tank under certain conditions. A relation determining the conditions under which inviscid or viscous processes will dominate in the rebound of the dipole from a boundary is obtained.