Scattering of an eddy advected by a current towards a topographic obstacle

Abstract

Contour dynamics is used to compute the two-dimensional (f-plane) motion of an initially circularly symmetric barotropic eddy with piecewise-uniform vorticity as it is advected around a circular obstacle by a uniform upstream current. For grazing incidence of this ‘shielded’ eddy (compensating positive and negative vorticity) the main effect of the vortex images (inside the obstacle) is to change the speed of those particles in the outer portion of the eddy that are closest to the obstacle; a lesser velocity is induced on the oppositely signed vortices near the eddy centre. The result is a systematic separation of the centroids of the ± vortices in the eddy, and the eddy emerges far downstream with an invariant dipole moment (m = 1 azimuthal mode). This causes the eddy to move with a constant velocity V normal to the uniform basic flow. The ratio of the numerically computed V to the accompanying far-field dipole moment agrees with a previous analytical theory for a completely isolated eddy subjected to a small-amplitude m = 1 initial disturbance. The scattering effect might be realizable in a rotating homogeneous fluid by translating a cylinder relative to an otherwise stationary eddy. Application to a density-stratified model is suggested.