INTERACTION BETWEEN VORTICES AND WAVES IN A SIMPLE-MODEL OF GEOPHYSICAL FLOW

A basic vortex-wave interaction in quasigeostrophic flows is investigated. Specifically, the interaction between a point vortex and an initially horizontal interface separating two regions of uniform potential vorticity is considered. In the asymptotic limit of small amplitude interface motions, the exact solution of the initial value problem is presented. If there exists an interface wave whose phase speed matches the drift speed of the point vortex, a spreading packet of such waves forms to the lee of the vortex, and these waves induce the vortex to drift toward or away from the interface. Such an interaction corresponds to a radiative transfer of momentum from the vortex to the interface. The effect is generalized to include more complex shear flows stabilized by variations in depth or Coriolis force with latitude. It is shown that a stable vortex strip repels or attracts point vortices according to their sign and that a pair of vortex strips focuses a vortex onto the line midway between them. The results support the hypothesis that in a stable shear flow, a positive (cyclonic) vortex drifts in the direction of increasing potential vorticity by radiating Rossby waves. © 1990 American Institute of Physics.