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This paper explores an idealized model of the ocean surface in which widelyseparated surface-wave packets and point vortices interact in two horizontaldimensions. We start with a Lagrangian which, in its general form, depends onthe \emph{fields} of wave action, wave phase, stream function, and twoadditional fields that label and track the vertical component of vorticity. Byassuming that the wave action and vorticity are confined to infinitesimallysmall, widely separated regions of the flow, we obtain model equations that areanalogous to, but significantly more general than, the familiar systemconsisting solely of point vortices. We analyze stable and unstable harmonicsolutions, solutions in which wave packets eventually coincide with pointvortices (violating our assumptions), and solutions in which the wave vectoreventually blows up. Additionally, we show that a wave packet induces a netdrift on a passive vortex in the direction of wave propagation which isequivalent to Darwin drift. Generalizing our analysis to many wave packets andvortices, we examine the influence of wave packets on an otherwise unstablevortex street and show analytically, according to linear stability analysis,that the wave packet induced drift can stabilize the vortex street. The systemis then numerically integrated for long times and an example is shown in whichthe configuration remains stable, which may be particularly relevant for theupper ocean.

Particle description of the interaction between wave packets and point vortices