Point vortex dynamics within a background vorticity patch

Recent experiments and simulations have observed that the interaction of st rong vortices with a low vorticity background can strongly affect the dynam ics of both vortices and background. This paper considers an idealized mode l of this interaction. The background is treated as a patch of uniform vort icity with a nearly circular shape. The strong vortices are treated as poin t vortices, and their total circulation lambda is assumed to be small compa red to that of the background. It is found that Kelvin waves on the boundar y of the background patch can be driven to large amplitude by the strong vo rtices, eventually resulting in wave breaking and filamentation. A multisca le analysis finds that the wave-breaking time scales as lambda (-1) ln lamb da (-1), in agreement with contour dynamics simulations. (C) 2001 American Institute of Physics.