Vortex Motion Driven by a Background Vorticity Gradient

The motion of self-trapped vortices on a background vorticity gradient is examined numerically and analytically. The vortices act to level the local background vorticity gradient. Conservation of momentum dictates that positive vortices (``clumps'') and negative vortices (``holes'') react oppositely: clumps move up the gradient, whereas holes move down the gradient. A linear analysis gives the trajectory of small clumps and holes that rotate against the local shear. Prograde clumps and holes are always nonlinear, and move along the gradient at a slower rate. This rate vanishes when the background shear is sufficiently large.