Two-Dimensional Vortex Motion Driven by a Background Vorticity Gradient: From Planetary Atmospheres to Pure Electron Plasmas

Physics

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3300 Meteorology And Atmospheric Dynamics, 3346 Planetary Meteorology (5445, 5739), 3379 Turbulence, 4500 Oceanography: Physical, 4520 Eddies And Mesoscale Processes

Scientific paper

Two-dimensional vortex motion through a background shear-flow occurs in a wide variety of systems, ranging from planetary atmospheres to magnetized electron plasmas. Computer simulations and laboratory experiments of this motion generally show that positive vortices (rotating counter-clockwise) move to peaks in background vorticity, whereas negative vortices (rotating clockwise) move to minima. In general, the rate of this migration increases with the magnitude of the background vorticity gradient, whereas it decreases as the background shear intensifies. Positive and negative vortices can also be classified as either prograde or retrograde, depending on whether they rotate with or against the local background shear. Surprisingly, a retrograde vortex moves up or down a background vorticity gradient orders of magnitude faster than a prograde vortex of equal strength. An accurate expression for the velocity of a weak retrograde vortex is obtained from an analytic calculation, in which the response of the background flow to the vortex is linearized. However, this linear theory fails for prograde vortices of any strength. Interestingly, the velocity of a prograde vortex can be obtained from a simple estimate, which accounts for the nonlinear ``trapping'' of background fluid around the vortex. The analytic expressions for the velocities of both prograde and retrograde vortices are in good quantitative agreement with vortex-in-cell simulations, and with electron plasma experiments, when the background shear is below a critical level. When the ratio of background shear to background vorticity gradient exceeds a critical level, gradient-driven vortex motion is suppressed, and the vortex comes into equilibrium with the background. An estimate of this critical shear compares favorably to vortex-in-cell simulations.

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