THE DIFFERENCE BETWEEN MONOPOLE VORTICES IN PLANETARY FLOWS AND LABORATORY EXPERIMENTS

This work is an attempt to explain observations of vortices in experim ents with shallow water in rotating paraboloidal vessels. The most lon g-lived vortices are invariably anticyclones, while cyclones quickly d isperse, and they are larger than the Rossby radius. These experiments are designed to simulate geophysical flows, where large, long-lived, anticyclonic vortices are common. The general condition for vortices t o be steady is that they propagate faster than linear Rossby waves, so that the vortex energy is not dispersed by coupling to linear waves. The propagation velocity is determined by a general integral relation that gives the velocity of the centre of mass. In geophysical flows, t o lowest order in the Rossby number, the difference between the centre -of-mass velocity and the maximum phase velocity of the Rossby waves i s proportional to the relative perturbation of the fluid depth. Since for anticyclones the difference is positive they may be steady, wherea s cyclones cannot be. In the laboratory experiments this velocity diff erence is absent because of the latitudinal dependence of the effectiv e gravity caused by the centrifugal force. However, to the next order in the Rossby number, there is another nonlinear contribution, so that anticyclones (but not cyclones) still propagate faster than the linea r Rossby waves, and may thus be steady. The velocity difference is sma ller than for geophysical flows, and vanishes in the,limit of small Ro ssby number. The existence conditions also show that we can expect the experimental vortices to be smaller (as measured by the Rossby radius ) than the planetary vortices. The theory does not apply to vortices t hat are much smaller than the Rossby radius.