Theory of solitary anticyclones in rotating fluid

An experiment with a thin layer of fluid in a rotating parabolic vessel made it possible to produce long-live anticyclones called Rossby solitons. The laboratory studies were made with a considerable thickening of the fluid layer at the center of the eddy; in some cases the eddy scale was 2 to 3 times less than predicted by the theory of solitary low-amplitude waves. An effort has been made of explain this discrepancy. A study was made of a wave moving westward with the velocity u in a thin layer of rotating fluid. Equations are derived which describe solitary anticyclones moving to the west and low-amplitude waves. Analysis of the derived system shows that with a decrease in the phase velocity of a wave its amplitude decreases, the horizontal scale increases and theorbital velocity becomes close to geostrophic. It is shown that allowance for the finite amplitude of a solitary wave does not eliminate the discrepancy between theory and experiment. As a result of change in Coriolis force the eddy begins to be displaced westward. The anticyclone moves more rapidly than linear Rossby waves and can be transformed into a solitary wave. A cyclone moves more slowly than linear Rossby waves and as a result of generation of Rossby waves cannot be transformed into a stationarily moving solitary wave. The difference from an anticyclone is caused by a decrease in the level in the cyclone.