Interaction of vortices in a fluid on the surface of a rotating sphere

The interaction of 3 point vortices, initially situated on the same circle of latitude on the surface of a rotating sphere, is studied under the assumption that the deviation in latitude is small. A linear stability analysis of the equilibrium motion is performed. The purpose of this work is to simulate and understand the motion of anticyclones and cyclones in the atmosphere: the results may help explain observed phenomena. Under certain boundary conditions a linear analysis shows that a ring of sub-tropical anticyclones is stable, however a ring of cyclones would be unstable. This result is due to the variation of Coriolis force with latitude over the surface of a sphere. The “β-plane” effect induces a rotation of a ring of anticyclones, but opposing the direction of rotation of a ring of cyclones. Unless the strength of the cyclonic vorticity is very strong, this effect causes instability in the system of cyclones. The arguments show that in the atmosphere an anticyclone system can exist at subtropical latitudes, whereas cyclonic vorticity will be confined to the polar regions. These results agree with the observed distribution of the major high and low pressure systems in the earth's atmosphere.