Dynamics of an isolated barotropic eddy on a beta-plane

The dynamics of a Gaussian isolated barotropic eddy on a β-plane is considered. The analytical solution of the evolution of an isolated vortex is constructed by analogy to the theory of a point vortex. The results of a numerical experiment are compared with the conclusions of the theory for the case of the Gaussian vortex. Characteristics of the vortex such as its radius, trajectory of movement, kinetic energy, residual vorticity, and the structure of the vortex are discussed. The analysis of the numerical results shows that the experimentally determined radius of the vortex, its energy, and residual vorticity are in good agreement with the theory. On the other hand there is a difference between analytical and experimental values of velocity components, and hence in the trajectory of the centre of the vortex. The location of the separatrix of the streak function and its saddle point are considered as important characteristics of the structure of the vortex. We consider the phenomenon of the generation of the vortex sheet connected with the separatrix location as a cause of the difference between the experimental and analytical estimates of the velocity of the vortex.