In this paper, several refinements of the point-vortex model to describe the motion of a dipole vortex on the β-plane are undertaken. These include the effects of finite β, squeezing and stretching of the dipole vortices due to bottom topography, and effects of the secondary vorticity fields associated with the advection of the ambient fluid.
Shivamoggi, B. K., & Van Heijst, G. J. F. (1998). Generalized point-vortex model for the motion of a dipole-vortex on the β-plane. Fluid Dynamics Research, 23(2), 113–124. https://doi.org/10.1016/S0169-5983(97)00056-7