Effects of external forcing and frictional dissipation on the evolution of vortex system

A large number of ocean vortex interactions have been recorded in satellite imagery, nevertheless, only a restricted number of researches have focused on these phenomena, which found that external forcing and frictional dissipation play an important role in vortex interactions. Therefore, this paper aims to investigate the effects of external forcing and frictional dissipation on vortex interactions. A two-dimensional Boussinesq model is derived from a shallow-water model containing external forcing and frictional dissipation. The asymptotic analytical solution for the model is found through the application of the pseudo-spectral and Newton iterative methods, ultimately, numerical simulations are conducted using the derived vortex model, and the original state of the vortex is constructed using solution obtained. The experimental findings demonstrate that the vortex interactions are either inhibited or promoted depending on the strength of the external forcing and the center distance, when frictional dissipation is also considered, the symmetry leading to the vortex evolution is altered. In addition, the strength of external forcing and frictional dissipation can not only weaken the strength of the vortex, but the combined effect of these two factors combined with the distance between the centers can also have a certain moderating effect on the merging and rotation of the vortex.