Theoretical solution of vortex splitting due to islands effect on the vortex

Islands, acting as transitional areas between land and sea, significantly influence their surrounding environments. Studying the changes in vortex structure resulting from the interaction between islands and mesoscale vortices is crucial for understanding the dynamic characteristics and ecological processes of the marine environment. Previous theoretical studies have shown that in a domain without boundaries, due to the conservation of angular momentum, a vortex cannot split by itself. This paper establishes the conditions for the splitting of an anticyclonic vortex when it collides with two square islands. By linking the initial and final states of islands effect on the vortex and utilizing conserved quantities such as angular momentum and mass, along with the slow variation approximation, a nonlinear theoretical solution is constructed. The analysis shows that when the interaction between the vortex and the two islands leads to vortex splitting, the length of the islands, the vortex radius, and the distance between the islands must satisfy a certain condition $O\left(\frac{L}{R}\right)$∼$O\left(\frac{w}{R}\right)$∼$O\left(1\right)$. These results provide support for subsequent analyses of the impact of various parameters on vortex structure when the North Brazil Current (NBC) ring encounters the Lesser Antilles in the tropical western Atlantic.