Investigating the dynamics of point helical vortices on a rotating sphere to model tropical cyclones.

This article focuses on developing an exact weak solution to the absolute vorticity conservation equation (AVCE) for a thin incompressible fluid layer on a rotating sphere, incorporating the helicity of point vortices and variable layer depth. Using this framework, the authors model the dynamics and interactions of helical vortices (HVs), including their behavior near solid boundaries and mutual interactions, to better understand phenomena such as tropical cyclone (TC) trajectories, abrupt recurvature, and landfall. The study analytically derives conditions for cyclone–anti-cyclone asymmetry related to the rotation of the sphere and demonstrates how the rotation influences vortex dynamics and fusion, exemplified by the Fujiwhara effect between two TCs. Additionally, the work generalizes the AVCE solutions to the beta-plane approximation, providing a finite-dimensional dynamical system for HVs that accounts for nonlinear interactions and boundary effects, offering insights into geophysical vortex behavior relevant to atmospheric and oceanic flows.