Localized vortices figure prominently in hydrodynamics, geophysics, the physics of magnetized plasma, and theories of superfluids, and superconductivity. Understanding their dynamics is important for both theoretical and practical purposes, especially for predicting tropical cyclone trajectories.

Chefranov et al. propose a relatively simple simulation of sharp turns in such trajectories based on analysis of finite-dimensional dynamics of point spiral vortices on a rotating sphere, which corresponds to the exact solution of the equations of hydrodynamics.

Previously, studies simulating complex cyclone trajectories, like those caused by the “Fujiwhara effect,” have been confined to modeling on a plane. This new modeling allows for consideration of point spiral vortices on a sphere, and of the rotation of the sphere itself.

“The approach we are developing makes it possible to identify the key mechanisms that determine the movement features of tropical cyclones during their long-range interaction with the mainland,” said author Sergey Chefranov.

The model complements traditional numerical solutions and analyses of three-dimensional systems of equations that describe atmosphere-ocean interactions used to predict conditions around a cyclone’s landfall, thereby reduce its catastrophic consequences. It also describes how a tropical cyclone’s long-range interaction with the mainland can attract a subsequent cyclone – what Chefranov said is “analogous to the well-documented phenomenon of attraction of a tornado’s whirlwind funnel to a solid boundary.”

“Our results help reveal the essential role of the sphere’s rotation in the dynamics of helical vortex interactions, with one another and with boundaries,” said Chefranov. “The solutions can be useful in different studies, including problems of turbulence, the collapse of vortices, anomalous turbulent energy dissipation, and atmospheric dynamics.”

Source: “Investigating the dynamics of point helical vortices on a rotating sphere to model tropical cyclones,” by Sergey G. Chefranov, Igor I. Mokhov, and Alexander G. Chefranov, Physics of Fluids (2023). The article can be accessed at http://doi.org/10.1063/5.0143023.