Simulation of Thermal Effects on Two-Dimensional Vorticity Dynamics Evolution

This study presents a class of exact solutions for vortex-temperature interactions in 2D Boussinesq flows using Hermite polynomial expansions. We derive a novel class of solutions for N vortices coupled with N temperature particles, proving rigorous convergence and establishing a direct link between thermal diffusivity kT and vortex stability. Numerical simulations reveal that temperature gradients induce asymmetric vortex deformation and accelerate destruction, with smaller kT values amplifying these effects. Our framework generalizes classical vortex methods to thermally active fluids, offering a unified approach for geophysical and industrial applications. The results suggest that vortices persist under symmetric thermal forcing, while asymmetric forcing leads to faster degradation when kT is sufficiently small.