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<p>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 <i>N</i> vortices coupled with <i>N</i> temperature particles, proving rigorous convergence and establishing a direct link between thermal diffusivity <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(k_{T}\)</EquationSource></InlineEquation> and vortex stability. Numerical simulations reveal that temperature gradients induce asymmetric vortex deformation and accelerate destruction, with smaller <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(k_{T}\)</EquationSource></InlineEquation> 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 <InlineEquation ID="IEq3"><EquationSource Format="TEX">\(k_{T}\)</EquationSource></InlineEquation> is sufficiently small.</p>

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Simulation of Thermal Effects on Two-Dimensional Vorticity Dynamics Evolution

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月25日

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  • Mahdi Kamandar,
  • Hari Mohan Srivastava,
  • Mohammad Izadi

摘要

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 \(k_{T}\) and vortex stability. Numerical simulations reveal that temperature gradients induce asymmetric vortex deformation and accelerate destruction, with smaller \(k_{T}\) 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 \(k_{T}\) is sufficiently small.