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<p>This work examines dynamic transitions for the convection in a square cavity filled with porous media. First, we show that the equilibrium of the equation loses its linear stability if the critical parameters (<i>Da</i>,&#xa0;<i>Ra</i>) are greater than a threshold, and the corresponding principle of exchange stability (PES) condition is then verified. Second, we simplify the infinite dynamical system to a finite one using the center manifold theory, and then establish the nonlinear transition theorems with the help of a few non-dimensional transition numbers. Finally, detailed graphical analysis and numerical computations are carried out to determine the critical parameters and the multiplicity of the eigenvalues involved. Our results indicate that temperature differences and the permeability of porous media can both contribute to and exacerbate the occurrence of instabilities.</p>

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The Transition and Bifurcation for the Convection in a Square Cavity Filled with Porous Media

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月28日

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  • Junyan Li,
  • Lili Zhang,
  • Tossapol Phoophiwfa,
  • Piyapatr Busababodhin

摘要

This work examines dynamic transitions for the convection in a square cavity filled with porous media. First, we show that the equilibrium of the equation loses its linear stability if the critical parameters (Da, Ra) are greater than a threshold, and the corresponding principle of exchange stability (PES) condition is then verified. Second, we simplify the infinite dynamical system to a finite one using the center manifold theory, and then establish the nonlinear transition theorems with the help of a few non-dimensional transition numbers. Finally, detailed graphical analysis and numerical computations are carried out to determine the critical parameters and the multiplicity of the eigenvalues involved. Our results indicate that temperature differences and the permeability of porous media can both contribute to and exacerbate the occurrence of instabilities.