Linearised instability and nonlinear stability bounds for thermal convection in a fluid-filled porous finite box are derived. A nonuniform temperature field in the steady state is generated by maintaining the vertical walls at different temperatures. The linearised instability threshold is shown to be well above the global stability boundary, which is strongly suggested by the lack of symmetry in the perturbed system. The numerical results are evaluated utilising a newly developed Legendre-polynomial-based spectral method.
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Communicated by S. Roux
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Hill, A.A. Horizontal thermal convection in a porous medium. Continuum Mech. Thermodyn. 18, 253–258 (2006). https://doi.org/10.1007/s00161-006-0026-5
- Energy method
- Porous medium
- Spectral methods