Large-Scale Thermal Convection in a Horizontal Porous Layer

Denis S. Goldobin; Elizaveta V. Shklyaeva

doi:10.1103/physreve.78.027301

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arXiv · 0804.2825

Large-Scale Thermal Convection in a Horizontal Porous Layer

Denis S. Goldobin·Elizaveta V. Shklyaeva

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Abstract

In a range of physical systems, the first instability in Rayleigh-Bernard convection between nearly thermally insulating horizontal plates is large scale. This holds for thermal convection of fluids saturating porous media. Large-scale thermal convection in a horizontal layer is governed by remarkably similar equations both in the presence of a porous matrix and without it, with only one additional term for the latter case, which, however, vanishes under certain conditions (e.g., two-dimensional flows or infinite Prandtl number). We provide a rigorous derivation of long-wavelength equations for a porous layer with inhomogeneous heating and possible pumping.

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Denis S. Goldobin, Elizaveta V. Shklyaeva. 2008-08-20. Large-Scale Thermal Convection in a Horizontal Porous Layer. https://doi.org/10.1103/physreve.78.027301

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