Large-Scale Thermal Convection in a Horizontal Porous Layer

Details Large-Scale Thermal Convection in a Horizontal Porous Layer Large-Scale Thermal Convection in a Horizontal Porous Layer

2008-04-17

arxiv.org/abs/0804.2825v3

Phys. Rev. E 78(2), 027301 (2008)

Physics

Fluid Dynamics

4 pages, no figures, published as a Brief Report in Physical Review E

Scientific paper

10.1103/PhysRevE.78.027301

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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