Large-Scale Thermal Convection in a Horizontal Porous Layer

TL;DR

This paper investigates large-scale thermal convection in horizontal porous layers, deriving long-wavelength equations and highlighting similarities with fluid convection, with implications for understanding instabilities in various physical systems.

Contribution

It provides a rigorous derivation of long-wavelength equations for porous layers with inhomogeneous heating, extending understanding of large-scale convection phenomena.

Findings

Large-scale convection is governed by similar equations in porous and non-porous layers.

Additional terms in equations vanish under certain conditions like 2D flows or high Prandtl number.

Derived equations apply to inhomogeneous heating and pumping scenarios.

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.