High-Rayleigh-number convection in porous-fluid layers

TL;DR

This study numerically investigates high-Rayleigh-number convection in a layered porous-fluid system, revealing heat flux behaviors, confirming the non-contribution of subcritical penetrative convection, and analyzing temporal coupling effects between layers.

Contribution

It introduces a single-domain numerical approach for high-Rayleigh-number convection in porous-fluid layers and clarifies the role of penetrative convection and layer coupling.

Findings

Heat flux can be predicted from individual layer convection results.

Subcritical penetrative convection does not enhance heat flux.

Fluid layer acts as a low-pass filter on porous layer variability.

Abstract

We present a numerical study of convection in a horizontal layer comprising a fluid-saturated porous bed overlain by an unconfined fluid layer. Convection is driven by a vertical, destabilising temperature difference applied across the whole system, as in the canonical Rayleigh-B\'enard problem. Numerical simulations are carried out using a single-domain formulation of the two-layer problem based on the Darcy-Brinkman equations. We explore the dynamics and heat flux through the system in the limit of large Rayleigh number, but small Darcy number, such that the flow exhibits vigorous convection in both the porous and the unconfined fluid regions, while the porous flow still remains strongly confined and governed by Darcy's law. We demonstrate that the heat flux and average thermal structure of the system can be predicted using previous results of convection in individual fluid or porous layers. We revisit a controversy about the role of subcritical "penetrative convection" in the porous medium, and confirm that such induced flow does not contribute to the heat flux through the system. Lastly, we briefly study the temporal coupling between the two layers and find that the turbulent fluid convection above acts as a low-pass filter on the longer-timescale variability of convection in the porous layer.