= Darcy thermal-time Rayleigh number
{c}
{title2=$R=g\alpha\Delta T Kd/(\nu\kappa_T)$}
With permeability $K$, depth $d$, <kinematic viscosity> $\nu$ and the relevant effective <thermal diffusivity> $\kappa_T$, the Darcy <Rayleigh number> compares <buoyancy>-driven Darcy <advection> to thermal diffusion. It differs from the clear-fluid <Rayleigh number> by replacing $d^3$ with $Kd$. Effective heat capacity and porosity factors may be absorbed into the definition of $\kappa_T$ and the thermal-time scale, and must be kept consistent with the chosen <Darcy law> convention.
Back to article page
