= Thermal-diffusion scaling of a convection layer
{title2=$t_\kappa=d^2/\kappa,\ u_\kappa=\kappa/d$}
Using layer depth $d$ and <thermal diffusivity> $\kappa$ gives time scale $d^2/\kappa$, <velocity> scale $\kappa/d$, and perturbation <pressure> scale $\rho_0\kappa^2/d^2$. With temperature scale $\Delta T$, the <Linearized Boussinesq equations> have viscous coefficient <Prandtl number> $\mathrm{Pr}=\nu/\kappa$ and buoyancy coefficient $\mathrm{Ra}\,\mathrm{Pr}$, where <Rayleigh number> $\mathrm{Ra}=g\alpha_T\Delta T d^3/(\nu\kappa)$.
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