= Porous gravity current with background flow
{title2=$\phi h_t+(Uh-K_bhh_x)_x=0$}
A shallow buoyant <porous gravity current> in a deep aquifer with uniform imposed <Darcy velocity> $U$ obeys $\phi h_t+(Uh-K_bhh_x)_x=0$ away from sources, where $K_b=k\Delta\rho g/\mu$. Here $k$ is <permeability of a porous medium>, $\phi$ is <porosity>, and $\mu$ is <dynamic viscosity>. The pore-fluid drift speed is $u=U/\phi$, and the gravity <diffusion> coefficient multiplying $(hh_x)_x$ is $a=K_b/\phi$. The sharp-interface model neglects capillary trapping and dissolution.
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