Porous gravity current
= Porous gravity current
A porous gravity current spreads because a density difference creates a lateral hydrostatic-pressure gradient. For a two-dimensional current of thickness $h$, density deficit $\Delta\rho$, permeability $k$, viscosity $\mu$, and porosity $\phi$,
$$
\phi h_t=\frac{k\Delta\rho g}{\mu}(h h_x)_x.
$$