= Inclined porous gravity current
{title2=$\phi h_t+\partial_x[uh-u\cot\theta\,hh_x]=0$}
For a thin buoyant layer beneath an inclined impermeable roof, the <hydrostatic approximation> and <Darcy's law> give $u=k g\Delta\rho\sin\theta/\mu$ and the <volume flux per unit width> $F=uh-u\cot\theta\,hh_x$. The first term transports fluid upslope; the second spreads the layer through its hydrostatic pressure gradient. The <porosity> multiplies the stored fluid volume, so the advection speed is $u/\phi$, not the <Darcy velocity> $u$.
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