= Depth-dependent inclined porous-current equation
{title2=$\partial_T h^\alpha+\partial_Xh^\beta=\nabla\cdot(h^\beta\nabla h)$}
For <porosity> $Pz^{\alpha-1}$ and <permeability of a porous medium> $Kz^{\beta-1}$ above an inclined impermeable plane, stored liquid volume per area is $Ph^\alpha/\alpha$. The depth-integrated <Darcy flux> is $\rho gKh^\beta(\sin\theta-\cos\theta\,h_x,-\cos\theta\,h_y)/(\beta\mu)$. <Conservation of mass> yields the displayed equation with $X=x\tan\theta$, $Y=y\tan\theta$ and $T=t\alpha\rho gK\sin\theta\tan\theta/(\beta\mu P)$.
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