= Unconfined aquifer with depth-dependent permeability
With <permeability of a porous medium> $k(z)=k_0(1+\beta z)$, the <Dupuit approximation> gives
$$
q=-u_b\left(h+\frac\beta2h^2\right)h_x,\qquad \phi h_t+q_x=R,\qquad u_b=\frac{k_0\rho g}{\mu}.
$$
Here $\phi$ is <porosity> and $R$ is recharge. The low-height limit has mobility proportional to $h$, whereas large heights have mobility proportional to $h^2$. This changes both the <forced filling similarity for power-law diffusion> and the <separable draining profile for power-law diffusion>.
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