= Melting-front instability due to permeability contrast
A planar <advection-driven melting front in a porous matrix> with permeabilities $k$ ahead and $k+\Delta k$ behind has the ideal sharp-front <growth rate>
$$
\sigma=|\alpha|V\frac{\Delta k}{2k+\Delta k}.
$$
This follows by matching <harmonic> pressure perturbations and normal <Darcy flux>, then converting flux to front speed by the <enthalpy> balance. It predicts no finite fastest-growing wavelength when $\Delta k>0$.
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