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 rateThis 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 $\Delta k>0$.