Porous gravity current

A porous gravity current spreads because a density difference creates a lateral hydrostatic-pressure gradient. For a two-dimensional current of thickness $h$, density deficit $\Delta \rho$, permeability $k$, viscosity $\mu$, and porosity $\varphi$,

A leaky porous gravity current loses flux through a localized fracture or a distributed permeable boundary. At a point fracture, mass conservation makes the horizontal Darcy flux discontinuous by exactly the leakage rate.