Horizontal Infiltration of Water through Porous Snow as a Gravity Current

On the surface of the Greenland ice sheet or around the margins of the Antarctic ice shelf, water infiltrates porous ice. While studies have considered the thermodynamics and fluid mechanics of water vertically percolating through snow under gravity, here we consider the horizontal spreading of water with freezing under gravity. In this study, we construct a one-dimensional depth-integrated model for water horizontally infiltrating porous ice via gravity current as a Darcy flow from a source of constant depth. We first analyze the infiltration process in the absence of phase change and find that the source-driven infiltration behaves self-similarly. We then capture the infiltration process subject to freezing with an analytical relationship between the source porosity and the time over which the pores at the source are frozen shut. Once the source is frozen shut, residual infiltration in the snowpack as a wetting front becomes weaker and a freezing front develops from the source. Under these freezing dynamics, we bound the region of liquid water by using the similarity solution to locate the wetting front and approximate the freezing front evolution. We then discuss methods to validate and apply the model through experiments and field observations.