A network model for fluid transport through sea ice

Abstract

AbstractThe flow of liquid through porous sea ice is a fundamental process affecting problems in polar biology, oceanography and geophysics. The geometry and connectedness of the pore microstructure of sea ice determine its fluid permeability, which depends strongly on temperature. Here we analyze a simple pipe network as a basis for modeling fluid flow through the complex porous microstructure, and for numerical approximations of the fluid permeability of sea ice as a function of temperature. For slow flow the fluid system is equivalent to an electrical resistor network, and the network is solved using a fast multi-grid method. The radii of the pipes in the network are chosen randomly from distributions describing measured cross-sectional areas of brine inclusions in sea ice. At this stage, the model reflects only the most general features of brine microstructure and its evolution with temperature. Preliminary results for a basic implementation in two dimensions are presented. They are consistent with theoretical bounds on the vertical fluid permeability of sea ice found recently. Moreover, the results agree roughly with laboratory data for higher porosities. For lower porosities and colder temperatures, the fully connected network of pipes in the model, albeit with smaller radii, overestimates observed values. This finding provides evidence that the brine network becomes more disconnected with lower temperatures, which is consistent with transitional behavior near a percolation threshold.