Pacific Institute for the Mathematical Sciences - PIMS

Mathematical modeling of ice flow

The drainage of meltwater under glaciers affects the motion of the glacier as a whole. High water pressure weakens ice-bed contacts and allows more rapid slip at the interface. A glacier flow model therefore requires a component that predicts water pressure. Such models have proved difficult to formulate in more than one dimension, because water flow has the ability to channelize into large, discrete conduits. Here I show results from a network model that allows the size of each conduit in the network to evolve as the result inward creep of the ice, erosion of the ice through melt, and opening of ice-glacier bed gaps in the lee side of asperities on the glacier bed. The model predicts a physically expected bifurcation from a distributed system in which flow is spread out over a large number of conduits to one in which it concentrates into a few as water input is increased. I also show that the model produces a number of features that are qualitatively consistent with what field observations suggest about the seasonal evolution of glacier flow speeds during the summer. The model as formulated has numerous drawbacks, notably that it requires all conduits to be resolved, and that it allows both, water pressure that is negative and water pressure that exceeds overburden (the hydrostatic pressure in the ice above). I will describe some recent work with Ian Hewitt (Math, UBC) and Mauro Werder (Earth Sciences, SFU) in which we have incorporated a continuum description of some conduits and inequality constraints that account for bubble cavitation and a simplified description of hydrofracture, which are relevant to water pressure reaching atmospheric pressure or overburden.

12:30pm -- 2:00pm, WMAX 110

Sushi and pop will be provided!