Front outstripping of coupled gravity currents, and the route to ice-sheet surges.

Subglacial lubrication networks are believed to play a key role in the flow and stability of ice sheets, having the capacity to drive ice-sheet surges and to form ice streams. Fluid mechanically, a lubricated ice sheet can be modelled as a viscous gravity current of strain-rate softening fluid lubricated by a rela- tively inviscid and denser Newtonian fluid. Such a coupled system can remain axisymmetric, as has been shown in experiments in which the two fluids were discharged in constant flux. In such a situation the front of the lubricating fluid could intercept and outstrip the ice-fluid front, thereby lubricate the entire base of the ice fluid and potentially trigger a surge. We explore theoretically the conditions that can lead to such a front outstripping. Specifically we consider a general power-law fluid lubricated by a Newtonian fluid, where both fluids are discharged at the origin and their volumes grow in time like a power law. We identify two potential mechanisms by which front outstripping could occur. The first is when the viscosity ratio of the two fluids grows beyond a critical value, and the second, when the exponents of the non-Newtonian fluid and of the volume discharge satisfy a certain relation.