Glacial lake drainage: a stability analysis

Abstract

A model has been formulated to determine the stability regimes for water flow in a Subglacial conduit draining from a reservoir. The physics of the water flow is described with a set of differential equations expressing conservation of mass, momentum and energy. Non-steady flow of water in the conduit is considered, the conduit being simultaneously enlarged by frictional heating and compressed by plastic deformation in response to the pressure difference across the tunnel wall. With the aid of simplifying assumptions, a mathematical model has been constructed from two time-dependent, non-linear, ordinary differential equations, which describe the time evolution of the conduit cross-sectional area and the water depth in the reservoir. The model has been used to study the influence of conduit area and reservoir levels on the stability of the water flow for various glacier and ice-sheet configurations. The region of the parameter space where the system can achieve equilibrium has been identified. However, in the majority of cases the equilibrium is unstable, and an initial perturbation from equilibrium may lead to a catastrophic outburst of water which empties the reservoir.