STABILITY OF QUASI-STEADY FLOW IN AN ENGLACIAL CONDUIT

The stability of water flow in an englacial conduit is examined with p articular reference to catastrophic outbursts of water. Quasi-steady f low of water in a conduit is considered, the conduit being simultaneou sly enlarged by frictional heating and compressed by plastic deformati on in response to the pressure difference across the tunnel wall. The conduit is fed by an ice-dammed reservoir. With the aid of simplifying assumptions, we have devised a mathematical model consisting of two t ime-dependent, non-linear, dimensionless ordinary differential equatio ns, which describe the time evolution of the conduit cross-section and the water depth in the reservoir. The conditions leading to different types of time-dependent flow behaviour are examined. Regions of the p arameter space where the water flow is stable and unstable have been i dentified. In the unstable regime, the process of emptying the reservo ir has either an oscillatory or an exponential character. In the stabl e regime, the system's return to equilibrium, following a perturbation , also exhibits an oscillatory or exponential character. Examples of t his time-dependent behaviour are presented. The model has also been us ed to study the influence of the glacier, conduit and reservoir geomet ries on the system's stability. The results show that an increase in t he horizontal area of the water reservoir or an increase in the slope of the conduit enhance the likelihood of a sudden outburst. However, a n increase in the glacier thickness or the conduit length stabilizes t he equilibria. (C) 1997 John Wiley & Sons, Ltd.