Stability of quasi-steady flow in an englacial conduit

✍ Scribed by Krzysztof Szilder; Edward P. Lozowski

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 151 KB
• Volume: 11
• Category: Article
• ISSN: 0885-6087
• DOI: 10.1002/(sici)1099-1085(19971030)11:13<1737::aid-hyp602>3.0.co;2-f

✦ Synopsis

The stability of water ¯ow in an englacial conduit is examined with particular reference to catastrophic outbursts of water. Quasi-steady ¯ow of water in a conduit is considered, the conduit being simultaneously enlarged by frictional heating and compressed by plastic deformation in response to the pressure dierence 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 time-dependent, non-linear, dimensionless ordinary dierential equations, which describe the time evolution of the conduit cross-section and the water depth in the reservoir. The conditions leading to dierent types of time-dependent ¯ow behaviour are examined. Regions of the parameter space where the water ¯ow is stable and unstable have been identi®ed. In the unstable regime, the process of emptying the reservoir has either an oscillatory or an exponential character. In the stable regime, the system's return to equilibrium, following a perturbation, also exhibits an oscillatory or exponential character. Examples of this time-dependent behaviour are presented. The model has also been used to study the in¯uence of the glacier, conduit and reservoir geometries on the system's stability. The results show that an increase in the horizontal area of the water reservoir or an increase in the slope of the conduit enhance the likelihood of a sudden outburst. However, an increase in the glacier thickness or the conduit length stabilizes the equilibria.