UBC Theses and Dissertations
Pattern-forming instabilities in the coupling of ice sheets and subglacial drainage systems Whiteford, Arran
Sharp spatial changes discovered in the basal conditions of an ice sheet do not always have an obvious source. By modelling instabilities in the coupling of an ice sheet and subglacial drainage system, we describe physical feedback mechanisms that force the formation of sharp spatial structures in basal conditions and ice flow. This model predicts the spontaneous formation of periodic subglacial `sticky spot'-lake pairs, that correspond in shape to previous empirical and modelled descriptions of similar structures. The instability that forms this structure is driven by a feedback whereby periodic humps in ice thickness redirect subglacial water to slippery spots that lie immediately downstream of the ice humps: the slippery regions increase ice flux into the ice humps, making them grow. Scaling a one-dimensional model ice sheet coupled to a basal drainage system, we find conditions for the instability with linear stability analysis. Solutions in the full nonlinear model are simulated numerically, using operator splitting and finite difference methods. The instability requires a bed permeability weakly dependent on water pressure changes, negligible bed slopes, and a water velocity much greater than ice velocity. The `sticky spot'-lake pairs are predicted to form with periodic spacing and migrate upstream.
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