[1] We combine the dynamics of ice, bed, and ocean in a new elastic model for the tidal-timescale migration of grounding lines on deformable foundations. Previous interpretations of tidal flexure using models of elastic ice shelves with fixed grounding lines were found to be inconsistent, suggesting an elasticity of ice that varies spatially and temporally and that is significantly smaller than measured experimentally. We argue here that with our model, a consistent, purely elastic interpretation can be made. Combining this new approach with remote-sensing measurements, we show that the grounding line migrates several kilometers during a tidal cycle, that we can infer the effective elastic properties of the bed, and that the elastic pressure of the ice leads to a hydrological barrier near the grounding line that controls subglacial hydrology. Our findings imply that subglacial lubrication and melting induced by the ocean thermal forcing can increase substantially during high tide.Citation: Sayag, R., and M. Grae Worster (2013), Elastic dynamics and tidal migration of grounding lines modify subglacial lubrication and melting, Geophys. Res. Lett., 40,[5877][5878][5879][5880][5881]

We analyse axisymmetric gravity currents of power-law fluids theoretically and experimentally. We use aqueous suspensions of Xanthan gum in laboratory experiments of constant-volume and constant-flux release to resolve the rheological parameters of the fluid, which we then compare with measurements made using a strain-controlled rheometer. We find that the constant-volume release of highly shear-thinning fluids involves an early-time evolution dominated by inertia, and non-convex free surfaces that make the application of similarity solutions of the late-time viscously dominated evolution inefficient at resolving material properties. In contrast, constant-flux release of the same fluids can be viscously dominated and consistent with the self-similar solution from early in the evolution, which makes it a more useful method for measuring rheological parameters.

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We show that a triple-valued sliding law can be heuristically motivated by the transverse spatial structure of an ice-stream velocity field using a simple one-dimensional model. We then demonstrate that such a sliding law can lead to some interesting stream-like patterns and time-oscillatory solutions. We find a generation of rapid stream-like solutions within a slow ice-sheet flow, separated by narrow internal boundary layers (shear margins), and analyse numerical simulations in two horizontal dimensions over a homogeneous bed and including longitudinal shear stresses. Different qualitative behaviours are obtained by changing a single physical parameter, a mass source magnitude, leading to changes from a slow creeping flow to a relaxation oscillation of the stream pattern, and to steady ice-stream-like solution. We show that the adjustment of the ice-flow shear margins to changes in the driving stress in the one-dimensional approximation is governed by a form of the Ginzburg–Landau equation and use stability analysis to understand this adjustment. In the model analysed here, the width scale of the stream is not set spontaneously by the ice flow dynamics, but rather, it is related to the mass source intensity and spatial distribution.