Tidal bending of glaciers: a linear viscoelastic approach

Abstract

In theoretical treatments of tidal bending of floating glaciers, the glacier is usually modelled as an elastic beam with uniform thickness, resting on an elastic foundation. With a few exceptions, values of the elastic (Young's) modulus E of ice derived from tidal deflection records of floating glaciers are in the range 0.9^3 GPa. It has therefore been suggested that the elastic-beam model with a single value of E º 1GPa adequately describes tidal bending of glaciers. In contrast, laboratory experiments with ice give Eˆ9.3 GPa, i.e. 3^10 times higher than the glacier-derived values. This suggests that ice creep may have a significant influence on tidal bending of glaciers. Moreover, detailed tidal-deflection and tilt data from Nioghalvfjerdsfjorden glacier, northeast Greenland, cannot be explained by elastic-beam theory. We present a theory of tidal bending of glaciers based on linear viscoelastic-beam theory. A four-element, linear viscoelastic model for glacier ice with a reasonable choice of model parameters can explain the observed tidal flexure data. Implications of the viscoelastic response of glaciers to tidal forcing are discussed briefly.

Insights into ice stream dynamics through modelling their response to tidal forcing

“…The rheological model is the same as that used by Gudmundsson (2011), and a more detailed description can be found there. Work by Reeh et al (2003) showed that linear elastic models of ice were not adequate over tidal timescales, and they proposed instead the use of a linear viscoelastic Burgers model of ice rheology. Following the arguments made in Gudmundsson (2011) we use a nonlinear Maxwell model (consisting of a viscous damper and elastic spring connected in series) which has a close agreement to more complex Burgers model at the relevant timescales.…”

“…Initial measurements of tidal forcing on ice were limited to the surface of the ice shelves (Williams and Robinson, 1980) and the hinging zone where ice flexure occurs near the grounding line (Smith, 1991;Doake et al, 1987). In these regions, tidal effects can be simply described with analytical solutions and elastic beam theory (Holdsworth, 1969(Holdsworth, , 1977Reeh et al, 2003). Measurements made by Anandakrishnan and Alley (1997) on the Kamb ice stream first showed that these effects were not limited to regions within a few ice thicknesses of the ocean boundary but could be transmitted far upstream.…”

A numerical study of hydrologically driven glacier dynamics and subglacial flooding

“…Values derived from tidal deflection records of ice shelves are as low as 0.9 GPa, whereas laboratory experiments with ice give E = 9.3 GPa (Vaughan 1995;Reeh et al 2003). We select a value of E = 3.9 GPa for our simulations.…”

A Viscoelastic Model of Ice Stream Flow with Application to Stick-Slip Motion

“…Reeh et al, 2003;Walker et al, 2012). Boundary conditions for these perturbed momentum equations may be essential (specified velocities) or natural [specified stress rates, using (3), (4) in the weak forms of (11), (12)]; for our rectangular domains, natural boundary conditions amount to zero longitudinal stress (rate) at transverse boundaries and zero shear stress (rate) at lateral boundaries.…”