Abstract
We explain the force balance in flowing marine ice sheets and the ice shelves they often feed. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases $-$ the presence or absence of contact with sidewalls. The solution without sidewalls is a simple generalisation of that found by Robison (JFM, 648, 363), allowing us to obtain the equilibrium grounding line thickness using a simple computer model and to get an analytic approximation. For laterally confined shelves, we obtain an asymptotic theory valid for long shelves and define when this is. Our theory is based on the velocity profile across the channel being a generalised version of Poiseuille flow, which works when lateral shear dominates the force balance. We conducted experiments using a laboratory model for ice. This was an aqueous suspension of $0.5\%$ mass concentration xanthan, yielding $n \approx 3.8$ (similar to ice). Our theories agreed extremely well with our experiments for all relevant parameters (front position, thickness profile, lateral velocity profile, longitudinal velocity gradient and grounding line thickness). This strongly suggests that we have understood the dominant force balance in both types of ice shelf. In the real world, ice tongues are unlikely to rapidly disintegrate but can be shortened until they no longer exist, at which point the sheet becomes unstable and ultimately the grounding line should retreat above sea level. Prior to that point, the flow of ice into it should not be speeded up and the grounding line should also not retreat, assuming that only oceanic conditions change. However, laterally confined ice shelves experience significant buttressing. If removed, this leads to a rapid speedup of the sheet and a much smaller equilibrium grounding line thickness. Something similar may have occurred to the Larsen B ice shelf.
Highlights
This paper builds on previous work by Robison et al [1] on what are essentially ice tongues i.e. ice shelves with no lateral confinement
We provide some reasons for expecting the initial thickness to be constant
The flux retained by the sheet inevitably goes down to 0, but fairly slowly. This means that, even with a grounding line, the shelf will eventually converge to the similarity solution we found earlier
Summary
This paper builds on previous work by Robison et al [1] on what are essentially ice tongues i.e. ice shelves with no lateral confinement. This is because we assume that a section of shelf of length L is un affected by sidewalls, so it is outside our model (and creates something akin to a shift in position measurements) This region is essentially flat because the force balance was different when this region crossed the source (Figure 9). We see that there is no fundamental difference between an ice sheet and an ice shelf confined by sidewalls Both have gravity balancing viscous drag and they have similar boundary conditions, leading to a similar velocity profile. The flux retained by the sheet inevitably goes down to 0, but fairly slowly This means that, even with a grounding line, the shelf will eventually converge to the similarity solution we found earlier (whether we consider the length of the shelf only, or the position of the front). We never noticed such an effect in any of our experiments, suggesting that it may be irrelevant
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