Geophysical Fluid Dynamics: Modelling Non-Linearly Viscous Ice-Flow to Obtain Dates of Flow Change
Ice flows because at low stresses it deforms viscously; the viscosity depends upon the stress. The lubrication approximation (LA) states shear stress is proportional to the product of the ice depth and surface slope. At ice divides the slope and shear stress are zero meaning the viscosity could become very high, obstructing deformation. Other stresses come into play, preventing the viscosity becoming very large. This is known as the “Raymond Effect” (RE).
The RE creates an observable feature at divides, seen by the radar surveys; a stack of buried anticlines (“Raymond Arches”, RA). These have width approximately equal to the ice thickness, and when fully grown have amplitude of between a quarter and a third of the ice thickness. Formation times depend upon the rate of snow accumulation and the thickness of the ice, and range between a few millennia (ice rises) to several tens of millennia (Greenland and East Antarctica). Predictions of steady and developing arch amplitudes can be made by numerical solution of the Stokes equations, which allows dating of the repositioning of the ice divide and informs about how the ice-sheet has evolved.
Scientists (Aðalgeirsdóttir, Conway, Gillet, Kingslake, Hindmarsh, Mulvaney, Pritchard) have surveyed ice-rises in Antarctica and found RA at all but one. Two survey-types were performed; (i) translating mode (TM), where a radar is hauled, detecting isochrone geometry and bed depth along sections; and (ii) fixed mode (FM), where very accurate measurements of isochrone are made and repeated at intervals of one or more years, to measure ice vertical motion. Combination of results from the two modes of radar operation enable RE dating to be undertaken.
RE dating needs understanding of flow near the divide. I used COMSOL Multiphysics®, the CFD Module, and the Mixer Module to simulate plane ice flow around the divides utilizing the observed geometry. At distances from the divide of greater than a few ice thicknesses, the LA holds well, so boundary conditions are set appropriately; at the base the ice is frozen (zero velocity) while the upper surface is traction-free; all these boundary conditions can be represented in the CFD Module, as can stress-dependent viscosity.
A useful hypothesis is that the ice surface geometry is unchanged since the divide relocation. The Mixer Module is used to evolve the surface to steady state with a prescription of snowfall and ice rheology (from laboratory measurements). The steady ice surface provides a surface geometry close to that seen in the field, and the resulting calculated velocity fields are used to match FM observations and used in tracer calculations that compute isochrone geometry for comparison with the TM results. RA formation is predicted by the numeric solutions. RA amplitude depends on the divide relocation date, so we can estimate the date when the divide moved to its current location and make inferences regarding the history of ice-sheet area and thickness at several locations all around Antarctica.
