Radar data from both Greenland and Antarctica show folds and other disruptions to the stratigraphy of the deep ice. The mechanisms by which stratigraphy deforms are related to the interplay between ice flow and topography. Here we show that when ice flows across valleys or overdeepenings, viscous overturnings called Moffatt eddies can develop. At the base of a subglacial valley, the shear on the valley walls is transfered through the ice, forcing the ice to overturn. To understand the formation of these eddies, we numerically solve the non-Newtonian Stokes equations with a Glen's law rheology to determine the critical valley angle for the eddies to form. The decrease in ice viscosity with shear enhances shear localization and, therefore, Moffatt eddies form in smaller valley angles (steeper slopes) than in a fluid that does not localize shear, such as a Newtonian fluid. When temperature is incorporated into the ice rheology, the warmer basal ice is less viscous and eddies form in larger valley angles (shallower slopes) than in isothermal ice. We apply our simulations to the Gamburtsev Subglacial Mountains and solve for the ice flow over radar-determined topography. These simulations show Moffatt eddies on the order of 100 meters tall in the deep subglacial valleys.
- Mathematical Geoscience Seminar