Abstract
Internal isochronic layers in ice sheets sensed by radar show two characteristicrelationships to the basal topography: Either they override it, with layers above the crestsof rises lying essentially flat, or they drape over it, with the layers following rises andfalls in basal topography. A mechanical theory is presented which shows that overriding isthe expected behavior when topographic wavelengths are comparable with or less thanthe ice thickness, while draping occurs at longer wavelengths. This is shown withanalytical perturbation solutions for Newtonian fluids, numerical perturbation solutions fornonlinear fluids, and finite element solutions for nonlinear fluids and large-amplitudevariations. Bed variation from topography and changes in the basal boundary condition areconsidered, for fixed bed and sliding beds, as well as three-dimensional flows andthermomechanically coupled flows. In all cases, the dominant effect on draping/overridingis the wavelength of the topography or variation in basal boundary conditions. Resultsof these full mechanical system calculations are compared with those from the shallow iceapproximation and the longitudinal stress approximation. Some calculations are carriedout for zero accumulation, where the age of the ice and therefore isochrone geometry isnot defined. It is shown that there is a close relationship between isochrones andstreamlines, and that they behave similarly when bed wavelength divided by the icethickness is small compared with the ratio of ice velocity and accumulation rate, which is auseful approximation. Numerical comparisons of isochrones and streamlines show them tobe virtually coincident.
Hindmarsh, Richard C A