Modeling Long-term Stability of the Ferrar Glacier, East Antarctica: Implications for Interpreting Cosmogenic Nuclide Inheritance

The Ferrar Glacier extends from the Taylor Dome, through the Royal Society Range, to the Ross Sea. Its pathway is strongly influenced by large-scale topographic features. Ice thins and flows over these features, like water over a dam. Recently acquired evidence demonstrates that the profile of the Ferrar Glacier has been relatively static for the last 4 million years. This long record of stability is in sharp contrast to numerous other features in Antarctica and motivates an exploration of the stability with a numerical model. Large variations in ice thickness along the Ferrar profile make necessary a thermomechanically coupled model which includes higher-order stress terms. Such a model is presented here and then is used to investigate (1) glacial ice flow patterns, (2) stress fields, and (3) sensitivity to climate forcing. In all three cases, the Ferrar Glacier is shown to be generally insensitive to the changes and to have stability consistent with cosmogenic nuclide evidence. The modeling is novel in that the Ferrar Glacier is a member of a class of glaciers which has never before been modeled. Ice flow results indicate that curious flow patterns arise in the glacier, producing very old ice (100,000 years) near the surface up glacier of thinning points. This flow pattern is demonstrated to be of consequence when interpreting the inheritance of cosmogenic nuclides in two ways. First, the velocity field is used to determine the maximum time a cobble found on the glacier surface could have been exposed to cosmic radiation. Second, the flow entrains supraglacial material from the glacier’s surface, shielding it from cosmic rays for a period, and then deposits the material at the surface down glacier. Both flow effects are discussed in relation to cosmogenic nuclide inheritance and are quantified. The sensitivity of the results to past climates and glacier surfaces is also considered

Some Explicit Solutions for a Class of One-Phase Stefan Problems

Salva and Tarzia, [N.N. Salva, D.A. Tarzia, J. Math. Anal. Appl. 379 (2011) 240 - 244], gave explicit solutions of a similarity type for a class of free boundary problem for a semi-infinite material. In this paper, through an elementary approach and less stringent assumption on data, we obtain more general results than those given by their central result, and thereby construct explicit solutions for a wider class of Stefan problems with a type of variable heat flux boundary conditions. Further, explicit solutions of certain forced one-phase Stefan problems are given