A numerical study of scaling relations for non-Newtonian thin film flows with applications in ice sheet modelling
2013 (English)In: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 66, no 4, 417-435 p.Article in journal (Refereed) Published
This article treats the viscous, non-Newtonian thin-film flow of ice sheets, governed by the Stokes equations, and the modelling of ice sheets with asymptotic expansion of the analytical solutions in terms of the aspect ratio, which is a small parameter measuring the shallowness of an ice sheet. An asymptotic expansion requires scalings of the field variables with the aspect ratio. There are several, conflicting, scalings in the literature used both for deriving simplified models and for analysis. We use numerical solutions of the Stokes equations for varying aspect ratios in order to compute scaling relations. Our numerically obtained results are compared with three known theoretical scaling relations: the classical scalings behind the Shallow Ice Approximation, the scalings originally used to derive the so-called Blatter-Pattyn equations, and a non-uniform scaling which takes into account a high viscosity boundary layer close to the ice surface. We find that the latter of these theories is the most appropriate one since there is indeed a boundary layer close to the ice surface where scaling relations are different than further down in the ice. This boundary layer is thicker than anticipated and there is no distinct border with the inner layer for aspect ratios appropriate for ice sheets. This makes direct application of solutions obtained by matched asymptotic expansion problematic.
Place, publisher, year, edition, pages
2013. Vol. 66, no 4, 417-435 p.
Earth and Related Environmental Sciences Mathematics
IdentifiersURN: urn:nbn:se:su:diva-97872DOI: 10.1093/qjmam/hbt009ISI: 000327457200001OAI: oai:DiVA.org:su-97872DiVA: diva2:680852