The Use of a Rational Model in the Mathematical Analysis of a Polythermal Glacier

A.C. Fowler
1979 Journal of Glaciology  
AbstractWe here describe the process by which a complex model set of equations and boundary conditions may be rationally reduced to a simpler and more manageable set by the. processes of non-dimensionalization and asymptotic approximation. Such a reduced model (derived elsewhere) is then presented for an incompressible, two-dimensional ice flow. It consists of two coupled equations for the stream function and enthalpy variable, together with a complex set of boundary conditions.The important
more » ... ns.The important dimensionless parameters which arise are given, and various limiting values of these are commented on. Nye's (1960) equation for kinematic waves may be reproduced, and a non-linear analysis of this reveals that disturbances reach the glacier snout in finite time, and are uniformly bounded there: in the particular case considered here, one can also show that the temperature field is stable.It is shown that the effect of introducing a (realistic) sliding law which is continuously dependent on the temperature has a major effect on the bedrock temperature profile.Lastly we consider seasonal waves using a kinematic wave equation based on a plausible form of the sliding law when cavitation is present. The main observed features are qualitatively reproduced.
doi:10.1017/s002214300001491x fatcat:cht5xiatznhwffuyv4jfbp2yga