Hamilton-type principles applied to ice-sheet dynamics: new approximations for large-scale ice-sheet flow

摘要: Ice-sheet modelers tend to be more familiar with the Newtonian, vectorial formulation of continuum mechanics, in which motion an ice sheet or glacier is determined by balance stresses acting on at any instant time. However, there also equivalent and alternative mechanics where equations are instead found invoking a variational principle, often called Hamilton's principle. In this study, we show that slightly modified version principle can used derive ice-sheet motion. Moreover, provides pathway analytic numeric approximations made directly using Rayleigh-Ritz method. To end, use method describing large-scale flow sheets stitches shallow-ice shallow-shelf together. Numerical examples approximation yields realistic steady-state configurations for variety basal tractions sliding laws. Small parameter expansions reduces appropriate asymptotic limits shallow stream large small values traction number.