Three-Dimensional and Local Flow Effects in Glaciers and Ice Sheets

The investigations of ice-flow problems which have been undertaken in this book so far, have been rather qualitative and thus theoretical because only plane flow was considered and, furthermore, very simple glacier geometries were assumed. Either conditions near the strictly parallel-sided ice slab were analysed or the top and bottom surfaces were assumed to vary slowly in the horizontal directions. Three important problems, however, remained untouched; they are: (i)Valley glaciers are bounded by mountain sides. These flanks affect the flow and their influence is all the greater, the narrower the valley. Hence, ice flow in a channel of a finite cross-section should be analysed. As a first approximation, flow in a cylindrical channel provides sufficient indications as to the order of magnitude of the boundedness effect of the valley.(ii)The analyses of ice sheets were performed in Chapters 5 and 6 for plane motion, and it was shown that real ice sheets spread in both horizontal directions. In order to be able to predict real ice-sheet geometries, the solution procedures of Chapters 5 and 6 should, therefore, be generalized to include both horizontal dimensions.(iii)Most ice-flow problems in glaciers that are relevant in engineering, are of a local nature and so the simplifications of a nearly-parallelsided ice slab or the shallow-ice approximation do not apply. Under these circumstances, the full two- or three-dimensional boundary-value problem must be solved, but the complexity of these problems is generally so immense that no analytic solutions can be found. Numerical techniques, of which finite differences and finite elements are two alternatives, must then be resorted to. The latter profits from the existence of variational principles.