The steep-sided valleys and overdeepened basins of alpine landscapes are well-known products of glaciation, yet relatively little is known about how the dynamics of ice flow and glacial erosion give rise to such landforms. By linking a finite-element model for ice flow through a glacier cross-section with an erosion model, I investigate the development of one of the most striking of glacial landforms, the U-shaped valley. In addition to providing a detailed understanding of landform development, such modelling provides a way to test current understanding of the controls on glacial sliding and erosion.

To simulate valley development I first model flow through an initial cross section and calculate the glaciological parameters that govern erosion. I then numerically simulate erosion to produce a modified transverse profile, for which a new flow field and erosion pattern are computed. A number of iterations permits examination of the progressive transformation of cross-section form, which can be compared with field data.

Model predictions of the cross-section flow field are in close accord with data from the Athabasca Glacier, and include marked lateral variations in sliding velocity. With an erosion law dependent on basal velocity, the model predicts the rapid transformation of a V-shaped cross-section to a recognizably glacial form, and the development of a steady-state, quasi-parabolic glacier cross section. Better agreement with empirical data is obtained by including temporal variations in ice discharge, designed to mimic the characteristics of 100,000-year glacial cycles. The high discharge phase dominates form development, and at low discharges cross-section form is essentially inherited from the central part of the form developed during the preceding high discharge phase.

An alternative erosion model based on Hallet's analysis of glacial plucking predicts active erosion for conditions of rapid sliding and low effective pressures. Plucking is the primary process responsible for producing coarse sediments at the glacier bed, and to maintain bed roughness must be at least as effective as abrasion. However, the landform modelling application indicates that the plucking model is unable to predict active erosion across a wide range of glaciological conditions, suggesting that some reassessment of the model is necessary.