The shape of drumlins, their distribution in drumlin fields, and the nature of the sub-ice shaping forces

Abstract

This paper examines attempts to define and interpret drumlin shape; in particular the Chorley lemniscate and the Reed—Galvin—Miller ellipsoid. It also considers the Koenderink approach to describing shape, which ignores statistically defined shapes and concentrates on arbitrary smooth lumps of three-dimensional space. The basic shape of a drumlin at first sight appears to offer no clue to the rightness of any of the hypotheses or conjectures about drumlin formation. The shape suggests that a flowing fluid erodes the parts of landscape which have a lower shear strength than the adjacent parts. However, by considering whether the fluid is ice (very viscous) or water (less viscous), it is suggested that it is possible to distinguish between a drumlin formed by deformation and a drumlin formed by basal water erosion, by identifying subtle shape differences produced by different flow regimes. We find little indication, either from drumlin shape or disposition of drumlins in fields, that the basal water erosion mechanism causes the formation of drumlins. Observations of the growth and break-up of bubbles rising through a fluid may serve as an appropriate analogy for describing drumlin growth and eventual break-up. This bubble model is useful in suggesting an accretion model for drumlin growth and predicting that the form of a drumlin before break-up is similar to a spherical cap or parabolic drumlin. The bubble model and observation of flow past obstacles at very low Reynolds numbers suggest that a minimum resistance shape is not always a lemniscate. The variation of the critical stress and strength parameters across a drumlin field (essentially perpendicular to the ice-flow direction) suggests that the distribution could be zonal, that across a drumlin field a change in drumlin density should occur. Considering the drumlins as a whole-field phenomenon the “dimpled” surface of the drumlin swarm may actually reduce drag.