An instability mechanism for drumlin formation

Drumlins are subglacial bedforms that are formed by the interaction of ice flow with an erodible basal topography. The mechanism of their formation bears resemblance to similar processes that cause the formation of dunes and anti-dunes in rivers, and sand dunes in deserts. In 1998 Hindmarsh showed that the interaction of a shearing ice flow with a deformable basal till layer could cause an instability which promotes the growth of basal topography, though he was unable to give analytic criteria for the instability. Here we analyse Hindmarsh's model, and by using certain approximations, we are able to give concise analytical parametric criteria for this instability. The resultant instability occurs if the basal shear stress is larger than a critical value which increases with increasing basal effective pressure, and which also depends on the basal till thickness. It is hypothesized that this instability is the basic mechanism involved in the formation of Rogen moraine and drumlins.