Instability modelling of drumlin formation incorporating lee-side cavity growth

It is proposed that the formation of the subglacial bedforms known as drumlins occurs through an instability associated with the flow of ice over a wet deformable till. We pose a mathematical model that describes this instability, and we solve a simplified version of the model numerically in order to establish the form of finite-amplitude two-dimensional waveforms. A feature of the solutions is that cavities frequently form downstream of the bedforms; we allow the model to cater for this possibility and we provide an efficient numerical method to solve the resulting free boundary problem.