Coupled ice-till dynamics and the seeding of drumlins and bedrock forms

The geomorphological effects of ice sliding over till, internal deformation of till and till sliding over bedrock are considered. Two questions are examined: (I) is the till-sheet flow unstable, i.e. is a layer of uniform thickness maintained or not, and (2) does the slip of till over bedrock cause amplification of relief of the bedrock? Such instabilities seem to be necessary to explain such features as drumlins and whaleback forms. It is found that the answer to (1) and (2) depends on the position of the system in a parameter space, defined by the till rheology, and applied shear stress, the effective pressure at the ice-till interface, the thickness of ice and till and the wavelength of the instability. Two configurations are considered: one where the wavelength of the perturbation is much less than the the ice-thickness, which is related to the classical Nye-Kamb solution for flow over bumps; and one where the wavelength is much greater than the ice thickness, where the mechanics are described by the shallow-ice approximation. In both cases, substantial areas of parameter space, where till-sheet and bedrock modes are unstable, are found. The conceptually related Smalley-Unwin bifurcation is re-examined. The physical mechanisms by which ice and till flows couple are examined. At very short wavelengths (similar to 10 m), the ice is so rigid that it forces till waves to move at the ice velocity; while at long wavelengths (similar to 1000 m), the flows become essentially uncoupled and till waves move at the kinematic velocity At intermediate wavelengths (similar to 100 m), high growth rates occur; this is postulated to be the scale of drumlin seeding.