The sliding velocity over a sinusoidal bed at high water pressure

Abstract

AbstractUnder idealized conditions, when pressurized water has access to all low-pressure areas at the glacier bed, a sliding instability exists at a critical pressure, pc, well below the overburden pressure, p0. The critical pressure is given by , where l is the wave length and a is the amplitude of a sinusoidal bedrock, and T is the basal shear stress. When the subglacial water pressure, pw, approaches this critical value, the area of ice-bed contact, △l, becomes very small and the pressure on the contact area becomes very large. This pressure is calculated from a force balance and the corresponding rate of compression is obtained using Glen’s flow law for ice. On the assumption that compression in the vicinity of the contact area occurs over a distance of the order of the size of this area, Δl, a deformational velocity is estimated. The resultant sliding velocity shows the expected instability at the critical water pressure. The dependency on other parameters, such as wavelength l and roughness a/l, was found to be the same as for sliding without bed separation.