Glacier sliding without cavitation in a linear viscous approximation

Abstract A model (Nye 1969) of ice sliding over a smooth wavy surface is applied to a temperate glacier sliding over its rock bed. The linear viscous approximation enables one to take full account of the continuous spectrum of obstacle sizes and to see the part played by the 'controlling obstacle size' (Weertman 1957). The form of the power density spectrum of the bed is inferred from qualitative observations; it depends essentially on a single parameter that is connected with the roughness of the bed, roughness transverse to the direction of flow being included. The spectrum is used to calculate the drag, the dependence of the drag on scale, and the overburden pressure necessary to suppress cavitation. The thickness of the regelation layer calculated by the theory agrees well with the observations of Kamb & LaChapelle (1964).