Stress Variations with Ice Flow Over Undulations

The analysis of steady-state flow over bedrock perturbations of Budd(1970[a]) is extended to evaluate the stress variations associated with the flow. In particular the four separate terms of the fundamental one-dimensional (longitudinal) stress equation (Budd,1968) are examined to show explicitly how the longitudinal stress gradient G , the base stress τ , the surface slope stress s , and the integrated second derivative of the shear stress T all vary over-a given wave. The result shows an error of a factor of 2 in some earlier studies relating longitudinal stress variations to the slope. This error resulted from the erroneous assumption that remains constant at its regional value. In fact the basal stress varies over the undulations in a similar way to the longitudinal stress gradient, and this is the same as the surface slope stress for long waves, but for short waves or less) requires the addition of the fourth term T , which then becomes dominant.