A flow model for the polar caps of Mars

A mechanical model with circular symmetry is examined to test the hypothesis that the Martian ice caps are composed of flowing water ice, together with some rock debris. In contrast with most or all previous models, no assumption of a steady state is made. Instead the accumulation and ablation is assumed to be insignificant, and it is suggested that after a sufficient time the profile would have settled down to a particular collapsing form calculated by Halfar (1983). Higher modes of flow would have decayed relatively quickly. To calculate the time constant, it is necessary to consider carefully the distribution of temperature with depth. The time constant is sensitive to the grain-size; which is assumed to be 1-10 mm and is a significant unknown, as is also the effect of preferred crystal orientation. Apart from this, the main uncertainty is the value of the upward heat flux. With a heat flux of 30 mW m(-2), the water-ice hypothesis is consistent with an age of about 10(7) years for both the north and the south polar caps, the north cap being the younger by a factor of about 7.