Froude Criterion for Ice-Block Stability

Abstract

The conditions under which a floating fragment of ice is either entrained under the upstream edge of a down-stream ice cover or accumulated up-stream are examined by means of dimensional analysis and a simplified analysis of the moments acting on an idealized ice fragment. The significant parameter descriptive of the critical conditions is found to be a Froude number based on block thickness. The influence of the ratio of thickness to flow depth is shown to be due to the effect of the block constricting the flow cross-section, thus amplifying the velocity in accordance with simple continuity. Under-turning instability occurs at a lower critical velocity than required for vertical submergence. Comparison of experimental data with the theoretical results show good agreement and demonstrates the vital dependence on fragment thickness as well as providing a criterion readily applicable to special flow conditions where a Froude number based on flow depth is illogical.