On the frontal speeds of internal gravity surges on sloping boundaries

An expression for the slope dependence of the frontal velocity of an internal gravity surge in deep water is derived from the momentum equations for two‐dimensional, inviscid, steady flow. The effects of bottom friction are incorporated by assuming a universal shape for the head of the surge. The resulting expression is consistent with the slope dependence indicated by existing experimental results for small slopes (<5°–15°). The absolute velocity is not predicted by the theory, however, because an indeterminate parameter appears in the result. Furthermore, the experimental data indicate variations in the dependence of nose velocity on slope which depend upon the parameters of the flow itself. It is also shown that the entrainment constant may be estimated from experimental data at large slopes.