Submarine canyons of the Atlantic continental slope are found to have some remarkably analogous morphological properties to river networks, such as inverse power-law relations between channel gradient S and contributing area A (S~A^-q). Such relationships for bedrock-incising rivers have been interpreted using models in which bed erosion rates (E) depend on A and S according to E~A^mS^n, where the A^m term represents the effect of discharge increasing down-stream. For areas of spatially balanced erosion, the model predicts the inverse relation S~A^-m/n. It is argued here that erosion of canyon floors by turbidity currents involves similar processes to river bed erosion so that a similar model could be used to help interpret aspects of canyon morphology and differences between canyon systems. Discharge and flow power, however, do not vary down-stream in submarine canyons in the same way as in fluvial networks because tributaries are not usually active simultaneously. As turbidity currents and other sedimentary flows originate from failure of over-steepened deposits in canyon walls, the frequency of erosive flows experienced by the channel increases with A. This produces a down-stream erosive effect analogous to that of discharge in river networks. The model's applicability is explored here by comparing the ratio of gradients and areas at confluences where erosion rates of the converging branches must be equal (Seidl and Dietrich, 1992). The data show significant scatter due to canyon floor irregularities, but they suggest on average m/n=0.2-0.3 if E~A^mS^n. Gradient-area graphs of canyons heading at the shelf break and of those heading within the slope are identical. Therefore, although the classical sequence stratigraphic model predicts that shelf spillover during glacial lowstands is important for incising continental slopes, there is little evidence that it occurred by direct supply of sediment to canyon heads as this would have modified their gradient-area relationships differently.
Mitchell, N. C., "Form of submarine erosion from confluences in Atlantic USA continental slope canyons," American Journal of Science, 304, 590-611, 2004.