Resistance in steep open channels due to randomly distributed macroroughness elements at large froude numbers

Energy loss in a steep open channel due to randomly spaced spherically shaped macroroughness elements such as boulders was investigated using a three-dimensional fluid dynamics solver. First, a relationship for energy loss at large Froude numbers due to a single boulder was derived as a function of flow rate, flow depth, and boulder diameter. Nondimensional energy loss increases with Froude number and decreases with the relative submergence. However, the exponents in the power law relationship are different for three different ranges of submergence ratio: < 0.5, 0.5-1.0, and > 1.0. The energy loss attributable to a cluster of boulders depends on cluster density, Froude number, and submergence ratio. For the same number of boulders, energy loss decreases as cluster density increases. However, variation in the pattern of boulder arrangement has only a marginal effect (< 4%) when the submergence ratio is more than 0.5. The simple procedure proposed for estimating energy loss due to a cluster of randomly distributed boulders of equal size predicts energy loss within 10% accuracy.