Continuity of Instantaneous Wave Overtopping Discharge with Application to Stream Power Concepts

During nine small-scale laboratory experiments simulating combined wave overtopping and storm surge overflow on a trapezoidal levee, time series measurements of flow thickness and velocity were acquired at a location on the levee crest and at a location on the landward-side slope. Flow thickness and velocity were combined to estimate time series of the instantaneous discharge. Comparisons of the calculated overtopping discharge time series at the two locations revealed that the time series of instantaneous discharge was the same at both locations with the only difference being a short phase lag. Individual peaks of the discharge time series were examined, and an empirical expression was determined for the root-mean-squared discharge peak. The largest discharge peaks were overestimated by the Rayleigh distribution. For locations on the landward-side slope where the friction slope is approximately the same as the levee slope, it is possible to derive a stream power probability density function based on the overtopping discharge cumulative exceedance probability. The stream power probability density function may be a useful tool for assessing erosion potential of overtopped earthen levees.