Abstract
A time-averaged probabilistic model is developed to predict irregular wave runup statistics on permeable slopes such as cobble beaches and revetments. The cross-shore variations of the mean and standard deviation of the free surface elevation and horizontal fluid velocities above and inside a porous layer are predicted using the time-averaged continuity, momentum, and energy equations. The mean and standard deviation of the shoreline elevation measured by a runup wire are estimated from the predicted mean and standard deviation of the free surface elevation. The wave runup height above the mean water level, including wave setup, is assumed to be given by the Rayleigh distribution. The wave reflection coefficient is estimated from the wave energy flux remaining at the still water shoreline. This computationally efficient model is shown to be in fair agreement with 57 small-scale tests conducted on 1∕5 and 1∕2 permeable slopes situated inside surf zones on impermeable gentle slopes.
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