Transformation of wave height distribution

Abstract

The transformation of random wave heights during shoaling, including waves breaking in the surf zone, was measured with an extensive array of instruments in the field. The initially Rayleigh height distributions in 10‐m depth were observed to be modified by shoaling and breaking into new distributions which are again nearly Rayleigh but with some energy loss. Using locally measuredH_rms, the Rayleigh distribution describes the measured central moments ofH_1/3andH_1/10with average errors of −0.2% and −1.8%, respectively. The Rayleigh distribution is used to describe the random nature of wave heights in a single‐parameter transformation model based on energy flux balance. The energy losses associated with wave breaking are parameterized using observed breaking wave distributions coupled with a periodic bore dissipation model. Using incident waves measured in 10‐m depth as input conditions, the model predictsH_rmsat shoreward locations within a rms error of ±9%. The single free parameter of the model, a constantBrepresenting the fraction of foam on the face of a wave, was chosen to best fit the data. The resulting large value ofBimplies that the simple periodic bore dissipation function substantially underestimates the actual dissipation.