Transformation of wave height distribution

TLDR

The study develops a single‑parameter shoaling model that uses a Rayleigh distribution to describe random wave heights, incorporates energy‑flux balance, and parameterizes breaking losses with observed breaking‑wave statistics and a periodic bore dissipation function, with the free parameter B tuned to fit field data. Field measurements show that shoaling and breaking transform the initial Rayleigh height distribution into a nearly Rayleigh distribution with reduced energy, and the model predicts shoreward H rms within ±9% rms error, while the large fitted B value indicates the periodic bore dissipation function underestimates actual dissipation.

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 measured H rms , the Rayleigh distribution describes the measured central moments of H 1/3 and H 1/10 with 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 predicts H rms at shoreward locations within a rms error of ±9%. The single free parameter of the model, a constant B representing the fraction of foam on the face of a wave, was chosen to best fit the data. The resulting large value of B implies that the simple periodic bore dissipation function substantially underestimates the actual dissipation.