Shoaling gravity waves: comparisons between field observations, linear theory, and a nonlinear model

Abstract

Observed statistics of non-breaking ocean-surface gravity waves shoaling between 4 and 1 m depths are compared with the predictions of linear finite-depth theory and a nonlinear model. The linear theory included effects of the directional distribution of energy within each frequency component. The nonlinear model, which does not consider directional effects, is based on Boussinesq-type equations for a sloping bottom (Freilich & Guza 1984). Given initial conditions in 4 m depth, the nonlinear model more accurately predicts the evolution of energy spectra, coherence and phase speed between sensors, and lengths of runs of high waves than does the linear theory. In four out of five cases, observed trends in the evolution of sea-surface-elevation skewness are predicted by the nonlinear model, while linear theory predicts zero skewness. Neither model can explain changes in the directional spectra observed between 9 and 4 m depths.