Propagation speeds of ocean surface waves in shallow water

Abstract

Nonlinear effects on the dispersion relation of waves in shallow water are examined with measurements collected on a mild sloping sandy beach during the recent Sandy Duck experiment. Four arrays of bottom pressure sensors were deployed in depths ranging from 3 - 6 m during August-November, 1997. For each of these arrays, a root-mean-square average wavenumber was estimated as a function of frequency from the cross-spectra of one-hour-long pressure records. The observed wavenumbers are compared to linear finite depth theory predictions and to predictions based on a stochastic formulation of weakly nonlinear Boussinesq equations that incorporate both frequency and amplitude dispersion effects. The observed wavenumbers are generally in agreement with the nonlinear theory predictions and deviate significantly (maximum errors averaged over the spectrum of about 25%) from the linear theory predictions. In high energy conditions with breaking or nearly breaking waves, the effects of amplitude and frequency dispersion tend to cancel, and all components of the wave spectrum travel with approximately the shallow water wave speed. These results are consistent with previous studies.