Bispectra Of Shoaling Ocean Surface Gravity Waves

Aspects of the nonlinear dynamics of waves shoaling between 9 and 1 m water depths are elucidated via the bispectrum. Bispectral signal levels are generally high, indicating significant nonl i near coupling. In 9 m depth, the biphases of interactions involving frequencies at, and higher than, the peak of the energy spectra are sU~9estive of `jtoke~-like nonlinear ities. Further shoaling gradually modifies these biphases to values consistent with a wave profile that is pitched shoreward, relative to a vertical axis. Bicoherence and biphase observations of waves with a double peaked (swel 1 and wind wave) power spectrum provide evidence for excitation of modes at intermediate frequencies via difference interactions, well aS the sum interactions respon~jble for ~~rmoni c growth. Shoreward propagating low frequency (Sur~ beat) energy is shown to have statistically slgnlflcant coupling to higher frequency modes within the power spectral peak. In lB m depth, the biphase of these interactions is close to 180o, a value consistent with the classical concept of bound long waves. In shallower water, however, biphase evolution occurs, substantial and there is no longer a unique phase relationship between surf beat and the envelope" of high frequency waves. The observed bispectral evolution is predicted accurately by a model based on the nonl i near Boussinesq equations.