Wind-Wave Nonlinearity Observed at the Sea Floor. Part I: Forced-Wave Energy

This is Part 1 of a study of nonlinear effects on natural wind waves. Array measurements of pressure at the sea floor and middepth, collected 30 km offshore in 13-m depth, are compared to an existing theory for weakly nonlinear surface gravity waves. In this depth, free surface waves (obeying the linear dispersion relation) an weakly attenuated at the sea bed at sea and swell frequencies (0.05–0.3 Hz) but very strongly attenuated at frequencies higher than about 0.35 Hz. Only nonlinearly driven motions can reach the sea floor at these high frequencies. Nonlinear interactions between free (primary) waves of about the same frequency, travelling in nearly opposing directions, theoretically excite long-wavelength, double-frequency forced (secondary) waves that are only weakly attenuated at the sea door and form a mechanism for the generation of microseisms at great depth. In 13-m depth, wind-generated free waves and corresponding long-wavelength, high-frequency forced waves can be simultaneously observed on the sea floor, and the coupling, between the two examined in some detail. Bottom-pressure spectra observed over a 4-day period show large O(102) fluctuations in high-frequency (0.35–0.6 Hz) forced-wave energy levels at the sea floor occurring in only a few hours. Correspondingly rapid changes in estimates of the free-wave frequency-directional spectrum show that forced-wave energy levels are weak in unidirectional seas and increase dramatically in response to nearly opposing seas, consistent with the theoretical generation mechanism. On one occasion, directionally opposing seas, and a corresponding double-frequency forced-wave peak, followed a rapidly veering wind. However, comparable increases in forced-wave energy levels were observed in response to the arrival of nonlocally generated seas with directions much different than local winds and seas. Although the accuracy of theoretical forced-wave predictions is limited by the directional resolution of the small aperture (20 m × 20 m) middepth array, predicted and observed forced-wave energy levels agree within about a factor of 2. The observed weak decay between middepth and sea-floor wave pressure at double sea frequencies is also consistent with theoretically expected long wavelengths. Wavelengths, propagation directions, and phase coupling between free and forced waves are examined using the bottom-pressure array data in Part 2.