Observations of bispectra of shoaling surface gravity waves

Abstract

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 nonlinear coupling. In 9 m depth, the biphases of interactions involving frequencies at, and higher than, the peak of the energy spectra are suggestive of Stokes-like nonlinearities (Hasselman, Munk & MacDonald 1963). 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 with a double-peaked (swell and wind-wave) power spectrum provide evidence for excitation of modes at intermediate frequencies via difference interactions, as well as the sum interactions responsible for harmonic growth. Shoreward-propagating low-frequency (surf-beat) energy is shown to have statistically significant coupling to higher-frequency modes within the power-spectral peak. In 18 m depth, the biphase of these interactions is close to 180°, a value consistent with the classical concept of bound long waves. In shallower water, however, substantial biphase evolution occurs, and there is no longer a unique phase relationship between surf beat and the envelope of high-frequency waves. The contributions to sea-surface-elevation skewness and asymmetry (with respect to a vertical axis) from interactions among various wave triads are given by the real and imaginary parts of the bispectrum, respectively. In very shallow water, coupling between surf beat and higher-frequency waves results in a skewness with sign opposite to, and about 40% of the magnitude of, the skewness resulting from interactions between the power-spectral-peak frequency and higher frequencies.

Observations of swash under highly dissipative conditions

“…Swash, the time-varying position of the shoreward edge of water on a beach, results from standing waves, formed by the reflection of incident waves off the shoreline [e.g., Miche, 1951;Elgar and Guza, 1985;Guza and Thornton, 1985;. There is still considerable debate as to how swash is related to environmental conditions such as local beach slope and offshore wave characteristics, despite the numerous studies that have been devoted to this subject.…”

Introduction of a Simple Cnoidal Wave Formulation Based on Nonlinear Interaction of Wave-Wave Principles

“…The generation and amplification of these harmonics were studied and investigated by several observational and numerical studies (4)(5)(6)(7)(8). Results showed that these harmonics are bound with the spectral peak (8)(9)(10)(11). The second and third peaks of energy spectrum on two and three times of spectral peak frequency are very usual for field measurements (12,13).…”

Wave modelling – The state of the art

“…Elgar and Guza, 1985), and induce radiation of long waves at the 'beat' frequencies of the incident wave field, generally referred to as 'surfbeat' (e.g., Munk, 1949).…”

“…In general triad interactions transfer energy from the incident wave components to higher-(e.g., harmonic) and lower-(e.g., infra-gravity) frequency components (see, e.g., Freilich and Guza, 1984;Elgar and Guza, 1985;Agnon et al, 1993;Kaihatu and Kirby, 1995;Agnon and Sheremet, 1997;Herbers and Burton, 1997;Ruessink, 1998;Kaihatu, 2001;Sheremet et al, 2003;Janssen et al, 2003, and many others). These interactions not only broaden the frequency spectrum in shallow water, but also phase-couple the spectral components, causing the characteristic steepening and pitching forward of nearbreaking wave crests.…”