Groups of waves in shallow water

Abstract

Wave group statistics predicted by linear theories are compared to numerical simulations, thus determining ranges of spectral shapes for which the theories are valid. It is found that these theories are not generally valid for ocean data because of many assumptions and simplifications beyond linearity and random phase or because their range of applicability does not include the vast majority of ocean conditions. The simulations also provide quantitative information about the variability of linear wave group statistics which is useful when examining ocean field data. The simulation technique is used to show that important ocean gravity wave group statistics are not inconsistent with an underlying wave field composed of linearly superposed random waves. The majority of the field data examined were collected in 10 m depth; significant wave heights varied from about 20 to 200 cm, and the spectral shapes ranged from fairly narrow to broad (1 < Q•, < 6). For the 10-m depth data, the observed mean run length, variance of run length, and probabilities of runs of a given number of waves were statistically consistent with the simulations. In contrast to the apparently linear groups observed in 10 m depth, waves in 2-3 m depth showed marked departures from the linear simulations.

Testing and calibrating parametric wave transformation models on natural beaches

“…Although the models are based on the assumption that the waves are narrow banded in frequency, model errors are uncorrelated with spectral width, possibly because several other sources of error exist, and possibly because wave heights have a Rayleigh p.d.f. even for relatively broad spectra [Elgar et al, 1984]. Model errors also are not correlated with the (usually small) difference between the centroidal and peak frequencies.…”

A discrete correction scheme for envelope approach of wave group statistics

“…(6)) is used in numerical simulation. Although the sea waves are generally nonlinear, Elgar et al (1984) demonstrated that the statistical characteristics of wave groupiness derived (based on discrete counting) from linear simulations of ocean waves agree well with field data except for the very shallow water case. In this paper, we consider only the deepwater case.…”

“…Although these correction schemes achieved some success, Elgar et al (1984) and Masson and Chandler (1993) found that (1) these authors had employed incorrect function of P(H)for narrow spectra, hence yield incorrect results for narrow spectra waves and (2) for H ! l, H and j should be identical (H !…”

Change of the nature of a test when surrogate data are applied

“…Surrogate data are generated by replacing the phases 1 , 2 ,... by random values 1 * , 2 * ,... in (2) and (3). Here 1 * , ... , m * are independent and identically distributed U͓0,2͔ and independent of N/2 * (when N is even), which is 0 or with a probability of 0.5.…”

“…The term "surrogate data" was first introduced by [1], but the basic idea appeared in a number of earlier publications (see [2][3][4]). The method in [3] is called multivariate scaling analysis.…”