Wave grouping is analysed by the envelope approach, with envelopes being computed from wave records through the Hilbert transform technique. To specify wave groups, the group height factor and length factor are defined in terms of parameters of both wave and envelope spectral parameters. Based on the analysis and definition, a method is developed to simulate irregularly grouped wave signals with both specified wave and envelope spectra as target. A series of simulated examples is presented to demonstrate the feasibility of the method.

A joint probability density function (PDF) for surface slopes in two arbitrary directions is derived on the basis of Longuet-Higgins's linear model for three-dimensional (3-D) random wave field, and the correlation moments of surface slopes, as parameters in the PDF, are expressed in terms of directional spectrum of ocean waves, So long as the directional spectrum model is given, these parameters are determined. Since the directional spectrum models proposed so far are mostly parameterized by the wind speed and fetch, this allows for substituting these parameters with the wind speed and fetch. As an example, the wind speed and fetch are taken to be 14m/s and 200km, and the Hasselmann and Donelan directional spectra are, respectively, used to compute these parameters. Some novel results are obtained. One of the interesting results is thai the variances of surface slope in downwind and cross-wind directions determined by the Donelan directional spectra are close to those measured by Cox and Munk (1954). Some discussions are made on these results.

The analytical model of Snyder and Kennedy [1983] for the whitecap coverage W and that of Srokosz [1985] for the probability of wave breaking B are developed into practically appiicablc forms by closely combining theoretical analysis and data fitting. The database consists of two parts: the data collected Irom published literature and those recently measured in the Bohai Bay, A time-averaging techniquc is used to estimate the fourth spectral moment of the mean Joint North Sea Wave Project spectrum. The resulting expressions are simple, in which W and B depend only on the nondimensional fotch for a fetch-limited sea.

Relationships between the mean wavelength and mean wave-period of wind waves are derived for fetch-limited and fully developed seas. The derivations start from the Rice solution of zero-crossing problem and use the JONSWAP and Pierson-Moscowitz spectra, respectively. The spectral moments of order 4 involved in the derivations are estimated through a time-averaging technique. Experiments were conducted in a wind-wave channel. Comparisons between the relationships and the experimental results show a favorable agreement.

[1] On the basis of a narrow-band Gaussian process, two theoretical probability density functions (PDFs) are derived by applying an approximate Hilbert transform to the process represented by a general form. The first PDF is for the joint distribution of the wave period t and amplitude r of sea waves. It has the same merits as the PDF previously derived by Longuet-Higgins [1983], in being asymmetric in t and depending only on the spectral width parameter n, but gains an advantage that it predicts an exactly Rayleigh distribution of r and so facilitates its handling in theory and application in practice. In virtue of the advantage, a relatively simple conditional PDF of t assuming r is derived, which may be used to predict an arbitrarily defined characteristic conditional wave period assuming the wave height from the average wave period. The second PDF is for the joint distribution of wavelengths and amplitudes in a unidirectional Gaussian wave field with narrow spectrum. It has the same form as the first PDF but depends only on the parameter m defined by μ2=m0m4/m2- 1, where mn is the nth moment of spectrum. From this joint PDF, a PDF for the distribution of wavelengths of sea waves is also derived. Numerical simulation and laboratory experiments of wind waves and their results are reported. It is shown that the PDFs derived in this paper give fairly good fits to the simulated data and suitably filtered laboratory data. INDEX TERMS: 0624 Electromagnetics: Guided waves; 3384 Meteorology and Atmospheric Dynamics: Waves and tides; 4263 Oceanography: General: Ocean prediction