Some Improvements On The Statistical Theory Of Sea Waves

The statistical distributions of wave parameters, such as amplitudes, periods and wavelengths of sea waves have long been interesting due to their great importance to marine science. Based on the envelope theory of Gaussian noise applied to the linear theory of sea waves, great progress has been made in wave statistics, such as some well known representative work developed by Longuet-Hinggins (1975, 1983) and Sun (1987, 1988). Recently, Stansell et al. (2004) and Zheng et al. (2004) pointed out that the probability distributions of local wave parameters are different from that of individual waves, and accordingly, a modification to wave statistics is proposed. The modified distributions have overcome some inherent drawbacks of the old ones. Following the idea of this modification, an improved joint probability distribution function (PDF) of the wave heights and wavelengths has been proposed in this thesis. The improved PDF is somewhat a more accurate approximation to the joint PDF of individual wave heights and wavelengths from the physical point of view. The mean wavelength calculated from the improved joint PDF is the mean zero up-crossing wavelength, also, an interpretation is given that the mean wavelengths calculation method which suggested by Sun (1988) is reasonable.The mean wavelength of sea waves is an important environmental parameter in marine science, such as in ocean engineering and in oceanic remote sensing. Taking account of the difference between the joint PDFs of local wave parameters and the individual ones, an improved method for estimating the mean periods and mean wavelengths of individual waves from the surface elevation records has been proposed, which was based on the modified wave statistics. Lab experiments were conducted in a wind-wave flume, and a new experimental relationship between the mean wavelength and mean period is obtained by the application of the improved data analysis method. The new relationship gives an explanation for that the coefficient in the relationship proposed by Xu et al. (1999) is larger than it should be. The new relationship deviates from that of Xu et al. (1999) while it is very close to the one proposed by Kinsman (1965), although the last one is theoretically deficient.Wave steepness is an important characteristic of severity of sea state in ocean engineering. A PDF of wave steepness has been derived under the linear theory frame of the local wave statistics proposed by Sun Fu. In this thesis, a new PDF of steepness is obtained for narrowband Gaussian processes based on the wave statistics amended by Stansell et al. (2004) and Zheng et al. (2004). The mathematical expression of the new PDF is simpler than the one derived by Zheng et al. (1999), and it is more close to the PDF of individual wave steepness in physical meaning. A drawback inherent in the previous theoretical PDFs of steepness disappeared in the new one. Unlike the PDF proposed by Zheng et al. (1999), this new PDF no longer predicts nonzero probability density at zero steepness. Lab experiments were conducted in a wind-wave flume to measure the wave steepness distribution. Comparisons among lab measurements and theoretical PDFs of steepness are made, which show that the new PDF generally agrees well with the measurements and it fits with measurements better than its counterpart proposed by Zheng et al. (1999), especially at the subrange of small wave steepness. The new PDF represents well the distribution of wind wave steepness at low to moderate wind speeds. However it deviates to the small steepness side at large wind speeds.