Nonlinear analysis of waves in finite water depth

This dissertation presents the results of a study on the nonlinear stochastic analysis of random waves in finite water depth, in particular, (1) clarification of nonlinearity in wave spectra and (2) development of a probability density function in closed form applicable to wave profiles.;In order to clarify the nonlinear characteristics associated with wave-wave interactions, which are particularly pronounced for waves in finite water depth, a method is developed to examine those frequencies having nonlinear energy components and their magnitudes. The nonlinear components of the spectral density at a specified frequency are considered to be the accumulation of nonlinear interactions associated with various pairs of two frequency components. Here, interaction includes not only the sum but also the difference of two frequencies. The separation of the nonlinear component of the energy density of a spectrum is achieved by applying the concept of the bicoherence spectrum.;The separation procedure is applied to wave spectra computed from data obtained in the ARSLOE Project during storm. The results demonstrate that nonlinear components are present at low and high frequencies but no nonlinear components exist in the neighborhood of the frequency where the spectrum peaks and that the ratio of nonlinear energy to the total energy increases significantly with a decrease in water depth.;In order to evaluate the statistical properties of nonlinear waves, a probability density function applicable to non-Gaussian random waves is developed in closed form. Currently, no probability density function in closed form representing non-Gaussian random processes is available.;In the derivation of the probability density function, the concept of Kac-Siegert's method developed for nonlinear mechanical system is applied. That is, the Kac-Siegert formula is asymptotically expressed in terms of a random variable that obeys a normal distribution with parameters evaluated from information on cumulants of the wave record. Then, by applying the transformation technique of random variables, the desired probability density function is developed in closed form. Comparisons between the newly developed probability density function and the histograms constructed from wave records at various water depths obtained in the ARSLOE Project during storm show excellent agreement.