Nonlinear interactions in random seas and crest-height statistics for sea-states in finite water depth
Creators: name: Zve, Sotiria Eleni
Publisher: name: Imperial College London
Year: 2022

description: The present thesis concerns an investigation on the effect of nonlinear wave-wave interactions on the statistical properties of random wave fields, with particular focus on the effect of nonlinearity above second-order in wave steepness. This investigation is put into a practical perspective by devising a prediction methodology for the short-term crest-height distribution; a key input for the design and safety assessment of offshore structures and vessels. The effect of nonlinearity is examined using a Higher-Order Spectral Model (HOSM), which is thoroughly validated. Particular focus has been devoted to establishing the effect of the progressive development of near-resonant interactions on the most likely magnitude of the largest waves arising in a 3-hour storm in a statistically reliable manner. In this respect, the present research aimed to fill a long unanswered research question regarding the quantification of the effect of energy focusing or defocussing arising from such interactions in finite water depth, in which the presence of wave-induced `mean flow’ has problematised many researchers so far. The presented results indicate that in uni-directional seas, energy focusing is relevant in relative water depths of kpd&gt;1.36 (kp being the wavenumber associated to the spectral peak frequency and d being the water depth) and energy defocussing in kpd&lt;1.36. This is in line with insights gained from previous works based on elementary wave interactions, and has a direct consequence on the crest-height distributions of the free waves, which are shown to deviate from the theoretical linear predictions. More importantly, it has been shown that, whilst energy focusing quickly attenuates with the introduction of directionality in kpd&gt;≈1.36, this is not the case for the effect of energy defocussing in kpd&lt;≈1.36. The latter is shown to persist for sea-states of increased directionality. As such, with the bound-wave contributions leading to the nonlinear increase of the total crest heights and the near-resonant interactions leading to a decrease in kpd&lt;≈1.36, wave nonlinearity is shown to include two competing processes. The proposed crest-height model includes the parameterisation of the effect of energy focusing/defocusing based on the dynamic kurtosis and the bound-wave contributions upon the skewness and bound kurtosis; the latter coupled to the dynamic kurtosis to account for the coupling of the two nonlinear processes. With all available analytical or theoretical solutions failing to provide an accurate prediction for all aforementioned statistical parameters, their prediction has been achieved by employing methodologies from the field of Machine Learning. The proposed crest-height model, which is valid in the effective depth range of kpd∈[0.5, 8], is extensively validated against an independent set of numerical, experimental and field-data results. While it is shown to consistently outperform the standard-industry Forristall (2000) model. Finally, an extension of the proposed crest-height model to account for the effect of wave breaking is presented based on a pragmatic approach.