A comprehensive experimental study was conducted to produce benchmark wave kinematics data for five different regular waves and the maxima of four different irregular wave trains. Two of the irregular waves generated are in the category of rogue waves. A series of experiments were conducted in a 2-D wave tank at Texas A&M University to measure wave velocities and accelerations using LDV and PIV systems. The wave crests of regular and rogue waves are the focus of this study. With the measured wave velocity field, the wave accelerations were computed using a centered finite difference scheme. Both local and convective components of the total accelerations are obtained from experimental data. Also, the nonlinear wave forces on a truncated slender cylinder are computed by applying the obtained wave kinematics to the Morison equation. The force results based on measured wave kinematics are compared with those based on the kinematics of linear extrapolation, Wheeler stretching, and modified stretching. The Wheeler stretching method generally underestimates the actual wave kinematics. The linear extrapolation method is very sensitive to the cutoff frequency of the wave spectrum. The modified stretching method tends to predict the maximum value of wave kinematics above the still water level (SWL) well except for the convective acceleration. The magnitude of convective acceleration in the regular waves was negligibly small, whereas the magnitudes of horizontal and vertical convective accelerations in the rogue wave were increased rapidly above the SWL.

Rogue waves are unexpected, individual ocean surface waves that are disproportionately large compared to the background sea state. They present considerable risk to mariners and offshore structures when encountered in large seas. Rogue waves have gone from seafarer’s folktales to an actively researched and debated phenomenon. In this work an easily derived spectral parameter, as an indicator of rogue wave risk, is presented, and further evidence for the generation mechanism responsible for these abnormal waves is provided. With the additional goal of providing a practical rogue wave forecast, the ability of a standard wave model to predict the rogue wave probability is assessed. Current forecasts, like those at the European Centre for Medium-Range Weather Forecasts (ECMWF), rely on the Benjamin Feir Index (BFI) as a rogue wave predictor, which reflects the nonlinear process of modulation instability as the generation mechanism for rogue waves. However, this analysis finds BFI has little predictive power in the real ocean. From the analysis of long term sea surface elevation records in nearshore areas and hourly bulk statistics from open ocean and coastal buoys in the Northeast Pacific, crest-trough correlation shows the highest correlation with rogue wave probability. These results provide evidence in support of a probabilistic prediction of rogue waves based on random linear superposition and should replace forecasts based on modulation instability. Crest-trough correlation was then forecast by a regional WAVEWATCH III ® wave model with moderate accuracy compared with the high performance of forecasting significant wave height. Results from a case study of a large fall storm October 21-22, 2021, are presented to show that the regional wave model produces accurate forecasts of significant wave height at high seas and presents a potential rogue wave probability forecast. / Graduate

Water waves are an important design consideration for engineers wishing to design structures in the offshore environment. Designers need to know the size and shape of the waves which any structure is likely to encounter. Engineers have developed approaches to predict these, based on a combination of field and laboratory measurements, as well theoretical analysis. However some aspects of this are still poorly understood; in particular there is growing evidence that there are rare "freak" waves which do not fit with our current understanding of wave physics or statistics. In the first part of this thesis a new approach is developed for measuring the directional spreading of a sea-state, when the free surface time-history at a single point is the only available information. We use the magnitude of the second order "bound" waves to infer this information. This is validated using fully non-linear simulations, for random waves in a wave-basin, and for field data recorded in the North Sea. We also apply this to the famous Draupner wave, which our analysis suggests was caused by two wave systems, propagating at approximate 120 degrees to each other. The second part of the thesis looks at the non-linear evolution of Gaussian wave-groups. Whilst much work has previously been done to investigate these numerically, we instead derive an approximate analytical model for describing the non-linear changes to the group, based on the conserved quantities of the non-linear Schrodinger equation. These are validated using a numerical model. There is excellent agreement for uni-directional waves. The analytical model is generally good for predicting change in shape of directionally spread groups, but less good for predicting peak elevation. Nevertheless, it is still useful for typical sea-state parameters. Finally we consider the effect of wind on the local modeling of extreme waves. We insert a negative damping term into the non-linear Schrodinger equation, and consider the evolution of "NewWave" type wave-groups. We find that energy input accentuates the non-linear dynamics of wave-group evolution which suggests it may be important in the formation of "freak" waves.