Aspects of wave dynamics and statistics on the open ocean - Adcock, T; T. A. A. Adcock (2009)
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.