Rogue waves in unidirectional seas: statistics and prediction

The ability of accurately predicting the occurrence of rogue waves(i.e. time, location and maximum height) in the open ocean is limited by sparsity of field measurements and accuracy in numerical models. The difficulties with the latter arise primarily from the ability of taking into higher order nonlinearity, as well as allowing various mechanisms in rogue wave formations. In this dissertation, several steps on quantitative analysis toward understanding the statistical properties of rogue waves are presented, followed by a pioneer study on rogue wave prediction in two dimensional framework.First, an approach to get averaged rogue wave profile was proposed to keep asymmetric trough shape respect to the main crest. The averaged profile using this new approach(i.e. approach II) and the blind averaging approach(i.e. approach I) were obtained in both space and time. By comparing the averaged shape using both approaches, we concluded that rogue wave is indeed asymmetric(i.e. the deeper trough can be as high as more than two times the shallower trough on two sides of the main crest). The widely used approach I omits this asymmetric feature in the averaged profile, thus rogue wave height can be strongly underestimated using approach I. This is especially important in estimating rogue wave height in space because we observed that rogue wave is generally more asymmetric in space compared with that in time. For example, rogue wave height in space is underestimated by 10% using approach I in sea state 5(i.e. Hs=3.25m, Tp=9.7s). Moreover, effect of nonlinearity was also addressed by quantitatively comparing the averaged shape of rogue waves with different order of nonlinearity in numerical simulations. Rogue wave formation is dominated by second-order nonlinear interaction, and further enhanced by higher-order nonlinearities.The effect of stratification on the formation of rogue waves was evaluated by studying rogue waves in both homogeneous fluid and stratified fluid(i.e. two-layer stratified fluid). Through resonant interactions, energy can be exchanged from surface modes on the free surface and interfacial modes on the interface. This effect was quantitatively analyzed by comparing the rogue wave height in both models with identical initial conditions. In relatively short term(i.e. 100Tp), we found that regular oceanic stratification(i.e. density variation is 1% in upper and lower layer) does not play a crucial role in rogue wave formation. However, in strongly stratified ocean(~5% density difference in upper and lower layer), rogue wave height can be strongly underestimated in relatively long term(500Tp). Finally, we quantitatively predicted rogue wave formation in the homogeneous fluid model for a short term(i.e. up to 100Tp) by tracking energy concentration in space. This is motivated by the observation that energy concentrates in space several periods before rogue wave occurrence. We evaluated this energy concentration by calculating the energy flux, which is defined as energy across a vertical plane from seabed to free surface. The height of normalized net energy flux was found to be a good precursor in predicting rogue wave occurrence. A relatively low false positive rate(i.e. ~20%) was achieved with most of the rogue waves being successfully predicted(i.e. more than 80% rogue waves are successfully predicted in the numerical database)