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Computations using a high-order spectral method with sufficient resolution are performed to describe the long-term evolution of deep-water Stokes waves perturbed by various sidebands. The roles of sideband instability and mode coupling in forming chaos, and the characteristics of waves in chaos are also investigated. Relationships between Fourier-modes evolution and the initial states of the primary mode and its sidebands are clarified. Simple evolution (the so-called FPU recurrence) is very rare and is possible only under the condition that only a single pair of sidebands may have energy permanently. Most evolutions are complex and finally result in chaotic behavior. This is because many non-zero unstable sidebands are newly excited through the coupling between the primary mode and the higher harmonics of long-wave modulational perturbations, even if the amplitude of only one pair of unstable sidebands is initially non-zero and the amplitudes of all other sidebands are zero. By means of high-order nonlinear modelling with sufficiently many degrees of freedom, the Stokes waves in deep water are shown to form a chaotic system. Further, the computational results imply that water waves in chaos converge on spectra obeying wave number power laws dependent only on the steepness ka , and may be regarded as a coherent bound-wave system where the Fourier modes with high wave numbers have approximately the same phase velocity.

The Edgeworth expansion with the measured skewness and kurtosis is shown to be capable to describe the measured nonlinear distributions of the surface elevation and horizontal velocity in the shoaling and surf zones. The moments involved in the energetics-based model are expressed in terms of the skewness and kurtosis and shown to be in agreement with available data. Stokes wave theory is applied to obtain a relationship between skewness and kurtosis. The relationship is adjusted empirically because of the limitation of Stokes wave theory in the shoaling and surf zones. The relative simple relationship for the higher moments obtained here may be applied for cross-shore sediment transport analysis.

Nonlinear four-wave interactions amplify wave heights of deep-water generating extreme wave such as a freak wave. However, it is not clear the behavior of generated freak waves in deep-water shoaling to shallow water regions. In this study, a series of physical experiments and numerical simulations with several bathymetry configurations were conducted for unidirectional random waves from deep to shallow water regions. The maximum wave heights increase with an increase in kurtosis by third-order nonlinear interactions in deep water regions. The dependence of the kurtosis on the freak wave occurrence is weakened due to second-order nonlinear interactions associated with wave shoaling on the slope. Moreover, it is possible to understand the behavior of the high-order nonlinearity and the freak wave occurrence in shallow water regions if appropriate correction of the insufficient nonlinearity of more than O(e^2) to the standard Boussinesq equation are considered analytically.

There are many researches and development for the coupled atmosphere, ocean and wave model due to the improvement of the models. On the other hand, the vigorous observations for the momentum transport between the atmosphere and ocean were carried out due to reconsider the bulk formulas for coupling model. A lot of formulas depending on the wind speed or on the wave information are proposed. Although a coupling model is useful for tropical cyclone assessment for coastal engineers, the parameterization at the air-sea interface give strong influence on storm surge modeling. In this study, the influences of the bulk formulas to ocean and wave models using the atmosphere-ocean-wave coupling model are examined.

The strong winter storm crossed from the west to east of the Sea of Japan developing rapidly in early April, 2012. The minimum pressure of the winter storm reached 964 hPa at 21:00 on 3rd April. The storm generated wind waves more than 10 m in the significant wave height and gave severe damages to coastal structures around Japan. This study analyzed observed wave records at 12 stations along the Sea of Japan. A series of numerical analysis was performed to understand the characteristics of extreme wave sea condition. The maximum wave heights were estimated based on the spectral wave model and nonlinear short wave statistical theory. The estimated maximum wave heights by the nonlinear theory show better agreement with the observed peak of maximum wave height than that by the linear theory.

Two powerful hurricanes successively passed close to US Virgin Islands in September 2017. Hurricane Irma developed into CAT5 with the lowest pressure around 914 hPa on 5th of September and passed north of USVI. Sequentially, CAT5 Hurricane Maria followed the similar track, but passed south of USVI. Two CAT5 hurricanes gave devastated damage along the Caribbean Islands. It is a rare event having two CAT5 with similar tracks within two weeks. This study presents hindcasts of waves and storm surge for the two hurricanes and discusses coastal damages with our survey data targeting on USVI.

Coupled atmosphere-ocean model has been developed in various organizations. Warner et al. developed fully coupled model, so-called COAWST, using the atmosphere model WRF, the ocean model ROMS and the wave model SWAN. Though there are several studies with coupled model, there is few research on tropical cyclone event analyzing the changes in ocean current and water temperature in detail. In this study, a series of numerical simulations was carried out targeting Typhoon Melor (2009), and it is analyzed against to the meteorologic and oceanic field data at Tanabe bay, Wakayama Prefecture in Japan. The results show that the wave energy dissipation by the wave model is effective in the change of ocean current and the thermal feedback by the atmospheric model is effective in the change of water temperature due to the typhoon passage.

Quasi-resonant four-wave interactions may influence the statistical properties of deep water surface gravity waves such as a freak wave. The freak wave prediction method developed by Mori and Janssen (2006) based on the quasi-resonant wave theory is compared with Europian Centre for Meidum Range Weather Forecasts wave analysis data. Mori and Janssen (2006) model shows low correlation with the observed wave data.To improve the forecasts score, the directional effects are considered by using a series of the Mote Carlo simulations of cubic Nonlinear Schrodinger equation. The broad band spectrum effects are also considered in the prediction method.

The inundation of the 2011 Tohoku Earthquake Tsunami showed complex behavior over the land. According to the surveys of the Tohoku Earthquake Tsunami in 2011, the behavior of tsunami in urban areas was different from that in rural areas and the damage was not only dependent on the inundation heights but also the local momentum. The buildings are commonly excluded and smoothed off in the topography in the conventional inundation simulation but it’s important to understand the local characteristics of tsunami run-up in urban areas. The purpose of this study is to understand and validate numerical models of tsunami in the urban area.