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This paper describes a new laboratory study in which a large number of waves, of varying frequency and propagating in different directions, were focused at one point in space and time to produce a large transient wave group. A focusing event of this type is believed to be representative of the evolution of an extreme ocean wave in deep water. Measurements of the water-surface elevation and the underlying water-particle kinematics are compared with both a linear solution and a second-order solution based on the sum of the interactions first identified by Longuet-Higgins & Stewart. Comparisons between these data confirm that the directionality of the wavefield has a profound effect upon the nonlinearity of a large wave event. If the sum of the wave amplitudes generated at the wave paddles is held constant, an increase in the directional spread of the wavefield leads to lower maximum crest elevations. Conversely, if the generated wave amplitudes are increased until the onset of wave breaking, at or near the focal position, an increase in the directional spread allows larger limiting waves to evolve. An explanation of these results lies in the redistribution of the wave energy within the frequency domain. In the most nonlinear wave cases, neither the water-surface elevation nor the water-particle kinematics can be explained in terms of the free waves generated at the wave paddles and their associated bound waves. Indeed, the laboratory data suggest that there is a rapid widening of the free-wave regime in the vicinity of a large wave event. For a constant input-amplitude sum, these important spectral changes are shown to be strongly dependent upon the directionality of the wavefield. These findings explain the very large water-surface elevations recorded in previous unidirectional wave studies and the apparent contrast between unidirectional results and recent field data in which large directionally spread waves were shown to be much less nonlinear. The present study clearly demonstrates the need to incorporate the directionality of a wavefield if extreme ocean waves are to be accurately modelled and their physical characteristics explained.

The occurrence of rogue waves is closely related to the non-Gaussianity of sea states, and this non-Gaussianity can be estimated using corresponding two-dimensional wave spectra. This paper presents an approach to non-Gaussianity estimation based on a phase-resolving model called the high-order spectral method (HOSM). Based on numerous HOSM simulations, a set of precalculated non-Gaussianity indicators was established that could be applied to real sea states without any calibration of spectral shapes. With a newly developed extraction approach, the indicators for given two-dimensional wave spectra could then be conveniently extracted from the precalculated dataset. The feasibility of the newly developed approach in a real wave environment is verified. Using the estimation approach, phase-resolved non-Gaussianity can now be illustrated throughout the evolution of sea states of interest, not just at a few specific times; and the level of non-Gaussianity at any time in a duration can be identified according to the statistics (e.g., quantities) of the phase-resolved indicators, that are obtained throughout the duration concerned.

In this paper, an example of a symbiotic combination of marine structures is studied. The base hydrodynamic performance of a traditional offshore oscillating water column (OWC) device is compared against the case in which it is constructed over a submerged breakwater. Numerical simulations are performed with the open source package OpenFOAM and the toolbox waves2Foam. The classical free surface capturing method volume of fluid (VOF) is employed to model first-order Stokes waves. The effects of the dimensions (height and length) of the submerged breakwater on the hydrodynamic characteristics, such as wave energy conversion efficiency ( ξ ), reflection coefficient ( C r ), transmission coefficient ( C t ), and energy dissipation ratio ( E D ) are explored thoroughly. Moreover, the effect of wave nonlinearity induced by increasing incident wave heights on the OWC device is examined. The results show that a proper configuration of the submerged breakwater is significantly helpful to optimize the energy conversion curve. Varying breakwater length will lead to a periodic variation in energy absorption efficiency. In addition, a higher incident wave height will lead to a lower energy absorption efficiency but a stronger dissipation ratio.

Traditionally, the directional distribution of ocean waves has been regarded as unimodal, with energy concentrated mainly on the wind direction. However, numerical experiments and field measurements have already demonstrated that the energy of short waves tends to be accumulated along two off‐wind directions, generating a bimodal directional distribution. Here, numerical simulations of the potential Euler equations are used to investigate the temporal evolution of initially unimodal directional wave spectra. Because this approach does not include external forcing such as wind and breaking dissipation, spectral changes are only driven by nonlinear interactions. The simulations show that the wave energy spreads outward from the spectral peak, following two characteristic directions. As a result, the directional distribution develops a bimodal form as the wavefield evolves. Although bimodal properties are more pronounced in the high wave number part of the spectrum, in agreement with previous field measurements, the simulations also show that directional bimodality characterizes the spectral peak.

In the laboratory experiment, 1:25 scaled models are constructed to investigate the effect of different swell and wind-sea proportions on the wave transformation. The source of the wave spectrum is related to the wave conditions in the Gulf of Guinea. Swell from the westerlies and local wind-sea forms the bimodal spectral waves in the region. To better understand the transformation of bimodal spectral waves, a series of wave conditions are measured by the wave gauges in a wave flume. Based on the wave spectrum at the Bight of Benin, the wave transformation along the slopes and variations of different swell proportions are analyzed. The result of the wave height variations shows that the slope and swell proportion play a significant role in the maximum wave height, and the wave height has an upward trend with a large swell proportion. The analysis of wave nonlinearity is conducted, showing that the large swell proportion in the wave spectrum leads to a more significant nonlinearity before wave breaking. Combining the variations of wave height and wave nonlinearity, the influence of bimodal spectral waves on nearshore wave prediction, shoreline change, marine operations, and structure design is discussed.

Zhang, C.; Zhang, Q.; Lei, G.; Cai, F.; Zheng, J., and Chen, K., 2018. Wave nonlinearity correction for parametric nearshore wave modelling. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 996–1000. Coconut Creek (Florida), ISSN 0749-0208. Many phase-averaged parametric nearshore wave models are based on the energy balance concept and use linear wave theory to calculate wave parameters (e.g., wave energy, wave height, wave setup). For a wave propagating into shallow water, however, its shape becomes skewed/asymmetric and the linear wave theory may not be appropriate. Seven cases of model-data comparison for regular wave transformation over sloping and barred beaches are carried out. It is shown that the model using linear wave theory underestimates the regular wave height near the breakpoint, and overestimates the breaking roller length in the surf zone. An empirical method is proposed to improve the performance of the parametric wave models in shallow waters by correcting the key model parameters to include wave nonlinearity effects. This includes (1) development of a new empirical formula for the nonlinear wave shape factor, (2) using a nonlinear wave celerity formula, and (3) implementing a new empirical formula for breaking roller slope. These formulas are functions of wave steepness and Ursell number. The proposed method systematically improves predictions of wave height, wave setup and roller evolution under regular wave transformation with different beach configurations. In particular, the peaks of wave height and mean water level near the breakpoint as well as the roller length variation in the surf zone are accurately captured by the wave nonlinearity-corrected model.

In this study, the Enhanced RAO-based Translation Process (ERTP) method, which is an enhanced version of the RAO-based Translation Process (RTP) method proposed in the previous study, is newly proposed. The RTP method approximates the Extreme Value Distribution (EVD) in arbitrary irregular waves from the nonlinear response in regular waves based on the idea of the transformation process, in which the nonlinear process is regarded as a transformation of a linear process. However, it was found that the RTP method is inaccurate when the response spectrum has multiple peaks, which is often the case for stresses in ship structures in waves. To solve this problem, the author developed the ERTP method, which defines a nonlinear transformation based on the L p -norm of the response spectrum. Direct Load and Structure Analysis considering the nonlinearity of wave loads was conducted and confirmed that the proposed method can reasonably estimate the EVD even for structural elements with a multi-peaked response spectrum with respect to the wave direction.

A number of vertical array records during eight destructive earthquakes in Japan are utilized, after discussing criteria for desirable requirements of vertical arrays, to formulate seismic amplification between ground surface and outcrop base for seismic zonation. A correlation between peak spectrum amplification and Vs (S-wave velocity) ratio (base Vs/surface Vs) was found to clearly improve by using Vs in an equivalent surface layer wherein predominant frequency or first peak is exerted, though the currently used average Vs in top 30 m is also meaningful, correlating positively with the amplification. We also found that soil nonlinearity during strong earthquakes has only a marginal effect even in soft soil sites on the amplification between surface and outcrop base except for ultimate soil liquefaction failure, while strong nonlinearity clearly appears in the vertical array amplification between surface and downhole base. Its theoretical basis has been explained by a simple study on a two-layered system in terms of radiation damping and strain-dependent equivalent nonlinearity.

A diffraction limited focal spot is used to create a single speckle in a preformed plasma. The single speckle, or hot spot, is the simplest irreducible element for studying laser plasma interactions. Using the single hot spot configuration, the nonlinear behavior of SRS driven Langmuir waves has been investigated in both a fluid dominated and a kinetic regime. A transition between the two regimes has been observed as a function of kλD where k is the Langmuir wave-number and λD is the Debye length.

The influence of cubic nonlinearity on the dispersion relation for long waves on a water surface is analyzed. In the long wavelength limit, it is shown that the dispersion relation is not affected by the cubic terms. The results are compared with the dispersion relation for stationary solutions to the Korteweg—de Vries equation.