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Takuji Waseda, Takeshi Kinoshita, and Hitoshi Tamura

Abstract

The evolution of a random directional wave in deep water was studied in a laboratory wave tank (50 m long, 10 m wide, 5 m deep) utilizing a directional wave generator. A number of experiments were conducted, changing the various spectral parameters (wave steepness 0.05 < ε < 0.11, with directional spreading up to 36° and frequency bandwidth 0.2 < δk/k < 0.6). The wave evolution was studied by an array of wave wires distributed down the tank. As the spectral parameters were altered, the wave height statistics change. Without any wave directionality, the occurrence of waves exceeding twice the significant wave height (the freak wave) increases as the frequency bandwidth narrows and steepness increases, due to quasi-resonant wave–wave interaction. However, the probability of an extreme wave rapidly reduces as the directional bandwidth broadens. The effective Benjamin–Feir index (BFIeff) is introduced, extending the BFI (the relative magnitude of nonlinearity and dispersion) to incorporate the effect of directionality, and successfully parameterizes the observed occurrence of freak waves in the tank. Analysis of the high-resolution hindcast wave field of the northwest Pacific reveals that such a directionally confined wind sea with high extreme wave probability is rare and corresponds mostly to a swell–wind sea mixed condition. Therefore, extreme wave occurrence in the sea as a result of quasi-resonant wave–wave interaction is a rare event that occurs only when the wind sea directionality is extremely narrow.

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Takuji Waseda, Takeshi Kinoshita, and Hitoshi Tamura

Abstract

Recent experimental study of the evolution of random directional gravity waves in deep water provides new insight into the nature of the spectral evolution of the ocean waves and the relative significance of resonant and quasi-resonant wave interaction. When the directional angle containing half the total energy is broader than ∼20°, the spectrum evolves following the energy transfer that can be described by the four-wave resonant interaction alone. In contrast, in the case of a directionally confined spectrum, the effect of quasi-resonant wave–wave interaction becomes important, and the wave system becomes unstable. When the temporal change of the spectral shape due to quasi resonance becomes irreversible owing to energetic breaking dissipation, the spectrum rapidly downshifts. Under such extreme conditions, the likelihood of a freak wave is high.

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Hitoshi Tamura, Takuji Waseda, Yasumasa Miyazawa, and Kosei Komatsu

Abstract

Numerical simulations were performed to investigate current-induced modulation of the spectral and statistical properties of ocean waves advected by idealized and realistic current fields. In particular, the role of nonlinear energy transfer among waves in wave–current interactions is examined. In this type of numerical simulation, it is critical to treat the nonlinear transfer function (Snl) properly, because a rigorous Snl algorithm incurs a huge computational cost. However, the applicability of the widely used discrete interaction approximation (DIA) method is strictly limited for complex wave fields. Therefore, the simplified RIAM (SRIAM) method is implemented in an operational third-generation wave model. The method approximates an infinite resonant quadruplet with 20 optimized resonance configurations. The performance of the model is assessed by applying it to fetch-limited wave growth and wave propagation against a shear current. Numerical simulations using the idealized current field revealed that the Snl retained spectral form by redistributing the refracted wave energy; this suggests that energy concentration due to ray focusing is dispersed via the self-stabilization effect of nonlinear transfer. A hindcast simulation using wind and current reanalysis data indicated that the difference in the average monthly wave height was substantial and that instantaneous wave–current interactions were highly sensitive to small current structures. Spectral shape was also modulated, and the spatial distributions of the directional bandwidth with or without current data were completely different. Moreover, the self-stabilization effect of the Snl was also confirmed in a realistic situation. These results indicate that a realistic representation of the current field is crucial for high-resolution wave forecasting.

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Sophia E. Brumer, Christopher J. Zappa, Ian M. Brooks, Hitoshi Tamura, Scott M. Brown, Byron W. Blomquist, Christopher W. Fairall, and Alejandro Cifuentes-Lorenzen

Abstract

Concurrent wavefield and turbulent flux measurements acquired during the Southern Ocean (SO) Gas Exchange (GasEx) and the High Wind Speed Gas Exchange Study (HiWinGS) projects permit evaluation of the dependence of the whitecap coverage W on wind speed, wave age, wave steepness, mean square slope, and wind-wave and breaking Reynolds numbers. The W was determined from over 600 high-frequency visible imagery recordings of 20 min each. Wave statistics were computed from in situ and remotely sensed data as well as from a WAVEWATCH III hindcast. The first shipborne estimates of W under sustained 10-m neutral wind speeds U 10N of 25 m s−1 were obtained during HiWinGS. These measurements suggest that W levels off at high wind speed, not exceeding 10% when averaged over 20 min. Combining wind speed and wave height in the form of the wind-wave Reynolds number resulted in closely agreeing models for both datasets, individually and combined. These are also in good agreement with two previous studies. When expressing W in terms of wavefield statistics only or wave age, larger scatter is observed and/or there is little agreement between SO GasEx, HiWinGS, and previously published data. The wind speed–only parameterizations deduced from the SO GasEx and HiWinGS datasets agree closely and capture more of the observed W variability than Reynolds number parameterizations. However, these wind speed–only models do not agree as well with previous studies than the wind-wave Reynolds numbers.

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