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Leland Jameson and Takuji Waseda

Abstract

A new method is presented for estimating numerical errors in simulations as a function of space and time. This knowledge of numerical errors can provide critical information for the effective assimilation of external data. The new method utilizes wavelet analysis for the detection of deviation from low-order polynomial structure in the computational data indicating regions of the domain where relatively large numerical errors will occur. This wavelet-based technique has a very low computational cost, and in practice the cost can be considered negligible compared to the computational cost of the simulation. It is proposed here that this be used in the field of data assimilation for fast and efficient assimilation of external data, and a numerical example illustrating that the new method performs better than the existing method of optimal interpolation is given.

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Wataru Fujimoto and Takuji Waseda

ABSTRACT

Freak/rogue waves are considered to be the causes of marine accidents and their generation mechanism is closely related to the formation of wave groups. However, observations that capture the spatiotemporal evolution of coherent wave groups in directional windsea are rather limited. The paper presents a new technique known as the surface wave reconstruction by ensemble adjoint-free data assimilation (SWEAD) method that enables reconstruction of a spatiotemporal wave field covering a large area from wave records limited in observational density and spatial extent. We reconstructed spatiotemporal profiles of nonlinear surface gravity waves from virtual observational data using the adjoint-free four-dimensional variational data assimilation (a4DVar) scheme. The higher-order spectral method (HOSM) is used as a forward deep-water nonlinear wave model in a realistic sea state. The a4DVar scheme uses perturbed ensemble simulations to calculate the cost function gradient and Hessian; thus, construction of an adjoint model is not needed. A few extensions of the a4DVar scheme are proposed in this study. For efficient wave reconstruction, perturbed ensemble simulation results are reused by increasing the searching direction dimension at each iteration while assuring conformity to the perturbed model’s linearity. For regularization, Fourier coefficient magnitudes are constrained by a known power spectrum from the phase-averaged wave model. Twin experiments were conducted for a unidirectional wave with virtual wave gauge data and a multidirectional wave with virtual stereo camera imaging data. For both unidirectional and multidirectional cases, nonlinear freak wave–related wave groups were well reproduced, which is impossible using a linear model.

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Leland Jameson, Takuji Waseda, and Humio Mitsudera

Abstract

The second generation of a new approach to data assimilation where wavelet analysis is used for error estimation is presented here. The first generation is known as EEWADAi. This modified and optimized method uses wavelet analysis to not only estimate numerical error but to also acquire an estimate of the variation at various scales of the model simulation. In the original EEWADAi, wavelet analysis on the finest scale was used to estimate numerical error. In the second-generation version, called SUgOiWADAi, wavelet analysis is used on a variety of scales to not only obtain an estimate of numerical error, finest-scale information, but to also obtain an estimate of model variation, information from coarser scales. This new algorithm is computationally very inexpensive and is very effective.

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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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Naoya Suzuki, Takuji Waseda, Mark A. Donelan, and Takeshi Kinoshita

Abstract

There exists considerable disagreement among the observed values of the drag coefficient C D. To develop a model of C D, the wind stress generally will be calculated from the eddy correlation method. A buoy is suitable to measure the wind stress in many sea surface conditions. However, the motion correction is very difficult because the anemometer measures the wind components, including the motion of the buoy. In this study, as a first approach, the motion of a prototype buoy system with a three-axis sonic anemometer and a six-axis motion sensor installed in the small-size GPS observation buoy was investigated. The wave tank is in the ocean engineering basin of the Institute of Industrial Science, University of Tokyo, Japan. The imposed conditions were wave periods from 1.1 to 2.5 s; wind speeds of 0, 2, and 5 m s−1; and the wave spectrum was either regular or irregular. The motion of the buoy was measured in 120 cases. For all the wave periods and without wind, the wind velocity measured by the sonic anemometer and the velocity of the anemometer motion calculated from the motion sensor data showed good agreement. Also, in the condition with wind speeds of 2 and 5 m s−1, the motion-corrected wind velocity, obtained by deducting the velocity of the anemometer motion from the wind velocity measured by the anemometer, yielded the true wind velocity with better-than-average (4.3%) accuracy. The friction velocity from corrected wind velocity components shows agreement with the friction velocity measured from a fixed sonic anemometer within expected intrinsic error. The buoy system is expected to be able to measure the wind stress in the field. The next stage is to do comprehensive field tests.

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Humio Mitsudera, Bunmei Taguchi, Takuji Waseda, and Yasushi Yoshikawa

Abstract

This paper discusses the role of the Izu Ridge in blocking the Kuroshio large meander from propagating eastward across the ridge. It is shown that a combination of the sloping bottom with baroclinicity in the Kuroshio flow is important for blocking of the large meander. It produces a cyclonic torque over the western slope of the ridge when the large meander impinges upon it. That is, the cyclonic torque is formed ahead of the large meander, which results in blocking and amplification of the meander upstream of the Izu Ridge. The baroclinicity of the Kuroshio over the ridge is caused by baroclinic topographic Rossby waves generated when the large meander encounters the ridge.

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Luigi Cavaleri, Francesco Barbariol, Alvise Benetazzo, and Takuji Waseda
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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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Henrique Rapizo, Takuji Waseda, Alexander V. Babanin, and Alessandro Toffoli

Abstract

Laboratory experiments were performed to investigate the effects of a coflowing current field on the spectral shape of water waves. The results indicate that refraction is the main factor in modulating wave height and overall wave energy. Although the structure of the current field varies considerably, some current-induced patterns in the wave spectrum are observed. In high frequencies, the energy cascading generated by nonlinear interactions is suppressed, and the development of a spectral tail is disturbed, as a consequence of the detuning of the four-wave resonance conditions. Furthermore, the presence of currents slows the downshifting of the spectral peak. The suppression of the high-frequency energy under the influence of currents is more prominent as the spectral steepness increases. The energy suppression is also more accentuated and long-standing along the fetch when the directional spreading of waves is sufficiently broad. This result indicates that the current-induced detuning of resonant conditions is more effective when exact resonances are the primary mechanism of nonlinear interactions than when quasi resonances prevail (directionally narrow cases). Additionally, the directional analysis shows that the highly variable currents broaden the directional spreading of waves. The broadening is suggested to be related to random refraction and scattering of wave rays. The random disturbance of wavenumbers alters the nonlinear interaction conditions and weakens the energy exchanges among wave components, which is expressed in the suppression of the high-frequency energy.

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