Current-Induced Modulation of the Ocean Wave Spectrum and the Role of Nonlinear Energy Transfer

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 highresolution wave forecasting.

Occurrence of extreme waves in three-dimensional mechanically generated wave fields propagating over an oblique current

“…This may partially contribute to the broadening of the directional spreading (cf. Tamura et al, 2008); it may also induce a weak variation of the mean direction of wave spectra, which was observed to slowly become increasingly current normal. Whereas the contribution of the current gradient is negligible at the first array (the directional spreading with and without current is consistent with the nominal condition), it becomes substantial at the last array (near the absorption beach), where the directional spreading is about 15% broader than in the absence of the current.…”

“…Moreover, when waves propagate over an area of increasing adverse current (positive current gradient), the wavelength is forced to shrink with a concurrent increase of the wavenumber and wave height (see Peregrine, 1976). This results in an enhancement of the wave steepness, which is suspected to make nonlinear processes, such as the modulational instability mechanism and hence extreme waves, more likely (see, for example, Gerber, 1987;Lai et al, 1989;Stocker and Peregrine, 1999;Lavrenov and Porubov, 2006;Tamura et al, 2008). Using numerical simulation of cubic nonlinear dynamics, in this respect, Janssen and Herbers (2009) and Hjelmervik and Trulsen (2009) have tried to quantify the effect of a nonuniform current on the probability of occurrence of extreme waves.…”

Interplay of Resonant and Quasi-Resonant Interaction of the Directional Ocean Waves

“…To prove this hypothesis, we have estimated the nonlinear energy transfer of distinct directional distributions using a simplified, but improved, numerical approximation to the Hasselmann's integral [Research Institute for Applied Mechanics (RIAM) method] (Komatsu and Masuda 1996;Tamura et al 2008). In this tank experiment, we are missing the wind input, and the whitecap dissipation is missing as well, for the condition we have selected to analyze in this section.…”

Predicting freakish sea state with an operational third-generation wave model

“…In this study, we have shown that the dangerous sea state can be well predicted with both DIA and SRIAM simulations. The response of the directional spectrum to changing wind condition is sensitive to the accuracy of the nonlinear interaction source term (Tamura et al, 2008). However, for operational use, the DIA is most commonly used.…”

“…The SRIAM method approximates the Hasselman's collision integral (Hasselmann, 1963) with 20 optimized combinations of resonant quartets instead of one in DIA. The SRIAM method was implemented in realistic simulations for the first time by Tamura et al (2008Tamura et al ( , 2009Tamura et al ( and 2010, demonstrating that the directional spectrum under rapidly changing wind conditions and the spectral tail are better resolved by the SRIAM method. In Tamura et al (2009), spectral evolution of swell and wind-wave interaction was hindcasted for the Suwa-Maru No.…”