Takuji Waseda

Laboratory observations of wave group evolution, including breaking effects

The nonlinear evolution of deep-water wave groups, which are initiated by unstable three-wave systems, have been observed in a large wave tank (50 m long, 4.2 m wide, 2.1 m deep), equipped with a programmable, high-resolution wave generator. A large number of experiments were conducted (over 80 cases) for waves 1.0-4.0 m long, initial steepness ∈ = 0.10-0.28, and normalized sideband frequency differences, δω/∈ω, 0.2-1.4. Using an array of eight high-resolution wave wires distributed in range (up to 43 m fetch), spectral evolution was studied in detail including the effect of background disturbances on the evolution. Minimizing those, new observations were made which extend the pioneering work of Lake et al. (1977) and of Melville (1982). Foremost, near recurrence without downshifting was observed without breaking, despite a significant but reversible energy transfer to the lower sideband at peak modulation; complete recurrence was prevented by the spreading of discretized energy to higher frequencies. Strong breaking was found to increase the transfer of energy from the higher to the lower sideband and to render that transfer irreversible. The end state of the evolution following strong breaking is an effective downshifting of the spectral energy, where the lower and the carrier wave amplitudes nearly coincide; the further evolution of this almost two-wave system was not studied here. Breaking during strong modulation was observed not only for the fastest growing initial condition, but over a wide parameter range. An explanation of the sideband behaviour in both the breaking and non-breaking case was given based on wave energy and momentum considerations, including the separate effects of energy and momentum loss due to breaking, and transfer to discretized higher frequencies throughout the spectra. Attention was drawn to the latter, which was almost universally observed.

Evolution of a Random Directional Wave and Freak Wave Occurrence

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 < e < 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...

Anticyclonic eddies and Kuroshio Meander Formation

A meander-formation mechanism of the Kuroshio that involves anticyclonic eddies propagating from the Kuroshio Extension, is presented using the analysis of observations of the TOPEX/POSEIDON (T/P) altimeter data and in-situ data. Support of the mechanism comes also from a numerical simulation. In October 1997, a current meter mooring over the Izu Ridge at 500-m-depth captured large velocity fluctuations of about 50 cm s−1 that were associated with a strong anticyclonic eddy. The observations from T/P show that the anticyclonic eddy propagated westward and collided with the Kuroshio off Kyushu. At collision, the anticyclonic eddy coupled with a cyclonic circulation accompanied by a small meander and formed a vortex pair. They were then advected downstream and finally formed a large-meander-like path off the south coast of Honshu. The meander lasted for a few months. Subsequently, the anticyclonic eddy was detached, and the meander grew smaller in amplitude. Numerical experiments successfully simulate this interaction between the Kuroshio and anticyclonic eddies.

Correlation of hydrodynamic features with LGA radar backscatter from breaking waves

Backscatter characteristics of 1-4-m-long, mechanically generated breaking waves have been investigated with a C-band frequency modulated continuous wave (FMCW) radar (up to 3.77-cm range resolution) in the large wind-wave tank at the Ocean Engineering Laboratory, University of California, Santa Barbara. The grazing angle was 6/spl deg/. Wave breaking was caused to occur in the test section due to wave group selfmodulation, just as it has been observed in the ocean. The central purpose of these experiments was to determine the hydrodynamic sources of the low grazing angle sea spike and its structure. Using typical, strong 2.3-m-long breakers, four phases of the breaking process with distinct hydrodynamic characteristics were identified visually and correlated with synchronous radar data. These breaking waves yielded a horizontal copolarization (HH) radar cross section (RCS) of up to 10 m/sup 2/ and concurrent copolarization ratios (HH/vertical copolarization[VV]) exceeding 40 dB. Synchronous high-speed video images showed that these peak values appeared just after a plunging jet developed at the breaker crest, well before it hit the front face of the wave. Focusing the electromagnetic energy on the jet by the parabolic front face of the breaking wave is suggested as a mechanism that yields both high HH returns and high HH/VV ratios. Statistics of HH peak RCS for the complete range of wavelengths tested show the dependence of radar backscatter from energetic breaking waves on their wavelength and implies a scaling law such that the optimum return is obtained when /spl lambda//sub wave/=40 /spl lambda//sub radar/. Under fixed conditions of /spl lambda//sub wave/ and /spl lambda//sub radar/, large deviations in HH RCS have been found and have been shown to be dependent on the strength of the breaker.

Experimental study of the stability of deep-water wave trains including wind effects

An experimental investigation on the initial instability of nonlinear deep-water wave trains including wind effects is reported. The experiment was conducted at the Ocean Engineering Laboratory wind-wave facility (50m long, 4.2 m wide, 2.1 m deep), with a fully computer-controlled mechanical wave generator to explore the parameter space: steepness; sideband frequency; wind speed. The estimated growth rates of the Benjamin-Feir instability from seeded wind-free experiments agreed well with the theoretical prediction derived from Krasitskiis four-wave reduced equation as computed here. Wind was added to the same wave system; the growth rates of the sidebands were reduced for weak, and enhanced for strong wind forcing. Experiments with naturally selected sidebands, i.e. unseeded, were conducted as well; measurements showed that wind did not inhibit the growth of sidebands in the case of either two-dimensional or three-dimensional instabilities. A comparison of the results with earlier work suggests that there are two independent effects of wind: first, the alteration of the inviscid growth for a given modulational frequency as shown by comparison with the seeded experiments without wind; second, a change in the natural modulational frequency appearing in the presence of wind which is a function of the wave age, as observed in unseeded experiments. Both effects combined will determine whether the modulational instability is enhanced or suppressed; comparison of experimental results with theoretical predictions suggests that the effect of wind on the natural selection of the modulational frequency is the dominant effect. It was shown that for moderate to old waves, the net effect of wind on the modulational instability is small. For all the experiments except a few unseeded cases with weak breakers, the modulation was small and no breaking was observed within the tank.

Excitation of rogue waves in a variable medium:An experimental study on the interaction of water waves and currents

We show experimentally that a stable wave propagating into a region characterized by an opposite current may become modulationally unstable. Experiments have been performed in two independent wave tank facilities; both of them are equipped with a wavemaker and a pump for generating a current propagating in the opposite direction with respect to the waves. The experimental results support a recent conjecture based on a current-modified nonlinear Schrödinger equation which establishes that rogue waves can be triggered by a nonhomogeneous current characterized by a negative horizontal velocity gradient.

Numerical Study on the Oyashio Water Pathways in the Kuroshio-Oyashio Confluence *

Abstract In this paper, results of a high-resolution regional model of the Kuroshio–Oyashio confluence, where the mixed water region (MWR) forms off the northeastern coast of Japan, are discussed. The model simulates major characteristics of the Kuroshio and the Oyashio system well, such as the separation of the Kuroshio Extension from the Japanese coast and southward intrusion of the Oyashio. Further, potential temperature and salinity structures in the intermediate layer σθ = 27.0 resemble those obtained from historical data. Upon the success of this simulation, the authors focus on the diagnosis of the Oyashio water pathways intruding into the subtropics. It is found that the pathways of the Oyashio water form in the vicinity of the Japanese coast, where warm core rings and the Oyashio intrusion are active. These pathways are shown to be primarily eddy driven. Of particular interest is the water that originates in the Sea of Okhotsk, characterized by low potential vorticity (PV). Impacts of the Okhotsk...

Wave Breaking in Directional Fields

Abstract Wave breaking is observed in a laboratory experiment with waves of realistic average steepness and directional spread. It is shown that a modulational-instability mechanism is active in such circumstances and can lead to the breaking. Experiments were conducted in the directional wave tank of the University of Tokyo, and the mechanically generated wave fields consisted of a primary wave with sidebands in the frequency domain, with continuous directional distribution in the angular domain. Initial steepness of the primary wave and sidebands, as well as the width of directional distributions varied in a broad range to determine the combination of steepness/directional-spread properties that separates modulational-instability breaking from the linear-focusing breaking.

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 reve...

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

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.