Phase-suppressed hydrodynamics of solitons on constant-background plane wave

Soliton and breather solutions of the nonlinear Schr\"odinger equation (NLSE) are known to model localized structures in nonlinear dispersive media such as on the water surface. One of the conditions for an accurate propagation of such exact solutions is the proper generation of the exact initial phase-shift profile in the carrier wave, as defined by the NLSE envelope at a specific time or location. Here, we show experimentally the significance of such initial exact phase excitation during the hydrodynamic propagation of localized envelope solitons and breathers, which modulate a plane wave of constant amplitude (finite background). Using the example of stationary black solitons in intermediate water depth and pulsating Peregrine breathers in deep-water, we show how these localized envelopes disintegrate while they evolve over a long propagation distance when the initial phase shift is zero. By setting the envelope phases to zero, the dark solitons will disintegrate into two gray-type solitons and dispersive elements. In the case of the doubly-localized Peregrine breather the maximal amplification is considerably retarded; however locally, the shape of the maximal focused wave measured together with the respective signature phase-shift are almost identical to the exact analytical Peregrine characterization at its maximal compression location. The experiments, conducted in two large-scale shallow-water as well as deep-water wave facilities, are in very good agreement with NLSE simulations for all cases.Comment: (14 pages, 12 figures

Experiments on higher-order and degenerate Akhmediev breather-type rogue water waves

A possible mechanism that is responsible for the occurrence of rogue waves in the ocean is the Benjamin–Feir instability or modulation instability. The deterministic framework that describes this latter instability of Stokes waves in deep water is provided by the family of Akhmediev breather (AB) solutions of the nonlinear Schrödinger equation (NLS). It is indeed very convenient to use these exact pulsating envelopes particularly for laboratory experiments, since they allow to generate extreme waves at any location in space at any instant of time. As such, using this framework is more advantageous compared to the classical initialization of the unstable wave dynamics from a three wave system (main wave frequency and one pair of unstable sidebands). In this work, we report an experimental study on higher-order AB hydrodynamics that describe a higher-order stage of modulation instability, namely, starting from five wave systems (main wave frequency and two pairs of unstable sidebands). The corresponding laboratory experiments, that have been conducted in a large water wave facility, confirm the NLS wave dynamics forecast while boundary element method-based numerical wave tank simulations show a very good agreement with the experimental data.A.C. acknowledges the support from the Japan Society for the Promotion of Science (JSPS) and the Burgundy Region (France). A.C. and T.W. acknowledges the support from the Japan Society for the Promotion of Science (JSPS) through Grants-in-Aid for Scientific Research (KAKENHI). B.K. is thankful for support from French project PIA2/ISITE-BFC. N.A. acknowledges the support of the Australian Research Council (Discovery Project numbers DP140100265 and DP150102057) and support from the Volkswagen Stiftung

Editorial-The 4th International Workshop on Modeling the Ocean (IWMO 2012)

The 4th International Workshop on Modeling the Ocean (IWMO; http://www.jamstec.go.jp/frcgc/jcope/htdocs/e/ iwmo2012.html) was held on May 21–24, 2012 in the vibrant city of Yokohama on the Tokyo Bay, Japan. The Workshop was hosted by Japan Agency for Marine-Earth Science and Technology (JAMSTEC)—the home of the famous “Earth Simulator”—one of the world\u27s most powerful supercomputers dedicated for simulating the complex interactive processes of the earth and its environment

Observation of wave propagation over 1,000 km into Antarctica winter pack ice

A drifting wave-ice buoy, which was configured by mounting the OpenMetBuoy on an ad hoc floating platform that we named Medusa, was deployed at the L\"utzow-Holm Bay (LHB) marginal ice zone in Antarctica on 4 Feb 2022 during the 63rd Japanese Antarctica research expedition. The wave-ice buoy, Medusa-766, survived the Antarctica winter as the measurement duration reached 333 days. During the winter months, it was located deep in the ice cover with the shortest distance to the ice-free Southern Ocean over 1,000 km; at this time, there was evidence of ocean wave signals at the buoy position. Using the directional wave spectra obtained from the ECMWF's reanalysis, we show that the Medusa-766 observed waves were likely generated by an extratropical cyclone in the Southern Ocean. Wave-induced ice breakup potential for such an event could extend 100s km into the ice field. When Medusa-766 was in LHB in the summer months, it did not detect sizeable wave energy despite the low sea ice concentration extent even during on-ice waves events. Characterising the considerable differences in the wave attenuation at LHB is needed to elucidate the relative contribution of ocean waves to the unstable LHB fast ice. The success of Medusa-766 demonstrates the robustness of the general design, hardware, firmware, and the high sensitivity of the sensor used. The result is promising for future LHB wave-ice interaction research

Directional Soliton and Breather Beams

Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the uni-directional nonlinear Schr\"odinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite, consequently, a beam dynamics forms. Spatio-temporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D+1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose-Einstein condensates, plasma, hydrodynamics and optics

An affordable and customizable wave buoy for the study of wave-ice interactions: design concept and results from field deployments

In the polar regions, the interaction between waves and ice has a crucial impact on the seasonal change in the sea ice extent. However, our comprehension of this phenomenon is restricted by a lack of observations, which, in turn, results in the exclusion of associated processes from numerical models. In recent years, availability of the low-cost and accurate Inertial Motion Units has enabled the development of affordable wave research devices. Despite advancements in designing innovative open-source instruments optimized for deployment on ice floes, their customizability and survivability remain limited, especially in open waters. This study presents a novel design concept for an affordable and customizable wave buoy, aimed for wave measurements in marginal ice zones. The central focus of this wave buoy design is the application of 3D printing as rapid prototyping technology. By utilizing the high customizability offered by 3D printing, the previously developed solar-powered wave buoy was customized to install a battery pack to continue the measurements in the high latitudes for more than several months. Preliminary results from field deployments in the Pacific and Arctic Oceans demonstrate that the performance of the instruments is promising. The accuracy of frequency wave spectra measurements is found to be comparable to that of considerably more expensive instruments. Finally, the study concludes with a general evaluation of using rapid prototyping technologies for buoy designs and proposes recommendations for future designs

Fourier amplitude distribution and intermittency in mechanically generated surface gravity waves

We examine and discuss the spatial evolution of the statistical properties of mechanically generated surface gravity wave fields, initialized with unidirectional spectral energy distributions, uniformly distributed phases, and Rayleigh distributed amplitudes. We demonstrate that nonlinear interactions produce an energy cascade towards high frequency modes with a directional spread and trigger localized intermittent bursts. By analyzing the probability density function of Fourier mode amplitudes in the high frequency range of the wave energy spectrum, we show that a heavy-tailed distribution emerges with distance from the wave generator as a result of these intermittent bursts, departing from the originally imposed Rayleigh distribution, even under relatively weak nonlinear conditions

Observation of anomalous spectral downshifting of waves in the Okhotsk Sea Marginal Ice Zone

Waves in the Marginal Ice Zone in the Okhotsk Sea are less studied compared to the Antarctic and Arctic. In February 2020, wave observations were conducted for the first time in the Okhotsk Sea, during the observational program by Patrol Vessel Soya. A wave buoy was deployed on the ice, and in situ wave observations were made by a ship-borne stereo imaging system and Inertial Measurement Unit. Sea ice was observed visually and by aerial photographs by drone, while satellite synthetic aperture radar provided basin-wide spatial distribution. On 12 February, a swell system propagating from east northeast was detected by both the stereo imaging system and the buoy-on-ice. The wave system attenuated from 0.34 m significant wave height to 0.25 m in about 90 km, while the wave period increased from 10 s to 15–17 s. This anomalous spectral downshifting was not reproduced by numerical hindcast and by applying conventional frequency-dependent exponential attenuation to the incoming frequency spectrum. The estimated rate of spectral downshifting, defined as a ratio of momentum and energy losses, was close to that of uni-directional wave evolution accompanied by breaking dissipation: this indicates that dissipation-driven nonlinear downshifting may be at work for waves propagating in ice

Estimating the elastic modulus of landfast ice from wave observations

Progress in our understanding of wave–ice interactions is currently hindered by the lack of in situ observations and information of sea-ice properties, including the elastic modulus. Here, we estimate the effective elastic modulus of sea ice using observations of waves in ice through the deployment of three open-source geophone recorders on landfast sea ice. From observations of low-frequency dispersive waves, we obtain an estimate of the effective elastic modulus in the range of 0.4–0.7 GPa. This is lower than the purely elastic modulus of the ice estimated at 1 GPa as derived from in situ beam experiments. Importantly, our experimental observation is significantly lower than the default value currently in use in wave models. While our estimate is not representative for all sea ice, it does indicate that considerably more measurements are required to provide confidence in the development of parameterizations for this complex sea-ice property for wave models