Experimental evidence of a hydrodynamic soliton gas

We report on an experimental realization of a bi-directional soliton gas in a 34~m-long wave flume in shallow water regime. We take advantage of the fission of a sinusoidal wave to inject continuously solitons that propagate along the tank, back and forth. Despite the unavoidable damping, solitons retain adiabatically their profile, while decaying. The outcome is the formation of a stationary state characterized by a dense soliton gas whose statistical properties are well described by a pure integrable dynamics. The basic ingredient in the gas, i.e. the two-soliton interaction, is studied in details and compared favourably with the analytical solutions of the Kaup-Boussinesq integrable equation. High resolution space-time measurements of the surface elevation in the wave flume provide a unique tool for studying experimentally the whole spectrum of excitations.Comment: accepted for publication in Physical Review Letter

Experimental study of integrable turbulence in shallow water

We analyze a set of bidirectional wave experiments in a linear wave flume of which some are conducive to integrable turbulence. In all experiments the wavemaker forcing is sinusoidal and the wave motion is recorded by seven high-resolution side-looking cameras. The periodic scattering transform is implemented and power spectral densities computed to discriminate linear wave motion states from integrable turbulence and soliton gas. Values of the wavemaker forcing Ursell number and relative amplitude are required to be above some threshold values for the integral turbulence to occur. Despite the unavoidable slow damping, soliton gases achieve stationary states because of the continuous energy input by the wavemaker. The statistical properties are given in terms of probability density distribution, skewness and kurtosis. The route to integrable turbulence, by the disorganization of the wavemaker induced sinusoidal wave motion, depends on the non-linearity of the waves but equally on the amplitude amplification and reduction due to the wavemaker feedback on the wave field

Impact of dissipation on the energy spectrum of experimental turbulence of gravity surface waves

We discuss the impact of dissipation on the development of the energy spectrum in wave turbulence of gravity surface waves with emphasis on the effect of surface contamination. We performed experiments in the Coriolis facility which is a 13-m diameter wave tank. We took care of cleaning surface contamination as well as possible considering that the surface of water exceeds 100~m$^2$. We observe that for the cleanest condition the frequency energy spectrum shows a power law decay extending up to the gravity capillary crossover (14 Hz) with a spectral exponent that is increasing with the forcing strength and decaying with surface contamination. Although slightly higher than reported previously in the literature, the exponent for the cleanest water remains significantly below the prediction from the Weak Turbulence Theory. By discussing length and time scales, we show that weak turbulence cannot be expected at frequencies above 3 Hz. We observe with a stereoscopic reconstruction technique that the increase with the forcing strength of energy spectrum beyond 3~Hz is mostly due to the formation and strenghtening of bound waves.Comment: accepted for publication in Physical Review Fluid

Experimental study of integrable turbulence in shallow water

La turbulence d'onde est un état statistique impliquant un grand nombre d'ondes couplées par effet non linéaire. Cet état générique est potentiellement décrit, dans la limite de faible non linéarité, par la théorie de la turbulence faible. Cette théorie prédit un phénoménologie proche de celle de la turbulence hydrodynamique avec en particulier une cascade d'énergie au travers des échelles. La thèse de doctorat se concentrera sur le cas d'ondes de gravité-capillarité à la surface d'un fluide dans la limite des grandes longueurs d'onde. Ce système est potentiellement représentatif d'états de mer lorsque la houle est développée. Des expériences seront menées dans le canal à Houle 1D de 36m du LEGI. Le cas des ondes unidirectionnelles est assez particulier dans le cadre général de la théorie de la turbulence faible. En effet il est prédit que la turbulence faible est instable dans ces conditions et que l'on devrait observer plutôt l'apparence de structures cohérentes de type soliton. Au cours de cette thèse, on testera différentes conditions de forçage pour tester les prédictions théoriques concernant les cascades d'énergie et de quantité de mouvement. On sortira également du cadre strict de la théorie pour étudier des régimes de forçage fort ou de faible profondeuIn the present PhD program, we will focus on the case of 1D surface gravity waves. This situation is related to the case of the swell observed in the ocean that shows usually a quasi unidirectional propagation. Wave turbulence in 1D shows fundamental particularities that are somewhat exotic depending on whetherthe wave propagation is uni or bi directional. Energy can cascade towards small scales or in contrast to large scales;weak turbulence can become unstable and lead to formation of solitons... Wave turbulence in 1D is a potentially veryrich framework related to oceanic issues.During this PhD, the graduatestudent will have to setup experiments in the 1D wave flume of theLEGI. This flume is 36 m long and it is currently used to study the sedimentdynamics in the vicinity of the shore(see picture). The student willdevelop a new scheme to generate and control the waves and a 2Dimagingsystem to record the free surface displacementin a way that isresolved both in time and space. For control purposes, additional ultrasoniclocal measurements of the surface displacement will be performed. Itwill then be possible to study in a very fine way, the weak or strong non-linearcouplings between waves, and perform advanced comparisons betweentheory and experiments. The student will also be associated to the otherstudies of the WATU project, in particular to share the measurement and data analysis techniques and so that to compare results among various configurations

Etude expérimentale de la turbulence intégrable en eau peu profonde

In the present PhD program, we will focus on the case of 1D surface gravity waves. This situation is related to the case of the swell observed in the ocean that shows usually a quasi unidirectional propagation. Wave turbulence in 1D shows fundamental particularities that are somewhat exotic depending on whetherthe wave propagation is uni or bi directional. Energy can cascade towards small scales or in contrast to large scales;weak turbulence can become unstable and lead to formation of solitons... Wave turbulence in 1D is a potentially veryrich framework related to oceanic issues.During this PhD, the graduatestudent will have to setup experiments in the 1D wave flume of theLEGI. This flume is 36 m long and it is currently used to study the sedimentdynamics in the vicinity of the shore(see picture). The student willdevelop a new scheme to generate and control the waves and a 2Dimagingsystem to record the free surface displacementin a way that isresolved both in time and space. For control purposes, additional ultrasoniclocal measurements of the surface displacement will be performed. Itwill then be possible to study in a very fine way, the weak or strong non-linearcouplings between waves, and perform advanced comparisons betweentheory and experiments. The student will also be associated to the otherstudies of the WATU project, in particular to share the measurement and data analysis techniques and so that to compare results among various configurations.La turbulence d'onde est un état statistique impliquant un grand nombre d'ondes couplées par effet non linéaire. Cet état générique est potentiellement décrit, dans la limite de faible non linéarité, par la théorie de la turbulence faible. Cette théorie prédit un phénoménologie proche de celle de la turbulence hydrodynamique avec en particulier une cascade d'énergie au travers des échelles. La thèse de doctorat se concentrera sur le cas d'ondes de gravité-capillarité à la surface d'un fluide dans la limite des grandes longueurs d'onde. Ce système est potentiellement représentatif d'états de mer lorsque la houle est développée. Des expériences seront menées dans le canal à Houle 1D de 36m du LEGI. Le cas des ondes unidirectionnelles est assez particulier dans le cadre général de la théorie de la turbulence faible. En effet il est prédit que la turbulence faible est instable dans ces conditions et que l'on devrait observer plutôt l'apparence de structures cohérentes de type soliton. Au cours de cette thèse, on testera différentes conditions de forçage pour tester les prédictions théoriques concernant les cascades d'énergie et de quantité de mouvement. On sortira également du cadre strict de la théorie pour étudier des régimes de forçage fort ou de faible profonde

Experimental investigation of 1D surface gravity wave turbulence

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The Energy Cascade of Surface Wave Turbulence: Toward Identifying the Active Wave Coupling

International audienceWe investigate experimentally turbulence of surface gravity waves in the Coriolis facility in Grenoble by using both high sensitivity local probes and a time and space resolved stereoscopic reconstruction of the water surface. We show that the water deformation is made of the superposition of weakly nonlinear waves following the linear dispersion relation and of bound waves resulting from non resonant triadic interaction. Although the theory predicts a 4-wave resonant coupling supporting the presence of an inverse cascade of wave action, we do not observe such inverse cascade. We investigate 4-wave coupling by computing the tricoherence i.e. 4-wave correlations. We observed very weak values of the tricoherence at the frequencies excited on the linear dispersion relation that are consistent with the hypothesis of weak coupling underlying the weak turbulence theory

The Energy Cascade of Surface Wave Turbulence: Toward Identifying the Active Wave Coupling

International audienceWe investigate experimentally turbulence of surface gravity waves in the Coriolis facility in Grenoble by using both high sensitivity local probes and a time and space resolved stereoscopic reconstruction of the water surface. We show that the water deformation is made of the superposition of weakly nonlinear waves following the linear dispersion relation and of bound waves resulting from non resonant triadic interaction. Although the theory predicts a 4-wave resonant coupling supporting the presence of an inverse cascade of wave action, we do not observe such inverse cascade. We investigate 4-wave coupling by computing the tricoherence i.e. 4-wave correlations. We observed very weak values of the tricoherence at the frequencies excited on the linear dispersion relation that are consistent with the hypothesis of weak coupling underlying the weak turbulence theory

Identifying four-wave-resonant interactions in a surface gravity wave turbulence experiment

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