Detuning and wave breaking during nonlinear surface wave focusing

The evolution of unidirectional wave trains containing a wave that gradually becomes steep is evaluated experimentally and numerically using the Boundary Element Method (BEM). The boundary conditions for the nonlinear numerical simulations corresponded to the actual movements of the wavemaker paddle as recorded in the physical experiments, allowing direct comparison between the measured in experiments' characteristics of the wave train and the numerical predictions. The high level of qualitative and quantitative agreement between the measurements and simulations validated the kinematic criterion for the inception of breaking and the location of the spilling breaker, on the basis of the BEM computations and associated experiments. The breaking inception is associated with the fluid particle at the crest of the steep wave that has been accelerated to match and surpass the crest velocity. The previously observed significant slowdown of the crest while approaching breaking is verified numerically; both narrow-/broad-banded wave trains are considered. Finally, the relative importance of linear and nonlinear contributions is analyzed.

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“…9(d) (Multimedia view). 11,13 The position of the wave crest at the inception of breaking in this experiment was estimated as x exp br = 8.43 m.…”

Section: Fig 8 As Inmentioning

confidence: 99%

“…An additional energetic wave-breaking criterion was introduced in Refs. [11][12][13]. It is well established that geometric criteria that do not take into account the spectral shape are oversimplified to predict accurately the inception of breaking.…”

Section: Introductionmentioning

confidence: 99%

On the kinematic criterion for the inception of breaking in surface gravity waves: Fully nonlinear numerical simulations and experimental verification

Khait

Shemer

2018

Physics of Fluids

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“…As a general observation, the relative error of the theoretical Kelvin and Poincaré wave frequencies derived from the linear dispersion relation [14,49] decreases from the lateral boundary to the interior. The substantial mismatch between the theoretical linear frequencies and the experimental results might be related with nonlinear resonant interactions [51] and viscous detuning [5,26,29,31]. Therefore, one might expect that the basin-scale wavefield in regions closer to the lateral boundary is more susceptible to viscous and nonlinear detuning, since it is subject to stronger nonlinearities (steepening, nonhydrostatic and rotating-induced dispersion) than the interior wavefield.…”

Section: Discussionmentioning

confidence: 97%

“…It is possible that the shifts in peak frequencies in Fig. 4, with respect to theoretical frequencies, correspond to nonlinear and viscous detuning [5,26,29,31]. The analytical solution (2a) most likely also tells us something about the relative height/ strength of the excited modes, but we will not discuss it here.…”

Section: Near-lateral Boundary Gravity Wavefieldmentioning

confidence: 96%

Evolution and decay of gravity wavefields in weak-rotating environments: a laboratory study

2018

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Gravity waves are prominent physical features that play a fundamental role in transport processes of stratified aquatic ecosystems. In a two-layer stratified basin, the equations of motion for the first vertical mode are equivalent to the linearised shallow water equations for a homogeneous fluid. We adopted this framework to examine the spatiotemporal structure of gravity wavefields weakly affected by the background rotation of a single-layer system of equivalent thickness h , via laboratory experiments performed in a cylindrical basin mounted on a turntable. The wavefield was generated by the release of a diametral linear tilt of the air-water interface, , inducing a basin-scale perturbation that evolved in response to the horizontal pressure gradient and the rotation-induced acceleration. The basin-scale wave response was controlled by an initial perturbation parameter,  * = 0 ∕h , where 0 was the initial displacement of the air-water interface, and by the strength of the background rotation controlled by the Burger number, . We set the experiments to explore a transitional regime from moderate-to weak-rotational environments, 0.65 ≤  ≤ 2 , for a wide range of initial perturbations, 0.05 ≤  * ≤ 1.0. The evolution of was registered over a diametral plane by recording a laser-induced optical fluorescence sheet and using a capacitive sensor located near the lateral boundary. The evolution of the gravity wavefields showed substantial variability as a function of the rotational regimes and the radial position. The results demonstrate that the strength of rotation and nonlinearities control the bulk decay rate of the basin-scale gravity waves. The ratio between the experimentally estimated damping timescale, T d , and the seiche period of the basin, T g , has a median value of T d ∕T g ≈ 11 , a maximum value of T d ∕T g ≈ 10 3 and a minimum value of T d ∕T g ≈ 5. The results of this study are significant for the understanding the dynamics of gravity waves in waterbodies weakly affected by Coriolis acceleration, such as mid-to small-size lakes.

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“…Il est important de souligner que le déferlement sur la pente empêche la focalisation parfaite, ce qui n'est pas l'objectif ultime de ce travail (WHITTAKER et al, 2017). La présence de la pente et le phénomène de focalisation prématurée (LIU et al, 2016) [12.13 ; 12.81] [12.07 ; 12.69] Thème 1 -Hydrodynamique côtière…”

Section: Matérielunclassified

Etude expérimentale de la propagation des trains d'ondes en zone côtière

Abroug¹,

Abcha²,

Jarno³

et al. 2020

XVIèmes Journées, Le Havre

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Notre travail repose sur une étude expérimentale de la propagation des trains d'ondes fortement non-linéaires se propageant en eau intermédiaire vers la zone côtière. Trois méthodes de génération ont été employées. Ces méthodes dépendent du spectre à partir duquel les trains d'ondes sont construits. Il s'agit du spectre gaussien, spectre de Pierson-Moskowitz et spectre de JONSWAP. Les essais ont été réalisés dans le canal à houle du laboratoire M2C (UMR 6143 Caen). Les signaux obtenus par les sondes résistives sont utilisés pour la détermination de l'évolution spatiale des transferts énergétiques et des interactions non-linéaires entre les composantes fréquentielles. Un partitionnement spectral a été effectué sur chaque spectre de référence pour quantifier les variations spatiales de l'énergie dans chaque gamme de fréquences. Des transferts énergétiques en amont et en aval de déferlement ont été mis en évidence et ensuite quantifiés. Une approche bispectrale par ondelettes a été utilisée dans le but de quantifier les interactions non-linéaires entre les composantes fréquentielles grâce à un paramètre appelé bicohérence. Au cours de la propagation, ce paramètre augmente progressivement et atteint des valeurs proches de 1 au moment du déferlement et décroit drastiquement en aval de ce déferlement.

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Detuning and wave breaking during nonlinear surface wave focusing

Cited by 18 publications

References 33 publications

On the kinematic criterion for the inception of breaking in surface gravity waves: Fully nonlinear numerical simulations and experimental verification

On the kinematic criterion for the inception of breaking in surface gravity waves: Fully nonlinear numerical simulations and experimental verification

Evolution and decay of gravity wavefields in weak-rotating environments: a laboratory study

Etude expérimentale de la propagation des trains d'ondes en zone côtière

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