On dispersion of directional surface gravity waves

Taklo, Tore Magnus Arnesen; Trulsen, Karsten; Krogstad, Harald E.; Borge, José Carlos Nieto

doi:10.1017/jfm.2016.817

Cited by 9 publications

(5 citation statements)

References 26 publications

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“…However, for the long-crested increased-amplitude wave groups in figure 20, the groups exhibit horizontal asymmetry. Here, the dispersion of the free waves is affected by cubic nonlinearity, shifting the location at which the waves focus, as also observed by Taklo et al (2017), among others. As discussed in § 3.3, this will not affect the extraction of the measured wave-averaged surface elevation, but will introduce a phase shift.…”

Section: Appendix D Measured Time Seriessupporting

confidence: 62%

The set-down and set-up of directionally spread and crossing surface gravity wave groups

et al. 2017

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For sufficiently directionally spread surface gravity wave groups, the set-down of the wave-averaged free surface, first described by Longuet-Higgins and Stewart (J. Fluid Mech. vol. 13, 1962, pp. 481-504), can turn into a set-up. Using a multiple-scale expansion for two crossing wave groups, we examine the structure and magnitude of this wave-averaged set-up, which is part of a crossing wave pattern that behaves as a modulated partial standing wave: in space, it consists of a rapidly varying standing-wave pattern slowly modulated by the product of the envelopes of the two groups; in time, it grows and decays on the slow time scale associated with the translation of the groups. Whether this crossing wave pattern actually enhances the surface elevation at the point of focus depends on the phases of the linear wave groups, unlike the set-down, which is always negative and inherits the spatial structure of the underlying envelope(s). We present detailed laboratory measurements of the wave-averaged free surface, examining both single wave groups, varying the degree of spreading from small to very large, and the interaction between two wave groups, varying both the degree of spreading and the crossing angle between the groups. In both cases, we find good agreement between the experiments, our simple expressions for the set-down and set-up, and existing second-order theory based on the component-by-component interaction of individual waves with different frequencies and directions. We predict and observe a set-up for wave groups with a Gaussian angular amplitude distribution with standard deviations of above 30-40• (21-28 • for energy spectra), which is relatively large for realistic sea states, and for crossing sea states with angles of separation of 50-70• and above, which are known to occur in the ocean.

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Section: Appendix D Measured Time Seriessupporting

confidence: 62%

The set-down and set-up of directionally spread and crossing surface gravity wave groups

et al. 2017

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“…Various theoretical and experimental works have been devoted to this question, see e.g. 5 , 36 , 41 – 47 . For water tanks equipped with transparent side walls, cameras may be used to record the full spatio-temporal dynamics 23 .…”

Section: Discussionmentioning

confidence: 99%

Nonlinear dispersion relation in integrable turbulence

Tikan

Bonnefoy

Ducrozet

et al. 2022

Sci Rep

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We investigate numerically and experimentally the concept of nonlinear dispersion relation (NDR) in the context of partially coherent waves propagating in a one-dimensional water tank. The nonlinear random waves have a narrow-bandwidth Fourier spectrum and are described at leading order by the one-dimensional nonlinear Schrödinger equation. The problem is considered in the framework of integrable turbulence in which solitons play a key role. By using a limited number of wave gauges, we accurately measure the NDR of the slowly varying envelope of the deep-water waves. This enables the precise characterization of the frequency shift and the broadening of the NDR while also revealing the presence of solitons. Moreover, our analysis shows that the shape and the broadening of the NDR provides signatures of the deviation from integrable turbulence that is induced by high order effects in experiments. We also compare our experimental observations with numerical simulations of Dysthe and of Euler equations.

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“…Various theoretical and experimental works have been devoted to this question, see e.g. [3,22,[26][27][28][29][30][31][32]. The central point of our strategy is to remove the carrier wave frequency in order to retrieve the NDR of the slowly varying envelope.…”

Section: C)mentioning

confidence: 99%