The surface signature of internal waves

Craig, Walter; Guyenne, Philippe; Sulem, Catherine

doi:10.1017/jfm.2012.364

Cited by 45 publications

(77 citation statements)

References 28 publications

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“…However, in a related problem, Craig et al [26] highlighted the physical relevance of resonance between internal and surface waves in a two-layer ocean when the speeds are different, and a similar study may be performed in the present configuration.…”

Section: Results (A) One Elastic Platementioning

confidence: 74%

Solitary interfacial hydroelastic waves

Părău¹

2017

Phil. Trans. R. Soc. A.

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Solitary waves travelling along an elastic plate present between two fluids with different densities are computed in this paper. Different two-dimensional configurations are considered: the upper fluid can be of infinite extent, bounded by a rigid wall or under a second elastic plate. The dispersion relation is obtained for each case and numerical codes based on integro-differential formulations for the full nonlinear problem are derived.

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Section: Results (A) One Elastic Platementioning

confidence: 74%

Solitary interfacial hydroelastic waves

Părău¹

2017

Phil. Trans. R. Soc. A.

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“…These reduced models mostly focus on either the dynamics of short-mode waves around the resonant k res at sufficiently long times or the linear modulations and the traveling wave solutions for short-mode surface waves. A particularly detailed prior discussion of surface signature phenomena was presented in (Craig et al 2012) using a coupled Korteweg-de Vries (KdV) and linear Schrödinger model (we compare this model with ours in appendix D). However, an intuitive understanding of the surface signature phenomena was still lacking, especially for the asymmetric behavior of SWs at the leading and trailing edges.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…(ii) Resonant excitations: The rough region travels along with the internal wave; that is, the SW group velocity is close to the internal-wave phase velocity (Osborne & Burch 1980;Kropfli et al 1999;Hwung et al 2009;Craig et al 2012). To understand the above two surface phenomena, we numerically study the surfacewave and interfacial-wave (IW) manifestation in a two-layer, density-stratified system using a weakly nonlinear Boussinesq-type model.…”

Section: Introductionmentioning

confidence: 99%

Modulation-resonance mechanism for surface waves in a two-layer fluid system

et al. 2019

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We propose a Boussinesq-type model to study the surface/interfacial wave manifestation of an underlying, slowly-varying, long-wavelength, baroclinic flow in a two-layer, density-stratified system. The results of our model show numerically that, under strong nonlinearity, surface waves, with their typical wavenumber being the resonant k res , can be generated locally at the leading edge of the underlying slowly-varying, long-wavelength baroclinic flow. Here, the resonant k res satisfies the class 3 triad resonance condition among two short-mode waves and one long-mode wave in which all waves propagate in the same direction. Moreover, when the slope of the baroclinic flow is sufficiently small, only one spatially-localized large-amplitude surface wave packet can be generated at the leading edge. This localized surface wave packet becomes high in amplitude and large in group velocity after the interaction with its surrounding waves. These results are qualitatively consistent with various experimental observations including resonant surface waves at the leading edge of an internal wave. Subsequently, we propose a mechanism, referred to as the modulation-resonance mechanism, underlying these surface phenomena, based on our numerical simulations. The proposed modulation-resonance mechanism combines the linear modulation (ray-based) theory for the spatiotemporal asymmetric behavior of surface waves and the nonlinear class 3 triad resonance theory for the energy focusing of surface waves around the resonant wavenumber k res in Fourier space.

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“…Class 3 triad resonance is believed to be responsible for the surface signature of the underlying internal waves [17,29,35,38]. The TWN model possesses two-mode waves, one slow and the other fast, and thus resonant interactions among different modes can occur during the energy exchange process [more details can be found in Appendix B].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…(3.31). Many early results [1,16,17,27,41] have confirmed that there exists a unique resonant wavenumber, denoted by k res , satisfying Eq. (2.50) in the two-layer fluid system.…”

Section: B Class 3 Triad Resonance Conditionmentioning

confidence: 99%

Asymmetric behavior of surface waves induced by an underlying interfacial wave

Jiang

Kovačič

Zhou

2019

Communications in Mathematical Sciences

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We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. We show that interfacial solitary-wave solutions of this model can capture the ubiquitous broadening of large-amplitude internal waves in the ocean. In addition, the model is capable of capturing three asymmetric behaviors of surface waves: (i) Surface waves become short in wavelength at the leading edge and long at the trailing edge of an underlying interfacial solitary wave. (ii) Surface waves propagate towards the trailing edge with a relatively small group velocity, and towards the leading edge with a relatively large group velocity. (iii) Surface waves become high in amplitude at the leading edge and low at the trailing edge. These asymmetric behaviors can be well quantified in the theoretical framework of ray-based theories. Our model is relatively easily tractable both theoretically and numerically, thus facilitating the understanding of the surface signature of the observed internal waves.

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The surface signature of internal waves

Cited by 45 publications

References 28 publications

Solitary interfacial hydroelastic waves

Solitary interfacial hydroelastic waves

Modulation-resonance mechanism for surface waves in a two-layer fluid system

Asymmetric behavior of surface waves induced by an underlying interfacial wave

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