Doubly periodic progressive permanent waves in deep water

Bryant, Peter J.

doi:10.1017/s0022112085002804

Cited by 28 publications

(34 citation statements)

References 12 publications

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“…Short-crested waves, as probably the simplest waves of permanent form that are two-dimensional, have received growing interest in experimental (Hammack, Scheffner & Segur 1989;Hammack et al 1995;Kimmoun, Branger & Kharif 1999;Hammack, Henderson & Segur 2005;Henderson, Patterson & Segur 2006;Henderson, Segur & Carter 2010), analytical (Roberts 1983;Bryant 1985;, 2012 and numerical (Chen & Liu 1995;Craig & Nicholls 2002;Fuhrman, Madsen & Bingham 2006;Nicholls & Reitich 2006;Xu & Guyenne 2009) investigations in recent years.…”

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confidence: 99%

On the existence of steady-state resonant waves in experiments

Liu

et al. 2014

J. Fluid Mech.

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This paper describes an experimental investigation of steady-state resonant waves. Several co-propagating short-crested wave trains are generated in a basin at the State Key Laboratory of Ocean Engineering (SKLOE) in Shanghai, and the wavefields are measured and analysed both along and normal to the direction of propagation. These steady-state resonant waves are first calculated theoretically under the exact resonance criterion with sufficiently high nonlinearity, and then are generated in the basin by means of the main wave components that contain at least 95 % of the wave energy. The steady-state wave spectra are quantitatively observed within the inherent system error of the basin and identified by means of a contrasting experiment. Both symmetrical and anti-symmetrical steady-state resonant waves are observed and the experimental and theoretical results show excellent agreement. These results offer the first experimental evidence of the existence of steady-state resonant waves with multiple solutions.

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confidence: 99%

On the existence of steady-state resonant waves in experiments

Liu

et al. 2014

J. Fluid Mech.

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“…Their strategy required that not only σ > 0 but also the absence of resonance (see § 2.2). Craig & Nicholls [23] extended these results with an application of the LyapunovSchmidt theory to (11) and noted that solutions come in surfaces rather than simply branches. Their analysis still required σ > 0 but permitted "finite" resonance (provided that p < ∞, see § 2.2).…”

Section: For Demonstrations)mentioning

confidence: 91%

“…Of particular interest for the simulation of the full Euler equations are: Schwartz [75] who studied two-dimensional traveling patterns via complex variable theory, the BIM of Schwartz & Vanden-Broeck [76], and the three-dimensional HOS simulations of Rienecker and Fenton [69]; Meiron, Saffman, and Yuen [48]; Roberts and Schwartz [72]; Saffman and Yuen [73]; and Bryant [11].…”

Section: Introductionmentioning

confidence: 99%

Boundary Perturbation Methods for Water Waves

Nicholls

2007

GAMM-Mitteilungen

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Key words Water waves, free-surface fluid flows, ideal fluid flows, boundary perturbation methods, spectral methods.The most successful equations for the modeling of ocean wave phenomena are the freesurface Euler equations. Their solutions accurately approximate a wide range of physical problems from open-ocean transport of pollutants, to the forces exerted upon oil platforms by rogue waves, to shoaling and breaking of waves in nearshore regions. These equations provide numerous challenges for theoreticians and practitioners alike as they couple the difficulties of a free boundary problem with the subtle balancing of nonlinearity and dispersion in the absence of dissipation. In this paper we give an overview of, what we term, "Boundary Perturbation" methods for the analysis and numerical simulation of this "water wave problem." Due to our own research interests this review is focused upon the numerical simulation of traveling water waves, however, the extensive literature on the initial value problem and additional theoretical developments are also briefly discussed.

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“…Roberts & Peregrine (1983) treated the important limit of grazing angles, where the short-crested deepwater waves become long-crested. Fully numerical computations have been performed by, for example, Bryant (1985), Craig & Nicholls (2002) and . In the present work we study the interaction of a monochromatic short-crested wave with a plane wave of another frequency, which is of similar fundamental interest, being the simplest extension beyond the monochromatic short-crested case.…”

Section: Third-order Theory For Multi-directional Irregular Wavesmentioning

confidence: 99%

Third-order theory for multi-directional irregular waves

Madsen

Fuhrman

2012

J. Fluid Mech.

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A new third-order solution for multi-directional irregular water waves in finite water depth is presented. The solution includes explicit expressions for the surface elevation, the amplitude dispersion and the vertical variation of the velocity potential. Expressions for the velocity potential at the free surface are also provided, and the formulation incorporates the effect of an ambient current with the option of specifying zero net volume flux. Harmonic resonance may occur at third order for certain combinations of frequencies and wavenumber vectors, and in this situation the perturbation theory breaks down due to singularities in the transfer functions. We analyse harmonic resonance for the case of a monochromatic short-crested wave interacting with a plane wave having a different frequency, and make long-term simulations with a high-order Boussinesq formulation in order to study the evolution of wave trains exposed to harmonic resonance.Key words: surface gravity waves, waves/free-surface flows IntroductionNonlinear irregular multi-directional water waves are commonly described to second order using the formulation by Sharma & Dean (1981). This is based on a double summation over all possible pairs of wave components, utilizing a second-order solution for bi-directional bichromatic waves as the kernel in the summation. In this work, we present a third-order analytical solution for trichromatic tri-directional waves, which is then used as the kernel in a triple summation over all triplets, plus a double summation over the relevant doublets. The outcome of this work is thus a third-order theory for multi-directional irregular waves in finite water depth, including the effect of ambient or wave-induced currents. The formulation is an extension of the work by Zhang & Chen (1999) from deep water to arbitrary depth, and from collinear interactions to multi-directional interactions. It is also an extension of the work by from third-order bi-directional bichromatic waves to multi-directional irregular waves. demonstrated the importance of accounting for third-order effects in boundary conditions for monochromatic short-crested waves in connection with numerical or laboratory experiments. They made numerical simulations using a high-order Boussinesq-type formulation and performed an analysis

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Doubly periodic progressive permanent waves in deep water

Cited by 28 publications

References 12 publications

On the existence of steady-state resonant waves in experiments

On the existence of steady-state resonant waves in experiments

Boundary Perturbation Methods for Water Waves

Third-order theory for multi-directional irregular waves

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