Nonlinear Four-Wave Interactions and Freak Waves

Janssen, Peter A. E. M.

doi:10.1175/1520-0485(2003)33<863:nfiafw>2.0.co;2

Cited by 663 publications

(746 citation statements)

References 33 publications

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“…Another important parameter characterizing the spectrum of the surface elevation at a fixed time, P (k, t), is the Benjamin-Feir index, BFI(t). Following Janssen [15], we define this parameter as…”

Section: Random Initial Datamentioning

confidence: 99%

“…Also in this case results are available from both laboratory experiments [25,29] and numerical simulations [15,33,12,28,32,36]. A central finding of such studies consists of the intensification of extreme wave activity for high values of the Benjamin-Feir index (see § 2.1), i.e., when the power spectrum of the surface elevation is sharply peaked around the fundamental wavenumber.…”

Section: Introductionmentioning

confidence: 99%

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Emergence of coherent wave groups in deep-water random sea

et al. 2013

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Section: Random Initial Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Emergence of coherent wave groups in deep-water random sea

et al. 2013

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“…While non-resonating components are bounded in time and receive only a limited pulse of energy from the primary components, the resonating components can receive a continuing energy transfer until they reach the level of the primary components. This is the key mechanism in the long-term evolution of wave spectra in the ocean, and the seminal work by Phillips (1960) had a major impact on the formulation of wave evolution models, such as Hasselmann (1962), Zakharov (1968), Krasitskii (1994) and Janssen (2003). Roberts (1981Roberts ( , 1983 identified the resonating higher harmonics for short-crested waves, and he found the resonances to be densely distributed but of relatively high P. A.…”

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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“…Recent work by Janssen (2003) suggests that quasi-resonant four-wave interactions play a major role in uni-directional wave field, in relation to the development of modulational instabilities and the occurrence of freak waves. Yet unclear is the role of non-resonant interactions in two-dimensional cases.…”

Section: Theorymentioning

confidence: 99%

Wave modelling – The state of the art

Cavaleri¹,

Alves²,

Ardhuin³

et al. 2007

Progress in Oceanography

462

177

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This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered.The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, non-linear interactions in deep water; 4, white-capping dissipation; 5, non-linear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments. Keywords

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Nonlinear Four-Wave Interactions and Freak Waves

Cited by 663 publications

References 33 publications

Emergence of coherent wave groups in deep-water random sea

Emergence of coherent wave groups in deep-water random sea

Third-order theory for multi-directional irregular waves

Wave modelling – The state of the art

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