The Cnoidal Theory Of Water Waves

Fenton, John D.

doi:10.1016/b978-088415380-1/50021-2

Cited by 9 publications

(8 citation statements)

References 23 publications

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“…ultra shallow water waves, we have used the cnoidal wave model (Fenton, 1998), consistently with what had been done in the work of Xie (2013);…”

Section: Methodsmentioning

confidence: 98%

“…They represent the solution of the Kortweg and deVries equation and in the limit of infinite wavelength, the cnoidal wave becomes a solitary wave. From the mathematical point of view, the complete solution has been given in terms of rational numbers (Fenton, 1998). We refer to this work in the following definitions.…”

Section: Problem Formulationmentioning

confidence: 99%

“…9 with the relevant symbols. The left boundary acts as a wavemaker where the cnoidal wave model of Fenton (1998) is applied in order to reproduce the waves with parameters given in Table 3. They propagate initially in a constant depth of 0.4 m with a wavelength of 3.70 and 10.76 m for the spilling and plunging breaker respectively.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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Numerical simulations of 2-D steady and unsteady breaking waves

Lupieri

Contento

2015

Ocean Engineering

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“…ultra shallow water waves, we have used the cnoidal wave model (Fenton, 1998), consistently with what had been done in the work of Xie (2013);…”

Section: Methodsmentioning

confidence: 98%

Section: Problem Formulationmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

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Numerical simulations of 2-D steady and unsteady breaking waves

Lupieri

Contento

2015

Ocean Engineering

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“…The coordinate system is the same as in the experimental study. The water surface elevation and the kinematics in the wave generation zone are specified using the 5th-order cnoidal wave theory presented by Fenton (1999). The incident wave height and period of the Cnoidal waves are H = 0.125m and T = 2.0s in the horizontal bed region.…”

Section: Computational Set-upmentioning

confidence: 99%

Breaking characteristics and geometric properties of spilling breakers over slopes

Chella

Bihs

Myrhaug

et al. 2015

Coastal Engineering

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A two-phase flow CFD model based on the Reynolds-Averaged Navier-Stokes (RANS) equations coupled with the level set method (LSM) and k − ω turbulence model is used to simulate spilling breakers over a sloping bed. In order to validate the present numerical model, the simulated results are compared with the experimental data measured by Ting and Kirby (1996). The simulated horizontal velocities and free surface elevations are in good agreement with the experimental measurements. Moreover, the present model is able to model the prominent features associated with the breaking process such as the motion of air pockets in the water, formation of a forward moving jet, the splash-up phenomenon and the mixing of air and water in the breaking region. The numerical model has been utilized to study the influences of three important environmental parameters; water depth, offshore wave steepness and beach slope on the characteristics and geometric properties of spilling breakers over slopes. A total of 39 numerical experiment cases are performed to investigate the characteristics of breaking waves such as breaking location, incipient breaker height and water depth at breaking, incipient breaker indices and geometric properties with different offshore wave steepnesses at different water depths over a wide range of beach slopes. The geometric properties associated with breaking waves in shallow water are described using the wave steepness and asymmetry factors introduced by Kjeldsen and Myrhaug (1978). The computed results appear to give reasonable predictions and consistency with previous studies.

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“…To address the problem described above, where the Fourier spectrum becomes broad for long waves, Fenton (1995) introduced a variant of the above methods, using cnoidal functions as the fundamental means of approximation, so that very long waves could be treated without any special measures. It was found that the method could be used for waves whose length is greater than eight times the water depth, and gave accurate results for all waves longer than this.…”

Section: Numerical Cnoidal Theorymentioning

confidence: 99%

Numerical Methods for Nonlinear Waves

Fenton¹

1999

Advances in Coastal and Ocean Engineering

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This Chapter gives a survey of numerical methods for solving fully-nonlinear problems of wave propagation in coastal and ocean engineering. While low-order theory may give insight, for accurate answers fully-nonlinear methods are becoming the norm. Such methods are often simpler than traditional methods, partly because the full equations are simpler than some of the approximations which are widely used. A lengthy description of the Fourier approximation method is given, which is the standard numerical method used to solve the problem of steadily-propagating waves. This may be used to provide an approximate solution for waves in rather more general situations, or, as is often the case, to give initial conditions for methods which go on to simulate the propagation of waves over more general topography. The family of such propagation methods is then described, including Lagrangian methods, marker-and-cell methods, finite difference methods-including some exciting recent developments, boundary integral equation methods, spectral methods, Green-Naghdi Theory, and local polynomial approximation. Finally a review is given of methods for analysing laboratory and field data and extracting wave information.

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The Cnoidal Theory Of Water Waves

Cited by 9 publications

References 23 publications

Numerical simulations of 2-D steady and unsteady breaking waves

Numerical simulations of 2-D steady and unsteady breaking waves

Breaking characteristics and geometric properties of spilling breakers over slopes

Numerical Methods for Nonlinear Waves

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