Nonlinear transient water waves—part I. A numerical method of computation with comparisons to 2-D laboratory data

Johannessen, Thomas B.; Swan, Chris

doi:10.1016/s0141-1187(97)00037-0

Cited by 32 publications

(15 citation statements)

References 12 publications

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“…This is in keeping with Baldock et al who found that second-order theory gave better predictions than linear theory for focused wave groups. It should be noted that Johannessen and Swan [32] have simulated the same cases and obtained very similar results using an extension of Fenton and Rienecker's [33] non-linear wave propagation model.…”

Section: Focused Wavementioning

confidence: 64%

Numerical wave tank based on a σ‐transformed finite element inviscid flow solver

Turnbull

Borthwick

Taylor

2003

Numerical Methods in Fluids

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SUMMARYInviscid two-dimensional free surface wave motions are simulated using a -transformed ÿnite-element model based on potential theory for irrotational, incompressible uid ow over a at ÿxed bed. The free surface boundary condition is fully non-linear, and so non-linear e ects up to very high order can be modelled. The -transformation involves linear stretching of the mesh between the bed and free surface. This has two major advantages. First, remeshing due to the moving free surface is avoided. Second, the mesh nodes are aligned vertically, allowing a high order calculation of the free surface vertical velocity component to be implemented without smoothing, except for very steep waves. The model however is further restricted to non-overturning, non-breaking waves because of the uniqueness of the -transformation. Excellent agreement is obtained with analytical and alternative numerical data for small amplitude free sloshing in a rectangular tank and forced sloshing in a horizontally baseexcited rectangular tank. At higher amplitudes, non-linear e ects are evident in the simulations by the present numerical model. The model is also able to reproduce steep progressive waves due to a wave-maker in agreement with Stokes 5th theory, second-order shallow water waves in agreement with cnoidal theory, and focused wave groups that match the experimental measurements acquired by Baldock et al. [A laboratory study of non-linear surface waves on water.

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Section: Focused Wavementioning

confidence: 64%

Numerical wave tank based on a σ‐transformed finite element inviscid flow solver

Turnbull

Borthwick

Taylor

2003

Numerical Methods in Fluids

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“…The knowledge of the underlying wave particle kinematics beneath the largest wave crests represents key information appropriate to the determination of the design loading (Smith & Swan, 2002). Johannessen & Swan (1997) showed that water particle kinematics is strongly dependent upon the nonlinear wave-wave interaction.…”

Section: Fully Nonlinear Models Of the Extreme Wavesmentioning

confidence: 99%

Physical mechanisms of the rogue wave phenomenon

Kharif

Pelinovsky

2003

European Journal of Mechanics - B/Fluids

993

764

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Abstract:A review of physical mechanisms of the rogue wave phenomenon is given. The data of marine observations as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. Simple statistical analysis of the rogue wave probability based on the assumption of a Gaussian wave field is reproduced. In the context of water wave theories the probabilistic approach shows that numerical simulations of freak waves should be made for very long times on large spatial domains and large number of realizations. As linear models of freak waves the following mechanisms are considered: dispersion enhancement of transient wave groups, geometrical focusing in basins of variable depth, and wave-current interaction. Taking into account nonlinearity of the water waves, these mechanisms remain valid but should be modified. Also, the influence of the nonlinear modulational instability (BenjaminFeir instability) on the rogue wave occurence is discussed. Specific numerical simulations were performed in the framework of classical nonlinear evolution equations: the nonlinear Schrödinger equation, the Davey -Stewartson system, the Korteweg -de Vries equation, the Kadomtsev -Petviashvili equation, the Zakharov equation, and the fully nonlinear potential equations. Their results show the main features of the physical mechanisms of rogue wave phenomenon.

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“…Even with a large number of frequency components, instead of generating them at the wavemaker in a random fashion, a frequency focusing technique is often used for a large peak to form at a prescribed location ͑Johan-nessen and Swan, [31][32][33] Shemer et al, 34 and Tian et al 15 ͒. A relatively less number of attempts have been made to validate nonlinear wave models with laboratory experiments for the evolution of true broadband irregular waves, in particular, when the wave steepness is finite.…”

Section: Introductionmentioning

confidence: 99%

A numerical and experimental study on the nonlinear evolution of long-crested irregular waves

Goullet

Choi

2011

Physics of Fluids

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The spatial evolution of nonlinear long-crested irregular waves characterized by the JONSWAP spectrum is studied numerically using a nonlinear wave model based on a pseudospectral ͑PS͒ method and the modified nonlinear Schrödinger ͑MNLS͒ equation. In addition, new laboratory experiments with two different spectral bandwidths are carried out and a number of wave probe measurements are made to validate these two wave models. Strongly nonlinear wave groups are observed experimentally and their propagation and interaction are studied in detail. For the comparison with experimental measurements, the two models need to be initialized with care and the initialization procedures are described. The MNLS equation is found to approximate reasonably well for the wave fields with a relatively smaller Benjamin-Feir index, but the phase error increases as the propagation distance increases. The PS model with different orders of nonlinear approximation is solved numerically, and it is shown that the fifth-order model agrees well with our measurements prior to wave breaking for both spectral bandwidths.

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Nonlinear transient water waves—part I. A numerical method of computation with comparisons to 2-D laboratory data

Cited by 32 publications

References 12 publications

Numerical wave tank based on a σ‐transformed finite element inviscid flow solver

Numerical wave tank based on a σ‐transformed finite element inviscid flow solver

Physical mechanisms of the rogue wave phenomenon

A numerical and experimental study on the nonlinear evolution of long-crested irregular waves

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