On the nonlinear dynamics of wave groups produced by the focusing of surface–water waves

Johannessen, Thomas B.; Swan, Chris

doi:10.1098/rspa.2002.1028

Cited by 53 publications

(45 citation statements)

References 28 publications

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“…In this latter case the energy transfers occur in a random sea and are characterized as being extremely slow, a small percentage of the total energy being transferred over hundreds of wave cycles. In contrast, Johannessen & Swan (2003) and Gibson & Swan (2007) showed that, in a deep-water-focused wave group, with the phasing far from random but the surface profile believed to be representative of an extreme wave event, the local nonlinearity is such that the third-order resonant interactions can be responsible for highly localized and very rapid energy transfers. In this case, significant energy transfers can occur over 5-10 wave cycles immediately preceding the extreme wave event.…”

Section: Introductionmentioning

confidence: 99%

“…In each case the time variation in the second-order correction to the maximum crest elevation, expressed as a percentage of the linearly predicted h max , is described on the right-hand axis. Earlier deep-water work (Johannessen & Swan 2003) suggests that, provided this percentage is less than 2 per cent, initial conditions defined by a simple linear solution were adequate. Unfortunately, this approach was based upon simplified laboratory spectra that were both relatively narrow-banded and truncated at the high-frequency end.…”

Section: Applications In Water Of Finite Depthmentioning

confidence: 99%

“…In previous work, notably Johannessen & Swan (2003) and Gibson & Swan (2007), third-order modifications to the free-wave regime corresponding to resonant or near-resonant interactions were identified by considering the difference between focused and inverse-focused wave groups, where the latter correspond to the focusing of wave troughs rather than wave crests and are simply achieved by inverting the input signal. If h c (x, t) corresponds to the focusing of wave crests at x = t = 0 and h t (x, t) the focusing of wave troughs, it follows that if…”

Section: (C) Resonant-wave Interactionsmentioning

confidence: 99%

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The evolution of large non-breaking waves in intermediate and shallow water. I. Numerical calculations of uni-directional seas

Katsardi

Swan

2010

Proc. R. Soc. A.

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In deep water it is well known that the evolution of the largest waves in realistic, broadbanded frequency spectra is governed by dispersive focusing. However, as the water depth reduces this process weakens and the relative significance of wave modulation is shown to be increasingly important. This leads to very different extreme wave groups, the properties of which are critically dependent upon the local nonlinearity. To explore these effects, and to provide a physical explanation for their occurrence, two complementary wave models are employed. The combined numerical results show that the nature of large uni-directional waves varies depending on the relative water depth. As the water depth reduces, both the bound and resonant interactions become more significant. However, the third-order resonant terms have the most profound influence. By modifying both the amplitude and phase of the underlying linear wave components, the largest waves arise as a local instability within a truncated quasi-regular wave train; the latter appearing because of an initial narrowing of the underlying frequency spectrum. Furthermore, the numerical calculations show that, with large changes in both the spectral shape and the phasing of the wave components, both the maximum crest elevations and wave heights are less than those predicted by linear theory.

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Section: Introductionmentioning

confidence: 99%

Section: Applications In Water Of Finite Depthmentioning

confidence: 99%

Section: (C) Resonant-wave Interactionsmentioning

confidence: 99%

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The evolution of large non-breaking waves in intermediate and shallow water. I. Numerical calculations of uni-directional seas

Katsardi

Swan

2010

Proc. R. Soc. A.

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“…In addition, it was also noted that the onset of wave breaking, principally by spilling, was also dependent on the directional spread; larger non-breaking waves were generated in directionally spread seas. In a follow-up paper, Johannessen & Swan [33] combined experimental observations and numerical predictions to show that the dominant effect arising above second order relates to local changes in the wave spectrum, involving energy shifts to the higher frequencies. The influence of these changes on the directionality of a large wave event has been considered by Gibson & Swan [34] and Adcock et al [35]; the former showing that such effects can be described in terms of the third-order resonant terms evaluated using the Zakharov [36] equation.…”

Section: Introductionmentioning

confidence: 99%

A laboratory study of wave crest statistics and the role of directional spreading

Latheef

Swan

2013

Proc. R. Soc. A.

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This paper concerns the crest height statistics arising in sea states that are broad banded in both frequency and direction. A new set of laboratory observations are presented and the results compared with the commonly applied statistical distributions. Taken as a whole, the data confirm that the crest-height distributions are critically dependent upon the directionality of the sea state. Although nonlinear effects arising at third order and above are most pronounced in uni-directional seas, the present data show that they are also important in directionally spread seas, provided the seas are sufficiently steep and not too short crested. The data also highlight the limiting effects of wave breaking. With individual breaking events dependent upon the local wave steepness, the directionality of the sea state again plays a significant role. Indeed, the present observations confirm that the two competing processes of nonlinear amplification and wave breaking can have a profound influence on the crest-height distributions leading to significant departures from established theory. In such cases, the key parameters are the sea state steepness and directional spread; the latter acting to counter the former in terms of nonlinear changes in the crestheight distributions.

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“…Numerical modeling of long wave generation by transient groups in deep and intermediate water depths is well established and in good agreement with laboratory data (see for instance Johannessen and Swan, 2003). Long-wave propagation in shallow water has been addressed using non-dispersive models based on the shallow water equations (Hibberd and Peregrine, 1979), and some aspects of the surf beat generation mechanism have been successfully reproduced by forcing these models with radiation stress gradients of wave heights across the group (List, 1992).…”

Section: Introductionmentioning

confidence: 80%

Numerical Computation of Infragravity Wave Dynamics and Velocity Profiles Using a Fully Nonlinear Boussinesq Model

Cienfuegos

Duarte

Suarez

et al. 2011

Int. Conf. Coastal. Eng.

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We present experimental and numerical analysis of nonlinear processes responsible for generating infragravity waves in the nearshore. We provide new experimental data on random wave propagation and associated velocity profiles in the shoaling and surf zones of a very mild slope beach. We analyze low frequency wave generation mechanisms and dynamics along the beach and examine in detail the ability of the fully nonlinear Boussinesq-type model SERR1D (Cienfuegos et al., 2010) to reproduce the complex dynamics of high frequency wave propagation and energy transfer mechanisms that enhance infragravity wave generation in the laboratory.

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On the nonlinear dynamics of wave groups produced by the focusing of surface–water waves

Cited by 53 publications

References 28 publications

The evolution of large non-breaking waves in intermediate and shallow water. I. Numerical calculations of uni-directional seas

The evolution of large non-breaking waves in intermediate and shallow water. I. Numerical calculations of uni-directional seas

A laboratory study of wave crest statistics and the role of directional spreading

Numerical Computation of Infragravity Wave Dynamics and Velocity Profiles Using a Fully Nonlinear Boussinesq Model

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