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K. Trulsen
sea states can vary in time in such a way that the occurrence of rogue waves may be
affected.
The presence of a ship in a wave field is known to locally affect the wave field
near the ship. If the ship appears suddenly into an already established wave field,
it may also represent a perturbation that brings the wave field temporarily out of
equilibrium [34, 35].
Indeed, in the recent review of Onorato and Suret [36] it is speculated that a
change of ambient conditions can bring a wave field out of equilibrium, thus provoking amplification of kurtosis before the wave field is brought back to equilibrium.
Conclusions
Rogue waves are known to occur more frequently than expected from linear wave
theory, more frequently than expected within Gaussian seas. The common nonlinear
theories for rogue waves explain such deviation by weakly nonlinear effects on top of
equilibrium linear sea states, or as the effect of modulational instability due to unstable perturbations of steady states. The degree of modulational instability of a steady
sea state is sometimes assessed by the so-called Benjamin–Feir Index (BFI). There is
however a different mechanism for rogue wave generation, viz. nonlinear dynamics
of wave fields that are not in an equilibrium state. This mechanism is not indicated by
the value of BFI, since the modulational instability is not relevant in the absence of a
steady state. We have recently performed experiments at the Department of Mathematics at the University of Oslo revealing that a substantial amplification of kurtosis
can occur in non-equilibrium wave fields that are not modulationally unstable.
Acknowledgements This work has been supported by the Research Council of Norway through
the project “EXtreme wave WArning criteria for MARine structures” (ExWaMar) RCN 256466.
References
1. Alber, I. E. (1978). The effects of randomness on the stability of two-dimensional surface
wavetrains. Proceedings of the Royal Society of London A, 363, 525–546.
2. Alber, I. E, Saffman, P. (1978). Stability of random nonlinear deep water waves with finite
bandwidth spectra. Technical Report, 31326–6035–RU–TRW Defense and Space System
Group
3. Benjamin, T. B. (1967). Instability of periodic wavetrains in nonlinear dispersive systems. Proceedings of the Royal Society of London A, 299, 59–75.
4. Benjamin, T. B., & Feir, J. E. (1967). The disintegration of wave trains on deep water. Journal
of Fluid Mechanics, 27, 417–430.
5. Benney, D. J., & Roskes, G. J. (1969). Wave instabilities. Studies in Applied Mathematics, 48,
377–385.
6. Bitner-Gregersen, E. M, Gramstad, O. (2016). Rogue waves—Impact on ships and offshore
structures. Technical Report, 05–2015, DNV-GL
K. Trulsen
sea states can vary in time in such a way that the occurrence of rogue waves may be
affected.
The presence of a ship in a wave field is known to locally affect the wave field
near the ship. If the ship appears suddenly into an already established wave field,
it may also represent a perturbation that brings the wave field temporarily out of
equilibrium [34, 35].
Indeed, in the recent review of Onorato and Suret [36] it is speculated that a
change of ambient conditions can bring a wave field out of equilibrium, thus provoking amplification of kurtosis before the wave field is brought back to equilibrium.
Conclusions
Rogue waves are known to occur more frequently than expected from linear wave
theory, more frequently than expected within Gaussian seas. The common nonlinear
theories for rogue waves explain such deviation by weakly nonlinear effects on top of
equilibrium linear sea states, or as the effect of modulational instability due to unstable perturbations of steady states. The degree of modulational instability of a steady
sea state is sometimes assessed by the so-called Benjamin–Feir Index (BFI). There is
however a different mechanism for rogue wave generation, viz. nonlinear dynamics
of wave fields that are not in an equilibrium state. This mechanism is not indicated by
the value of BFI, since the modulational instability is not relevant in the absence of a
steady state. We have recently performed experiments at the Department of Mathematics at the University of Oslo revealing that a substantial amplification of kurtosis
can occur in non-equilibrium wave fields that are not modulationally unstable.
Acknowledgements This work has been supported by the Research Council of Norway through
the project “EXtreme wave WArning criteria for MARine structures” (ExWaMar) RCN 256466.
References
1. Alber, I. E. (1978). The effects of randomness on the stability of two-dimensional surface
wavetrains. Proceedings of the Royal Society of London A, 363, 525–546.
2. Alber, I. E, Saffman, P. (1978). Stability of random nonlinear deep water waves with finite
bandwidth spectra. Technical Report, 31326–6035–RU–TRW Defense and Space System
Group
3. Benjamin, T. B. (1967). Instability of periodic wavetrains in nonlinear dispersive systems. Proceedings of the Royal Society of London A, 299, 59–75.
4. Benjamin, T. B., & Feir, J. E. (1967). The disintegration of wave trains on deep water. Journal
of Fluid Mechanics, 27, 417–430.
5. Benney, D. J., & Roskes, G. J. (1969). Wave instabilities. Studies in Applied Mathematics, 48,
377–385.
6. Bitner-Gregersen, E. M, Gramstad, O. (2016). Rogue waves—Impact on ships and offshore
structures. Technical Report, 05–2015, DNV-GL