242
K. Trulsen
modified nonlinear Schrödinger (MNLS) equation of Dysthe [18] for better representation of realistic bandwidths [55, 57].
Breather solutions [19, 28, 30, 44, 45] are long-time and long-distance solutions of the NLS equation, starting from an infinitesimal perturbation of a uniform
wave train, resulting in extreme waves localized in space and time, occurring once
or repeatedly in space and/or in time. Breather solutions have recently been studied
in laboratory experiments [9–11].
Related to the discovery of modulational instability of uniform wave trains, it was
also recognized that steady homogeneous wave fields are unstable to small inhomogeneous perturbations [1, 2, 12]. This instability occurs if the ratio between the
steepness and the spectral bandwidth of the wave field is above a threshold.
The Benjamin–Feir index (BFI), coined by Janssen [26], previously suggested
by Onoratoet al. [37, 39] under a different name, is precisely the ratio between the
steepness and the spectral bandwidth of the wave field. It has been suggested as an
indicator to predict increased probability of rogue waves. The BFI has been shown
to be useful as an indicator for extreme waves in unidirectional seas [40, 41] easily
reproduced in long and narrow laboratory tanks. However, the BFI has been found
to be less useful in directional seas in simulations [21, 38] and in laboratory tests
[42, 43] as well as an operational forecasting criterion [6].
A different path from swell and wind-sea interaction to freak wave generation was
suggested by Tamura et al. [51] who speculated that the nonlinear coupling between
swell and wind-sea could generate a narrow spectrum. Some ship accidents indeed
seem to have occurred in conditions of narrowing wave spectra [51, 62, 63]. It has
indeed been observed that the directional spread sometimes has been reduced ahead
of increased rogue wave occurrences at sea [54].
Recently, researchers have started suspecting that MI is not the correct or the
only path to explain real world ocean rogue waves, the waves being in general too
broad-banded and short-crested for the BFI to be useful (e.g. Fedele et al. [20]).
Case Study on Rogue Waves Through Common Theories:
The Prestige Accident
Freak waves are sometimes the subject of great controversies. There is for example
still no consensus on the cause of the Prestige oil tanker initial accident on 13/11–
2002, which subsequently led to a major environmental disaster after the sinking
of the ship on 19/11–2002. The magnitude of the environmental disaster provoked
heated debate in mass media and in court regarding the likelihood that the initial
accident could have been caused by a rogue wave (see Trulsen [59]).
In the recent study of Trulsen et al. [59] newly computed hindcast spectra for
every hour during the day of the accident were used as input data for four different
nonlinear models capable of computing the phase-resolved sea surface, allowing to
estimate statistical parameters that characterize the conditions for rogue waves. All
K. Trulsen
modified nonlinear Schrödinger (MNLS) equation of Dysthe [18] for better representation of realistic bandwidths [55, 57].
Breather solutions [19, 28, 30, 44, 45] are long-time and long-distance solutions of the NLS equation, starting from an infinitesimal perturbation of a uniform
wave train, resulting in extreme waves localized in space and time, occurring once
or repeatedly in space and/or in time. Breather solutions have recently been studied
in laboratory experiments [9–11].
Related to the discovery of modulational instability of uniform wave trains, it was
also recognized that steady homogeneous wave fields are unstable to small inhomogeneous perturbations [1, 2, 12]. This instability occurs if the ratio between the
steepness and the spectral bandwidth of the wave field is above a threshold.
The Benjamin–Feir index (BFI), coined by Janssen [26], previously suggested
by Onoratoet al. [37, 39] under a different name, is precisely the ratio between the
steepness and the spectral bandwidth of the wave field. It has been suggested as an
indicator to predict increased probability of rogue waves. The BFI has been shown
to be useful as an indicator for extreme waves in unidirectional seas [40, 41] easily
reproduced in long and narrow laboratory tanks. However, the BFI has been found
to be less useful in directional seas in simulations [21, 38] and in laboratory tests
[42, 43] as well as an operational forecasting criterion [6].
A different path from swell and wind-sea interaction to freak wave generation was
suggested by Tamura et al. [51] who speculated that the nonlinear coupling between
swell and wind-sea could generate a narrow spectrum. Some ship accidents indeed
seem to have occurred in conditions of narrowing wave spectra [51, 62, 63]. It has
indeed been observed that the directional spread sometimes has been reduced ahead
of increased rogue wave occurrences at sea [54].
Recently, researchers have started suspecting that MI is not the correct or the
only path to explain real world ocean rogue waves, the waves being in general too
broad-banded and short-crested for the BFI to be useful (e.g. Fedele et al. [20]).
Case Study on Rogue Waves Through Common Theories:
The Prestige Accident
Freak waves are sometimes the subject of great controversies. There is for example
still no consensus on the cause of the Prestige oil tanker initial accident on 13/11–
2002, which subsequently led to a major environmental disaster after the sinking
of the ship on 19/11–2002. The magnitude of the environmental disaster provoked
heated debate in mass media and in court regarding the likelihood that the initial
accident could have been caused by a rogue wave (see Trulsen [59]).
In the recent study of Trulsen et al. [59] newly computed hindcast spectra for
every hour during the day of the accident were used as input data for four different
nonlinear models capable of computing the phase-resolved sea surface, allowing to
estimate statistical parameters that characterize the conditions for rogue waves. All