Rogue Waves in the Ocean, the Role of Modulational . . .
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four models coincided that the wave conditions encountered by the tanker Prestige at
the moment of the accident were slightly more extreme than those of a Gaussian sea
state, and slightly less extreme than those of a Tayfun sea state. This study strongly
suggests that the probability of a rogue wave hitting the oil tanker was neither greater
than nor smaller than usual.
Rogue Waves in Non Equilibrium Wave Fields
Practical experience with the common theories for rogue waves, e.g. application of
the BFI as a warning criterion, suggests that some improvements may still be necessary for the warning criteria to be fully satisfactory [6]. We here point out that there
is indeed another path to the formation of rogue waves.
It is often observed that numerical simulation of nonlinear wave evolution, initialized with artificial initial conditions, can need some evolution time or distance
before the wave fields become well-behaved. During the initial transient evolution
extreme events are often seen to occur. Some effort has been made to suppress this
behavior, e.g. by Dommermuth [14], although the “problem” is typically dealt with
simply letting the numerical simulations run over sufficient time or distance before
the results are used. On the other hand, a very interesting situation would arise if this
“initial” strange behavior was the result of a sudden change of physical environment
rather than artificial initialization of a numerical integration.
Recently it has been observed that irregular wave fields that propagate from
deeper waters into shallower waters can have significant amplification of kurtosis and
freak wave statistics some distance inside the transition to the shallower depth. This
behavior was first discovered in an experimental dataset from MARIN in The Netherlands by Trulsen et al. [58], subsequently is was studied numerically by Sergeeva et
al. [49], Zeng and Trulsen [65], Gramstad et al. [22] and Viotti and Dias [60]. This
is a nonlinear effect that is neither explained by MI nor by linear refraction.
Recently Raustøl [47] carried out fine-resolution experiments and measured that
the kurtosis could be amplified to a value of 6, occurring at a location approximately
one wavelength on the inside of the depth transition to shallower water. She also
identified thresholds for water depths when this amplifying behavior took place. It
is interesting to note that this extreme amplification of kurtosis took place precisely
in a wave field that was not modulationally unstable.
It is common to treat a sea state as being statistically stationary when in fact it
varies. Meteorological forecasting services typically give forecasts for every three
hours. In Trulsen et al. [59] the Prestige accident was studied with hindcasts every
hour, making the assumption that the sea state was constant during each of the onehour intervals. In the case that the sea state varied dramatically within the one-hour
intervals, the nonlinear phase-resolving simulations of Trulsen et al. [59] could be
rendered invalid. An insufficient amount of work has been done to identify what
happens if the meteorological conditions and sea state change sufficiently fast that
the wave field is not in an equilibrium state. Indeed, Tamura et al. [51] suggested that
243
four models coincided that the wave conditions encountered by the tanker Prestige at
the moment of the accident were slightly more extreme than those of a Gaussian sea
state, and slightly less extreme than those of a Tayfun sea state. This study strongly
suggests that the probability of a rogue wave hitting the oil tanker was neither greater
than nor smaller than usual.
Rogue Waves in Non Equilibrium Wave Fields
Practical experience with the common theories for rogue waves, e.g. application of
the BFI as a warning criterion, suggests that some improvements may still be necessary for the warning criteria to be fully satisfactory [6]. We here point out that there
is indeed another path to the formation of rogue waves.
It is often observed that numerical simulation of nonlinear wave evolution, initialized with artificial initial conditions, can need some evolution time or distance
before the wave fields become well-behaved. During the initial transient evolution
extreme events are often seen to occur. Some effort has been made to suppress this
behavior, e.g. by Dommermuth [14], although the “problem” is typically dealt with
simply letting the numerical simulations run over sufficient time or distance before
the results are used. On the other hand, a very interesting situation would arise if this
“initial” strange behavior was the result of a sudden change of physical environment
rather than artificial initialization of a numerical integration.
Recently it has been observed that irregular wave fields that propagate from
deeper waters into shallower waters can have significant amplification of kurtosis and
freak wave statistics some distance inside the transition to the shallower depth. This
behavior was first discovered in an experimental dataset from MARIN in The Netherlands by Trulsen et al. [58], subsequently is was studied numerically by Sergeeva et
al. [49], Zeng and Trulsen [65], Gramstad et al. [22] and Viotti and Dias [60]. This
is a nonlinear effect that is neither explained by MI nor by linear refraction.
Recently Raustøl [47] carried out fine-resolution experiments and measured that
the kurtosis could be amplified to a value of 6, occurring at a location approximately
one wavelength on the inside of the depth transition to shallower water. She also
identified thresholds for water depths when this amplifying behavior took place. It
is interesting to note that this extreme amplification of kurtosis took place precisely
in a wave field that was not modulationally unstable.
It is common to treat a sea state as being statistically stationary when in fact it
varies. Meteorological forecasting services typically give forecasts for every three
hours. In Trulsen et al. [59] the Prestige accident was studied with hindcasts every
hour, making the assumption that the sea state was constant during each of the onehour intervals. In the case that the sea state varied dramatically within the one-hour
intervals, the nonlinear phase-resolving simulations of Trulsen et al. [59] could be
rendered invalid. An insufficient amount of work has been done to identify what
happens if the meteorological conditions and sea state change sufficiently fast that
the wave field is not in an equilibrium state. Indeed, Tamura et al. [51] suggested that