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GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L01607, doi:10.1029/2008GL036280, 2009
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Freakish sea state and swell-windsea coupling: Numerical study of the
Suwa-Maru incident
H. Tamura,1 T. Waseda,1,2 and Y. Miyazawa1
Received 10 October 2008; revised 19 November 2008; accepted 4 December 2008; published 14 January 2009.
[1] On 23 June 2008, a fishing boat with 20 crewmembers
onboard sank in reportedly moderate sea-state conditions in
the Kuroshio Extension region east of Japan. To determine
the sea state at the time of the incident, we conducted a
hindcast wave simulation, as realistically as possible, using
an improved third-generation wave model driven by wind
and current reanalysis products. Our results indicated that at
the time of the accident, the wave steepness increased and
the spectral peakedness narrowed, creating a sea state
favorable for freak wave occurrence due to quasi-resonance.
Detailed analyses of the spectral evolution revealed that
nonlinear coupling of swell and windsea waves was the key
to generating the narrow spectrum. Under the influence of
rising wind speed, the swell system grew exponentially at
the expense of the windsea energy, and the bimodal crossing
sea state transformed into a freakish unimodal sea.
Citation: Tamura, H., T. Waseda, and Y. Miyazawa (2009),
Freakish sea state and swell-windsea coupling: Numerical study
of the Suwa-Maru incident, Geophys. Res. Lett., 36, L01607,
doi:10.1029/2008GL036280.
1. Introduction
[2] A number of ships have been wrecked in the Kuroshio
Extension (KE) region, which is notorious for the occurrence
of abnormal waves. On 23 June 2008, the Suwa-Maru No.
58, a fishing boat with 20 crewmembers, sank in seemingly
moderate sea conditions (reported wave heights were 2 to
3 m) off Cape Inubosaki, Japan (144° –145°E, 35°– 36°N),
in the KE region. The Japan Coast Guard investigated the
incident and reported that the ship may have encountered
abnormal waves twice, sinking approximately 10 minutes
after being hit by the initial wave (at about 0400 UTC).
Other possibilities such as improper use of a para-anchor or
an encounter with unidentified submerged objects have also
been suggested, but at the time of writing this report, no
definitive conclusion had been reached.
[3] To predict ‘‘freak’’ or ‘‘rogue’’ wave occurrence, it is
first necessary to consider the three possible physical
mechanisms that may contribute to the formation of such
waves: wave-current interaction, inverse dispersion, and
nonlinear focusing [e.g., Kharif and Pelinovsky, 2003].
Recent studies [e.g., Onorato et al., 2001; Janssen, 2003;
Onorato et al., 2004] have suggested that due to nonlinear
focusing, the probability of freak wave occurrence increases
1
Frontier Research Center for Global Change, Japan Agency for
Marine-Earth Science and Technology, Yokohama, Japan.
2
Department of Ocean Technology Policy and Environment, Graduate
School of Frontier Sciences, University of Tokyo, Chiba, Japan.
Copyright 2009 by the American Geophysical Union.
0094-8276/09/2008GL036280$05.00
as the wave spectrum narrows in the frequency domain.
Onorato et al. [2002], Gramstad and Trulsen [2007], and
Waseda et al. [2008] extended past work to include the
effect of directionality and indicated that when waves lose
directionality and become long-crested, quasi-resonant
wave-wave interactions cause the wave train to become
unstable, which is a manifestation of the Benjamin-Feir (BF)
instability in random directional waves. This modulational
instability (i.e., the BF instability) is considered to be a likely
candidate for the generation of freak waves in the open ocean.
However, few studies have investigated the generation
mechanism of such a narrow-banded wave spectrum in the
frequency-direction domain under a realistic forcing field of
winds and currents.
[4] The present study was motivated by a desire to better
understand the sea state at the time of the Suwa-Maru
accident. We were particularly interested in how near or
how far the wave field was to the unstable conditions that
are favorable for the formation of freak waves. The first step
was to reproduce the sea state as realistically as possible in
the KE region. To accomplish this, we conducted a hindcast
experiment of ocean waves using an improved thirdgeneration operational wave model driven by surface wind
and ocean current reanalysis products (section 2). We then
investigated the physical aspects of the wave field, such as
the characteristic variation of the wave spectrum (section 3).
On the basis of those results, we discuss the possibility that
swell-windsea interaction led to the formation of abnormally narrow wave spectra at the time of the Suwa-Maru
accident (section 4). Finally, we present our conclusions
(section 5).
2. Hindcast Model
[5] We conducted a wave hindcast of the sea state in the
KE region from 1 to 30 June 2008 to investigate possible
causes of the accident. A third-generation wave model
based on WAVEWATCH III [Tolman, 2002] was used with
an improved nonlinear energy transfer function Snl [Tamura
et al., 2008]. The evolution of wave spectra, such as the
downshifting of the spectral peak and the self-stabilization
of the spectral form is controlled by Snl [e.g., Resio and
Perrie, 1991]. We used the SRIAM method [Komatsu
and Masuda, 1996] as an improved scheme for efficient and
accurate computation of Snl to reproduce the spectral shape
precisely. Tamura et al. [2008] assessed the performance of
the SRIAM method by applying it to both ideal and realistic
forcing fields of wind and currents. They demonstrated that
SRIAM improves evaluation of wave-current and wavewave interactions in complex situations.
[6] We used a nested model domain for grid resolutions
of 1° (nest1), 1/4° (nest2), and 1/16° (nest3). The outer two
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3-hourly wind stress estimated from grid point values
produced by the Mesoscale Model (MSM) of the Japan
Metrological Agency (JMA) and the reanalysis current data
from the Japan Coastal Ocean Predictability Experiment
(JCOPE2) [Miyazawa et al., 2008] to specify the states of
the Kuroshio and the KE. The hourly boundary spectral data
was obtained from the nest2 model. Initial fields for all
models were seeded with fetch-limited spectra based on
local wind speed; the initial transition period was excluded
from the rest of the analysis. Further details are described by
Tamura et al. [2008].
3. Meteorological Conditions, Sea State,
and Spectral Changes
Figure 1. Time history of (a) wind speed, (b) wind
direction, (c) significant wave height, (d) wave steepness,
(e) frequency peakedness, and (f) directional spreading from
17 to 25 June 2008. The location is 145°E, 36°N, indicated
by the black square in Figure 2.
nests of the Pacific Ocean (nest1) and the Japan coastal
region (nest2) were set up to provide the swell conditions to
the finest inner model (Kuroshio Extension Model, nest3
140° –150°E, 30° – 40°N). The nest3 model was driven by
[7] The temporal evolution of the surface wind and
associated wave field can be separated into three stages
(Figure 1). In Stage 1 (from 19 June to 0600 UTC 22 June),
wind speed and Hs variations were small. The sea state
during Stage 2 (from 0600 UTC 22 June to 0000 UTC
23 June) was characterized by a rapid increase of Hs
associated with strong local wind. Stage 3 (from 0000 to
0600 UTC 23 June) covers the time of the accident when
a cold front crossed over the accident site.
[8] The meteorological condition around the possible
location of the accident (144°– 145°E, 35°– 36°N) was
governed by synoptic- and sub-synoptic-scale features
(Figure 2a). A seasonal stationary front (around 30° – 35°N)
called the Baiu front was maintained by northwesterly and
southwesterly winds from early June to mid-July. The
southern part of the front was dominated by surface wind
blowing toward the northeast and east – northeast directions.
Four hours before the accident (0000 UTC 23 June), a surface
low pressure moved northeastward (Figure 2a). The
northward surface wind speed increased rapidly when the
low pressure approached the accident site at the end of
Stage 1 (Figure 1a), and reached its maximum (15 m/s and
higher) at the end of Stage 2. The accident occurred just
Figure 2. Instantaneous plane view of (a) significant wave height (contours) and wind vectors (black arrows) having
speeds greater than 8 m/s and (b) wave peak period (contours), peak direction (black arrows), and current vectors having
speeds greater than 2.5 m/s (white arrows). The time is 4 hours before the accident.
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Figure 3. Joint probability distribution function (PDF) of
Qp and sq for the KE region. Excluding the initial transition
period, the 28-day integration period (3 to 30 June) was
analyzed. The total number of (Qp, sq) is approximately
17.8 106. The black line indicates the trajectories of
Figures 1e and 1f overlapped in a joint PDF.
after the passage of the cold front followed by rapid
decrease of the wind speed and change of the direction in
Stage 3 (Figures 1a and 1b).
[9] The Hs was relatively stationary in Stage 1 (Figure 1c),
but as the local northward wind started to increase, Hs
increased rapidly and reached over 3 m in the beginning of
Stage 2. During the passage of this cold front, the wave
spectrum consisted of three wave systems; see the spatial
distribution of the peak period (Tp) and peak wave direction
in Figure 2b. Young wind waves (Tp: 57.5 s) developed
along the southeastern side of the front, and two swell
systems approached the accident site; a lower-frequency
swell (Tp: 910 s) propagating northwestward from the
Pacific (hereafter, swell-P), and a higher-frequency swell
(Tp: 89 s) generated by the seasonal surface wind along
the Baiu front propagated east – northeastward from the
southern coast of Japan (hereafter, swell-J). The distinct
peak periods of these swells can be attributed to the
difference in the effective fetch, long for swell-P and short
for swell-J.
[10] Seas with a high probability of producing freak
waves can be parameterized by the wave steepness and
the spectral bandwidths of frequency and direction. To
investigate the time evolution of the spectral shape, we used
three parameters representing wave steepness (ak defined
as 2 0.5 pHsLm 1 where Lm is a mean wavelength), frequency
peakedness (Qp) [e.g., Goda, 2000], and mean directional
spreading (sq) [Kuik et al., 1988; Tolman, 2002].
[11] Wave steepness (Figure 1d) increased rapidly in Stage
2 associated with the stronger local wind. At the same time,
the spectral shape became narrower as Qp increased and sq
decreased (Figures 1e and 1f). Wave steepness and spectral
peakedness (Qp and inverse spreading 1/sq) attained their
highest values throughout the three stages at the time of the
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accident (0400 UTC 23 June in Stage 3). Moreover, the
joint probability density function of Qp and sq indicated that
such a spectral shape was quite rare over a 1-month period
in the KE region (Figure 3). The values of Qp and sq at the
time of the incident appear to diverge significantly from the
most probable value, especially for Qp. The spectral peak
F(s, qpeak) becomes pointed as characterized by the increase
of the peak enhancement factor of the JONSWAP spectrum
g = 5.3, which is well within the parameter range where
quasi-resonant interaction is effective (g>5.0) [Waseda et
al., 2008]. On the other hand, the ‘‘A’’ parameter [Babanin
and Soloviev, 1998] which represents the directional spreading was 1.2 at the spectral peak F(s, qpeak). Quantitatively
the value suggests that quasi-resonance is weak (quasiresonance is enhanced for A > 4.0 according to Waseda et
al. [2008]), but the time history of the hindcast result clearly
indicates the decreasing trend of the wave directionality at
the time of the incident. This tendency of the spectral
evolution is favorable for the occurrence of freak waves as a
result of quasi-resonance, and therefore, we consider that
the current reanalysis captures the essence of the formation
of the narrow wave spectrum, but the estimated parameters
need to be calibrated against observation.
[12] The most important and obscure findings are the
narrowness of the wave spectral shape in both frequency
and directional domain at the time of the Suwa-Maru
incident. What caused the spectral shape to become so
narrow? To answer this question, we investigated the
evolution of the wave spectra and the associated nonlinear
resonant interaction source term Snl.
4. Formation of Narrow Wave Spectrum Due
to Swell and Windsea Coupling
[13] The temporal variability of the magnitude of the
frequency peakedness Qp and the mean directional spreading sq were well explained by Snl among wave systems
(Figure 4). Below, we show that the nonlinear coupling
between local wind waves and background swells in a
crossing sea state is the key to understanding the generation
of the narrow wave spectrum.
[14] In Stage 1, a local windsea developed and coexisted
with two background swell systems (Figure 4a, swell-P and
swell-J). Windsea development occurred in the local wind
direction (northward), with a spectral peak around 0.2 Hz
and spectral energy much smaller than that of the background swell (swell-J). Swell from the Pacific (swell-P)
propagated northwestward with broad directional spreading,
whereas swell from the Japan coast (swell-J) propagated
east –northeastward with a distinct spectral peak. Because
the total of wind input and dissipation was negligible
considering the magnitude of the total wave energy, the
sea state would have been almost in equilibrium.
[15] On the other hand, in Stage 2, the wind speed
increased (over 10 m/s), and the spectral energy of local
wind waves increased rapidly (Figure 4b; the peak value
was about 8.4 m2s). The peak of the windsea spectrum
shifted to the lower side (from 0.2 to 0.13 Hz) and
approached the spectral peak of the swell-J system. Whereas
the magnitude of the swell-P energy remained nearly
constant, its relative magnitude against the windsea and
swell-J decreased rapidly. As the local windsea developed
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Figure 4. Wave spectra and Snl. The contour intervals for wave spectra are 0.1 for the maximum wave spectrum and 0.2
for the maximum absolute value of Snl. Blue arrows in the wave spectra indicate the wind direction. Red (blue) represents
positive (negative) values of Snl.
and its spectral shape became steeper, the bimodal feature
with two spectral peaks (for the windsea and swell-J)
became pronounced around 0.11 – 0.15 Hz in the north to
east direction. At the same time, the local windsea energy
was transferred to swell-J as a result of Snl (Figure 4d). The
intensity of the Snl was about 20 times greater than that in
Stage 1, indicating vigorous interaction between the local
windsea and the swell (swell-J).
[16] The development of the local windsea could have
been significantly altered by the presence of the background
swell. Masson [1993] showed that under certain conditions,
considerable energy can be transferred to the swell. Young
[2006] also indicated that the spectral shape was controlled
almost completely by the Snl and input and dissipation terms
were of lesser importance. In the case of the Suwa-Maru
incident, the swell system (swell-J) grew at the expense of
the wind-wave energy that was maintained by the strong
local wind. The net source function of wind input and
dissipation (not shown here) was positive near the spectral
peak of the windsea and negative around the energy peak of
swell-J. Therefore, without nonlinear energy transfer, the
windsea should have grown while the swell decayed.
Because of the nonlinearity, the wind energy funneled to the
local windsea would have been efficiently transferred to the
swell. This nonlinear interaction works most effectively
when the wind waves and swell systems are close to each
other in the frequency-direction domain [Masson, 1993]. In
our analyses, the directional difference between the local
windsea and swell-J was about 45°, and the ratio of the two
peak frequencies was 0.92. This condition is consistent with
the investigation by Masson [1993] of the rate of change in
swell energy under the influence of windsea energy using
Hasselmann’s kinetic equation. The growth rate of swell
energy reached maximal value when the directional
difference between windsea and swell was approximately
30– 40° and their peak frequency ratio was about 0.85– 0.9.
On the other hand, as the two spectral peaks separated from
each other, the strength of Snl diminished rapidly.
[17] Finally in Stage 3, the bimodal wave spectrum had
transformed into a narrow unimodal spectrum (Figure 4c;
the peak value was about 22.2 m2s). The swell-J spectral
energy rapidly increased as a result of strong Snl from the
developed windsea. The time scale of the exponential
growth of swell-J energy was about 4 hours or only
approximately 1600 wave periods, which is much smaller
than the Hasselmann timescale ((ak)4 fp) 1 but longer than
the Benjamin-Feir timescale ((ak)2 fp) 1. The mechanism of
energy transfer from windsea to swell, as illustrated by
Masson [1993], was based on the exact resonance among
spectral components of the swell and the windsea when
their spectra do not overlap in the wave number space. The
growth rate of swell depends on the magnitude of the windwave energy, which is subject to growth on its own under
the action of local wind forcing. Therefore, we can infer that
the enhancement of the local wind-wave energy was the key
to producing narrower and steeper swell.
5. Conclusions
[18] A large number of ship accidents have occurred in
crossing sea conditions [Toffoli et al., 2005]. Onorato et al.
[2006] focused on the modulational instability of a crossing
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sea and investigated the growth rates using the two coupled
nonlinear Schrödinger equation. Our hindcast result for
conditions at the time of the Suwa-Maru incident also
indicated that a characteristic crossing sea state developed
4 hours before the accident. However, the wave condition
was unimodal at the time of the accident and was favorable
for the occurrence of the freak waves according to quasiresonance theory. Thus, for the case of the Suwa-Maru
incident, the crossing sea was a ‘‘precursor’’ to the
development of the narrow spectrum. Interaction of windsea
and swell took place as the wind speed increased and the sea
state rapidly developed into a unimodal freakish state.
[19] On the basis of these findings, we suggest that a
narrow wave spectrum may have developed in realistic sea
states where swells and windsea coexisted. In just a few
thousands wave periods, the wave spectrum deformed under
the influence of wind forcing, and a unimodal spectrum was
realized. Recent studies based on laboratory and numerical
experiments have suggested that an extremely narrow wave
spectrum is favorable for the generation of freak waves as
described in the introduction. However, these studies were
unable to demonstrate how such an extraordinary wave
condition is realized in the ocean. Through analyses of the
Suwa-Maru incident, our study provides, for the first time, a
plausible explanation of how such an abnormal condition
can arise. We can hypothesize that an abnormally narrow
wave spectrum forms due to resonant nonlinear interaction
between swell and windsea spectra; when the resulting
unimodal wave spectrum is sufficiently narrow and nonlinear, freak wave occurs due to modulational instability.
The results of the present study provided an example of the
first step and will have an important impact in the
forecasting of freak wave event.
[20] Acknowledgments. The authors would like to thank Alexander
Babanin at the Swinburne University of Technology and one anonymous
reviewer for their constructive comments, which were very helpful in
improving the manuscript. This work is part of the Japan Coastal Ocean
Predictability Experiment (JCOPE) supported by the Japan Agency for
Marine-Earth Science and Technology. Waseda was also supported by a
Grant-in-Aid for Scientific Research from the Japan Society for the
Promotion of Science.
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