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Keywords:

  • freak waves;
  • swell-windsea coupling;
  • Suwa-Maru incident

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Hindcast Model
  5. 3. Meteorological Conditions, Sea State, and Spectral Changes
  6. 4. Formation of Narrow Wave Spectrum Due to Swell and Windsea Coupling
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[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.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Hindcast Model
  5. 3. Meteorological Conditions, Sea State, and Spectral Changes
  6. 4. Formation of Narrow Wave Spectrum Due to Swell and Windsea Coupling
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[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 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 third-generation 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

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Hindcast Model
  5. 3. Meteorological Conditions, Sea State, and Spectral Changes
  6. 4. Formation of Narrow Wave Spectrum Due to Swell and Windsea Coupling
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[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 wave-wave 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 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 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

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Hindcast Model
  5. 3. Meteorological Conditions, Sea State, and Spectral Changes
  6. 4. Formation of Narrow Wave Spectrum Due to Swell and Windsea Coupling
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[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.

image

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.

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[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 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).

image

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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[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: 5∼7.5 s) developed along the southeastern side of the front, and two swell systems approached the accident site; a lower-frequency swell (Tp: 9∼10 s) propagating northwestward from the Pacific (hereafter, swell-P), and a higher-frequency swell (Tp: 8∼9 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 2−0.5πHsLm−1 where Lm is a mean wavelength), frequency peakedness (Qp) [e.g., Goda, 2000], and mean directional spreading (σθ) [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 σθ decreased (Figures 1e and 1f). Wave steepness and spectral peakedness (Qp and inverse spreading 1/σθ) attained their highest values throughout the three stages at the time of the accident (0400 UTC 23 June in Stage 3). Moreover, the joint probability density function of Qp and σθ 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 σθ at the time of the incident appear to diverge significantly from the most probable value, especially for Qp. The spectral peak F(σ, θpeak) becomes pointed as characterized by the increase of the peak enhancement factor of the JONSWAP spectrum γ = 5.3, which is well within the parameter range where quasi-resonant interaction is effective (γ>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(σ, θpeak). Quantitatively the value suggests that quasi-resonance is weak (quasi-resonance 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.

image

Figure 3. Joint probability distribution function (PDF) of Qp and σθ 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, σθ) is approximately 17.8 × 106. The black line indicates the trajectories of Figures 1e and 1f overlapped in a joint PDF.

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[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

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Hindcast Model
  5. 3. Meteorological Conditions, Sea State, and Spectral Changes
  6. 4. Formation of Narrow Wave Spectrum Due to Swell and Windsea Coupling
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[13] The temporal variability of the magnitude of the frequency peakedness Qp and the mean directional spreading σθ 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.

image

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.

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[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 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)4fp)−1 but longer than the Benjamin-Feir timescale ((ak)2fp)−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 wind-wave 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

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Hindcast Model
  5. 3. Meteorological Conditions, Sea State, and Spectral Changes
  6. 4. Formation of Narrow Wave Spectrum Due to Swell and Windsea Coupling
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[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 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 quasi-resonance 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.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Hindcast Model
  5. 3. Meteorological Conditions, Sea State, and Spectral Changes
  6. 4. Formation of Narrow Wave Spectrum Due to Swell and Windsea Coupling
  7. 5. Conclusions
  8. Acknowledgments
  9. References

[20] 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.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Hindcast Model
  5. 3. Meteorological Conditions, Sea State, and Spectral Changes
  6. 4. Formation of Narrow Wave Spectrum Due to Swell and Windsea Coupling
  7. 5. Conclusions
  8. Acknowledgments
  9. References
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