Crossing sea state and rogue wave probability during the Prestige accident

We discuss the crossing sea state and the probability of rogue waves during the accident of the tanker Prestige on 13 November 2002. We present newly computed hindcast spectra for every hour during that day at nearby locations, showing the development of a bimodal sea state with two wave systems crossing at nearly right angle. We employ four different nonlinear models capable of computing the phase-resolved sea surface from the hindcast spectra, allowing us to estimate statistics for the occurrence of rogue waves. At the location and moment of the accident, the models give expected values for the kurtosis κ = 3.0119 ± 0.0078. The models coincide that the maximum crest elevation was about 5–6% larger than the expected maximum crest elevation in a Gaussian sea at the moment of the accident. We also conclude that the possible nonlinear interaction between the two crossing wave systems practically did not modify neither the kurtosis nor the largest crest elevation.

[1]  Nobuhito Mori,et al.  On the Estimation of the Kurtosis in Directional Sea States for Freak Wave Forecasting , 2011 .

[2]  D. J. Benney,et al.  The Propagation of Nonlinear Wave Envelopes , 1967 .

[3]  I. E. Alber,et al.  The effects of randomness on the stability of two-dimensional surface wavetrains , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[4]  Miguel Onorato,et al.  The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains , 2000 .

[5]  Luigi Cavaleri,et al.  Modulational instability and non-Gaussian statistics in experimental random water-wave trains , 2005 .

[6]  Bruce J. West,et al.  A new numerical method for surface hydrodynamics , 1987 .

[7]  M. A. Tayfun,et al.  Narrow-band nonlinear sea waves , 1980 .

[8]  Mattias Marklund,et al.  Modulational instability of nonlinearly interacting incoherent sea states , 2006, nlin/0611039.

[9]  C. Soares,et al.  Probability distributions of wave heights and periods in combined sea-states measured off the Spanish coast , 2012 .

[10]  Henry C. Yuen,et al.  Three-Dimensional Instability of Finite-Amplitude Water Waves , 1981 .

[11]  Miguel Onorato,et al.  Freak waves in crossing seas , 2010 .

[12]  K. Trulsen,et al.  Fourth-order coupled nonlinear Schrödinger equations for gravity waves on deep water , 2011 .

[13]  Peter A. E. M. Janssen,et al.  Nonlinear Four-Wave Interactions and Freak Waves , 2003 .

[14]  Luigi Cavaleri,et al.  Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin , 2009, Journal of Fluid Mechanics.

[15]  Zakharov,et al.  Turbulence of capillary waves. , 1996, Physical review letters.

[16]  O. Andersen,et al.  Freak Waves: Rare Realizations of a Typical Population Or Typical Realizations of a Rare Population? , 2000 .

[17]  F. E. Laine-Pearson,et al.  The long-wave instability of short-crested waves, via embedding in the oblique two-wave interaction , 2005, Journal of Fluid Mechanics.

[18]  Karsten Trulsen,et al.  Can swell increase the number of freak waves in a wind sea? , 2010, Journal of Fluid Mechanics.

[19]  M. Markus,et al.  Fluctuation theorem for a deterministic one-particle system. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  E. Rogers,et al.  Semi-empirical dissipation source functions for ocean waves: Part I, definition, calibration and validation. Fabrice ArdhuinJean-Francois Filipot and Rudy Magne Service Hydrographique et Oceanographique de la Marine, Brest, France , 2010 .

[21]  Luigi Cavaleri,et al.  Rogue waves in crossing seas: The Louis Majesty accident , 2012 .

[22]  A. Osborne,et al.  Landau damping and coherent structures in narrow-banded 1+1 deep water gravity waves. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  C T Stansberg,et al.  Statistical properties of directional ocean waves: the role of the modulational instability in the formation of extreme events. , 2009, Physical review letters.

[24]  Khellil Sefiane,et al.  Experimental investigation of self-induced thermocapillary convection for an evaporating meniscus in capillary tubes using micro-PIV , 2005 .

[25]  Vladimir I. Piterbarg,et al.  Asymptotic Methods in the Theory of Gaussian Processes and Fields , 1995 .

[26]  M. Okamura Long time evolution of standing gravity waves in deep water , 1996 .

[27]  Jaak Monbaliu,et al.  Towards the identification of warning criteria: Analysis of a ship accident database , 2005 .

[28]  Dick K. P. Yue,et al.  A high-order spectral method for the study of nonlinear gravity waves , 1987, Journal of Fluid Mechanics.

[29]  E. Pelinovsky,et al.  Rogue Waves in Waters of Infinite and Finite Depths , 2009 .

[30]  A. Osborne,et al.  Freak waves in random oceanic sea states. , 2001, Physical review letters.

[31]  M. Okamura Instabilities of Weakly Nonlinear Standing Gravity Waves , 1984 .

[32]  Miguel Onorato,et al.  Extreme wave events in directional, random oceanic sea states , 2001, nlin/0106004.

[33]  Vladimir P. Krasitskii,et al.  On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves , 1994, Journal of Fluid Mechanics.

[34]  Harald E. Krogstad,et al.  Oceanic Rogue Waves , 2008 .

[35]  A. Osborne,et al.  On the relation between two numerical methods for the computation of random surface gravity waves , 2007 .

[36]  B. Eliasson,et al.  Evolution of rogue waves in interacting wave systems , 2009, 0904.0522.

[37]  O. Phillips Theoretical and experimental studies of gravity wave interactions , 1967, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[38]  Pierre Bénard,et al.  Integration of the fully elastic equations cast in the hydrostatic pressure terrain-following coordinate in the framework of the ARPEGE/Aladin NWP system , 1995 .

[39]  Karsten Trulsen,et al.  NOTE ON BREATHER TYPE SOLUTIONS OF THE NLS AS MODELS FOR FREAK-WAVES , 1999 .

[40]  Instability growth rates of crossing sea states. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Jaak Monbaliu,et al.  Extreme waves in random crossing seas: Laboratory experiments and numerical simulations , 2011 .

[42]  K. Dysthe,et al.  Probability distributions of surface gravity waves during spectral changes , 2005, Journal of Fluid Mechanics.

[43]  T. Waseda,et al.  Freakish sea state and swell‐windsea coupling: Numerical study of the Suwa‐Maru incident , 2009 .

[44]  Nonlinear multiphase deep‐water wavetrains , 1976 .

[45]  Takuji Waseda,et al.  Freakish sea index and sea states during ship accidents , 2012 .

[46]  C. Guedes Soares,et al.  Modeling the climatic variability of directional wave spectra , 2011 .

[47]  Karsten Trulsen,et al.  The Statistical Distribution of a Nonlinear Ocean Surface , 2005 .

[48]  T. Waseda,et al.  Predicting freakish sea state with an operational third-generation wave model , 2013 .

[49]  R. D. Pierce,et al.  On the validity of mean-field amplitude equations for counterpropagating wavetrains , 1994, patt-sol/9411002.

[50]  Mark A. Donelan,et al.  The Andrea Wave Characteristics of a Measured North Sea Rogue Wave , 2013 .

[51]  Karsten Trulsen,et al.  Influence of crest and group length on the occurrence of freak waves , 2007, Journal of Fluid Mechanics.

[52]  Alexey Slunyaev Nonlinear analysis and simulations of measured freak wave time series , 2006 .

[53]  C T Stansberg,et al.  Observation of strongly non-Gaussian statistics for random sea surface gravity waves in wave flume experiments. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  L Stenflo,et al.  Instability and evolution of nonlinearly interacting water waves. , 2006, Physical review letters.

[55]  E. Rogers,et al.  Semiempirical Dissipation Source Functions for Ocean Waves. Part I: Definition, Calibration, and Validation , 2009, 0907.4240.

[56]  R. D. Pierce,et al.  On the modulational stability of traveling and standing water waves , 1994 .

[57]  Elzbieta M. Bitner-Gregersen,et al.  Occurrence of rogue sea states and consequences for marine structures , 2014, Ocean Dynamics.

[58]  Luigi Cavaleri,et al.  Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves , 2006 .

[59]  C. Guedes Soares,et al.  Modelling of multipeaked directional wave spectra , 2009 .

[60]  M. Stiassnie,et al.  Sea-swell interaction as a mechanism for the generation of freak waves , 2008 .

[61]  Vladimir E. Zakharov,et al.  Stability of periodic waves of finite amplitude on the surface of a deep fluid , 1968 .

[62]  Jaak Monbaliu,et al.  Evolution of weakly nonlinear random directional waves: laboratory experiments and numerical simulations , 2010, Journal of Fluid Mechanics.

[63]  Henry C. Yuen,et al.  Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves , 1980 .

[64]  Diane M. Henderson,et al.  Progressive waves with persistent two-dimensional surface patterns in deep water , 2005, Journal of Fluid Mechanics.

[65]  Takuji Waseda,et al.  Evolution of a Random Directional Wave and Freak Wave Occurrence , 2009 .

[66]  Karsten Trulsen,et al.  On weakly nonlinear modulation of waves on deep water , 2000 .

[67]  Vladimir E. Zakharov,et al.  Modulation instability of Stokes wave → freak wave , 2005 .

[68]  K. Dysthe,et al.  Note on a modification to the nonlinear Schrödinger equation for application to deep water waves , 1979, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[69]  Jaak Monbaliu,et al.  The North Sea Andrea storm and numerical simulations , 2014 .

[70]  Karsten Trulsen,et al.  Spatial Extreme Value Analysis of Nonlinear Simulations of Random Surface Waves , 2004 .

[71]  A. Osborne,et al.  Modulational instability in crossing sea states: a possible mechanism for the formation of freak waves. , 2006, Physical review letters.