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Detection of surf-riding behavior of ships in irregular seas

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Abstract

From investigations with ship models tested in steep periodic following waves, it has been conjectured in the past that, if the speed is observed reaching (in transient) the celerity value, attraction toward the condition commonly identified as “surf-riding” is already in progress. The nonlinear dynamics of this phenomenon has been investigated in depth also theoretically; however, it is unknown whether the stated simple phenomenological detection rule is meaningful also for more natural sea wave profiles. A practical question that prompted the current investigation is whether the duration of attraction to surf-riding could be properly quantified as a percentage of the total time of exposure to a specified wave environment, so that a probability of surf-riding could be eventually calculated. Celerity is defined in the current work as the velocity of propagation of a suitable local property of the wave profile, such as a certain value of slope. For irregular seas, this leads to the concept of instantaneous celerity. Unfortunately, instantaneous celerity, in general, is not a smooth and bounded curve in time. An alternative definition of celerity fitting to the problem of surf-riding is thus investigated, where the propagated points of the profiles are those with the locally maximum slope. Simultaneous treatment of the “wave” and “ship” processes is implemented, and the potential of a condition based on local celerity for surf-riding prediction is examined. Various patterns of behavior before and into surf-riding are observed and discussed. The paper is a step in the direction of developing a probabilistic method of assessment for the dangerous phenomenon of surf-riding and indirectly, for the evaluation of the class of cross-disciplinary phenomena that obey similar nonlinear dynamics.

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References

  1. Grim, O.: Surging motion and broaching tendencies in a severe irregular sea. Ocean Dyn. 16, 201–231 (1963)

    Google Scholar 

  2. Grim, O.: Das Schiff in von achtern auflaufender See. Jahrbuch der Schiffbautechnischen Gesselschaft (STG) 45, 264–287 (1951)

    Google Scholar 

  3. Kan, M.: Surging of large amplitude and surf-riding of ships in following seas. Selected papers in Naval Architecture and Ocean Engineering, The Society of Naval Architects of Japan 28 (1990)

  4. Spyrou, K.J.: Dynamic instability in quartering seas: the behavior of a ship during broaching. J. Ship Res. 40, 46–59 (1996)

  5. Spyrou, K.J.: Asymmetric surging of ships in following seas and its repercussions for safety. Nonlinear Dyn. 43, 149–272 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Thompson, J.M.T., Stewart, H.B.: Nonlinear Dynamics and Chaos. Wiley, New York (2002)

    MATH  Google Scholar 

  7. Minorski, N.: Nonlinear Oscillations. Robert E. Krieger Publishing Company, Huntington, New York (1974)

    Google Scholar 

  8. Longuet-Higgins, M.S.: The statistical analysis of a random, moving surface. Philos. Trans. R. Soc. Lond. Series A Math. Phys. Sci. 249, 321–387 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  9. Podgórski, K., Rychlik, I., Sjo, E.: Statistics for velocities of Gaussian waves. Int. J. Offshore Polar Eng. 10, 91–98 (2000)

    Google Scholar 

  10. Sjo, E.: Simultaneous distributions of space–time wave characteristics in a Gaussian sea. Extremes 4, 263–288 (2001)

    Article  MathSciNet  Google Scholar 

  11. Baxevani, A., Podgórski, K., Rychlik, I.: Velocities for moving random surfaces. Probab. Eng. Mech. 18, 251–271 (2003)

    Article  Google Scholar 

  12. Aberg, S., Rychlik, I.: Role of wave velocity for encountered wave statistics. In: Proceedings of the Sixteenth (2006) International Offshore and Polar Engineering Conference. San Francisco, California, May 28–June 2 (2006)

  13. Aberg, S., Rychlik, I.: Doppler shift approximations of encountered wave statistics. Ocean Eng. 34, 2300–2310 (2007)

    Article  Google Scholar 

  14. Belenky, V., Weems, K.M., Bassler, C.C., Dipper, M.J., Campbell, B.L., Spyrou, K.J.: Approaches to rare events in stochastic dynamics of ships. Probab. Eng. Mech. 28, 30–38 (2012)

    Article  Google Scholar 

  15. Belenky, V., Spyrou, K.J., Weems, K.M.: Split-time method for surf-riding and broaching-to. In: Proceedings, 12th International Ship Stability Workshop, Washington DC. June 12–15, 163–168 (2011)

  16. Pierson Jr, W.J.: Wind-generated gravity waves. In: Landsberg, H.E. (eds). Advances in Geophysics, vol. 2, Academic Press Inc., New York (1955)

  17. Kinsman, B.: Wind Waves: Their Generation and Propagation On the Ocean Surface. Dover Publications, Mineola, New York (1984)

  18. Bishop, B., Belknap, W., Turner, C., Simon, B., Kim, J.: Parametric Investigation on the Influence of GM, Roll Damping, and Above-Water Form on the Roll Response of Model 5613. Report NSWCCD-50-TR-2005/027, Carderock, Washington DC (2005)

  19. Longuet-Higgins, M.S.: Integral properties of periodic gravity waves of finite amplitude. Proc. R. Soc. Lond. Series A Math. Phys. Sci. 342, 157–174 (1974)

    Article  MathSciNet  Google Scholar 

  20. Stokes, G.G.: Mathematical and Physical Papers. Cambridge University Press, New York (1880)

    Google Scholar 

  21. Gabor, D.: Theory of communication. J. IEE 93, 429–457 (1946)

    Google Scholar 

  22. Boashash, B.: Estimating and interpreting the instantaneous frequency of a signal Part 1: fundamentals. Proc. IEEE 80, 520–538 (1992)

  23. Mandel, L.: Interpretation of instantaneous frequency. Am. J. Phys. 42, 840–846 (1974)

    Article  Google Scholar 

  24. Vossers, G.: Behaviour of Ships in Waves, Volume IIC of Ships and Marine Engines. The Technical Publishing Company H. Stam N.V., Harlem (1962)

    Google Scholar 

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Acknowledgments

The research reported in this paper was funded by the Office of Naval Research (ONR) under Dr. Patrick Purtell. Also, by ONR Global under Dr. Richard Vogelsong and Dr. Woei-Min Lin. This support is gratefully acknowledged by the authors.

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Authors and Affiliations

  1. School of Naval Architecture, Ocean and Marine Engineering, National Technical University of Athens, Athens, Greece

    K. J. Spyrou & N. Themelis

  2. Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, Glasgow, UK

    K. J. Spyrou & N. Themelis

  3. David Taylor Model Basin, Carderock, Washington, DC, USA

    V. Belenky

  4. Science Applications International Corporation, McLean, VA, USA

    K. Weems

Authors
  1. K. J. Spyrou
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  2. V. Belenky
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  3. N. Themelis
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  4. K. Weems
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Correspondence to K. J. Spyrou.

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Spyrou, K.J., Belenky, V., Themelis, N. et al. Detection of surf-riding behavior of ships in irregular seas. Nonlinear Dyn 78, 649–667 (2014). https://doi.org/10.1007/s11071-014-1466-2

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  • DOI: https://doi.org/10.1007/s11071-014-1466-2

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