Definitions of Celerity for Investigating Surf-Riding in an Irregular Seaway

  • Kostas J. SpyrouEmail author
  • Vadim L. Belenky
  • Nikos Themelis
  • Kenneth M. Weems
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 119)


As is well-known, if the speed of a ship operating in high, fairly regular, following waves exceeds wave celerity, then surf-riding is realized. This motivates one to approach the calculation of the probability of surf-riding in irregular seas as a threshold exceedance problem. However, it is unknown whether such a simple phenomenological rule, using the celerity as threshold, could also be applicable for the ship dynamics associated with a stochastic wave environment. To clarify this, a suitable definition of wave celerity for an irregular seaway needs first to become available. In this chapter, we define celerity as the velocity of propagation of a fixed slope value of the wave profile. This leads to the concept of instantaneous celerity, opening up a window to the literature of instantaneous frequency in signal processing. As it turns out, instantaneous celerity is not always a consistently smooth and bounded curve. Other definitions of local celerity are also conceivable. We tested a few different selections, obtaining time-dependent celerity curves for various types of waves. Relaxing the requirement for a narrow-band spectrum, we offer some clues about the effect of spectrum’s bandwidth on celerity. In a further step, simultaneous treatment of the “wave” and “ship” processes is implemented, in order to investigate the potential of applying a local celerity condition for surf-riding’s prediction. Various patterns of ship motion, before and into surf-riding, are observed.


Surf-riding Wave celerity Irregular waves 



The research reported in this chapter was funded by the Office of Naval Research (ONR) under Dr. Patrick Purtell and by ONR Global under Dr. Richard Vogelsong. This support is gratefully acknowledged by the authors.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kostas J. Spyrou
    • 1
    Email author
  • Vadim L. Belenky
    • 2
  • Nikos Themelis
    • 1
  • Kenneth M. Weems
    • 2
  1. 1.School of Naval Architecture and Marine EngineeringNational Technical University of AthensAthensGreece
  2. 2.David Taylor Model Basin (NSWCCD)West BethesdaUSA

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