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Advances in Breaking-Wave Dynamics

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Wave Dynamics and Radio Probing of the Ocean Surface

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Abstract

Progress has been made recently not only in numerical methods of calculating steep waves but also in finding analytic solutions for overturning fluid motions. Thus, the tip of the wave can take the form of a slender hyperbola, in which the orientation of the axes and the angle between the asymptotes are both functions of the time. The initial stages of overturning are given approximately by a two-term expression for the potential, with a branch-point located in the “tube” of the wave. Most remarkably, plunging breakers appear experimentally to tend toward certain exact, time-dependent flows (recently discovered) in which the forward face is given by a simple parametric cubic curve. Dynamical aspects breaking waves are discussed, particularly in terms of angular momentum.

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References

  • Baker, G. R., and M. Israeli (1981): Numerical techniques for free surface motion with application to drip motion caused by variable surface tension. Lecture Notes in Physics 141, Springer-Verlag, Berlin, 61–67.

    Article  MathSciNet  Google Scholar 

  • Banner, M. L., and O. M. Phillips (1974): On small scale breaking waves. J. Fluid Mech. 65, 647–657.

    Article  MATH  Google Scholar 

  • Benjamin, T. B. (1967): Instability of periodic wavetrains in nonlinear dispersive systems. Proc. R. Soc. London Ser. A 299, 59–67.

    Article  Google Scholar 

  • Chen, B., and P. G. Saffman (1980): Numerical evidence for the existence of new types of gravity waves of permanent form on deep water. Stud. Appl. Math. 62, 1–21.

    MathSciNet  MATH  Google Scholar 

  • Cleaver, R. P. (1981): Instabilities of surface gravity waves. Ph.D. dissertation. University of Cambridge.

    Google Scholar 

  • Cokelet, E. D. (1977): Steep gravity waves in water of arbitrary uniform depth. Philos. Trans. R. Soc. London Ser. A 286, 183–230.

    Article  MathSciNet  MATH  Google Scholar 

  • John, F. (1953): Two-dimensional potential flows with a free boundary. Comm. Pure Appl. Math. 6, 497–503.

    Article  MathSciNet  MATH  Google Scholar 

  • Lamb, H. (1932): Hydrodynamics, 6th ed. Cambridge University Press, London.

    MATH  Google Scholar 

  • Longuet-Higgins, M. S. (1972): A class of exact, time-dependent free-surface flows. J. Fluid Mech. 55, 529–543.

    Article  MathSciNet  MATH  Google Scholar 

  • Longuet-Higgins, M. S. (1976): Self-similar, time-dependent flows with a free surface. J. Fluid Mech. 73, 603–620.

    Article  MathSciNet  MATH  Google Scholar 

  • Longuet-Higgins, M. S. (1978a): The instabilities of gravity waves of finite amplitude in deep water. Proc. R. Soc. London Ser. A 360, 471–505.

    Article  MathSciNet  MATH  Google Scholar 

  • Longuet-Higgins, M. S. (1978b): On the dynamics of steep gravity waves in water. Turbulent Fluxes Through the Sea Surface, Wave Dynamics, and Prediction (A. Favre and K. Hasselmann, eds.). Plenum Press, New York, 199–219.

    Chapter  Google Scholar 

  • Longuet-Higgins, M. S. (1980a): A technique for time-dependent, free surface flows. Proc. R. Soc. London Ser. A 371, 441–451.

    Article  MathSciNet  MATH  Google Scholar 

  • Longuet-Higgins, M. S. (1980b): On the forming of sharp comers at a free surface. Proc. R. Soc. London Ser. A 371, 453–478.

    Article  MathSciNet  MATH  Google Scholar 

  • Longuet-Higgins, M. S. (1980c): Spin and angular momentum in gravity waves. J. Fluid Mech. 97, 1–25.

    Article  MathSciNet  MATH  Google Scholar 

  • Longuet-Higgins, M. S. (1981): On the overturning of gravity waves. Proc. R. Soc. London Ser. A 376, 377–400.

    Article  MathSciNet  MATH  Google Scholar 

  • Longuet-Higgins, M. S. (1982): Parametric solutions for breaking waves. J. Fluid Mech. 121, 403–424.

    Article  MathSciNet  MATH  Google Scholar 

  • Longuet-Higgins, M. S., and E. D. Cokelet (1976): The deformation of steep surface waves on water. I. A numerical method of computation. Proc. R. Soc. London Ser. A 350, 175–189.

    Article  MathSciNet  MATH  Google Scholar 

  • Longuet-Higgins, M. S., and E. D. Cokelet (1978): The deformation of steep surface waves on water. IL Growth of normal-mode instabilities. Proc. R. Soc. London Ser. A 364, 1–28.

    Article  MathSciNet  MATH  Google Scholar 

  • Miles, J. W. (1980): Sohtary waves. Ann. Rev. Fluid Mech. 12, 11–43.

    Article  Google Scholar 

  • Miller, R. L. (1957): Role of vortices in surfzone prediction, sedimentation and wave forces. Beach and Nearshore Sedimentation (R. A. Davis and R. L. Ethington, eds.), Soc. Econ. Palaeontol. Mineral., Tulsa, Okla., 92–114.

    Google Scholar 

  • New, A. L. (1981): Breaking waves in water of finite depth. British Theor. Mech. Colloquium, Bradford, England, pp. 6–9.

    Google Scholar 

  • Olfe, D. B., and J. W. Rottman (1979): Numerical calculations of steady gravity-capillary waves using an integro-differential formulation. J. Fluid Mech. 94, 777–793.

    Article  MathSciNet  MATH  Google Scholar 

  • Vanden-Broeck, J.-M., and L. W. Schwartz (1979): Numerical computation of steep waves in shallow water. Phys. Fluids 22, 1868–1971.

    Article  MATH  Google Scholar 

  • Vinje, T. and Brevig, P. (1981): Breaking waves on finite water depths: a numerical study. Ship. Res. Inst. Norway, Report R-111.81.

    Google Scholar 

  • Williams, J. M. (1981): Limiting gravity waves in water of finite depth. Philos. Trans. R. Soc. London Ser. A 302, 139–188.

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England

    M. S. Longuet-Higgins

  2. Institute of Oceanographic Sciences, Wormley, England, GU85UB

    M. S. Longuet-Higgins

Authors
  1. M. S. Longuet-Higgins
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Editor information

Editors and Affiliations

  1. The Johns Hopkins University, Baltimore, Maryland, USA

    O. M. Phillips

  2. Max Planck Institute for Meteorology, Hamburg, Federal Republic of Germany

    Klaus Hasselmann

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© 1986 Plenum Press, New York

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Longuet-Higgins, M.S. (1986). Advances in Breaking-Wave Dynamics. In: Phillips, O.M., Hasselmann, K. (eds) Wave Dynamics and Radio Probing of the Ocean Surface. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8980-4_14

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  • DOI: https://doi.org/10.1007/978-1-4684-8980-4_14

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-8982-8

  • Online ISBN: 978-1-4684-8980-4

  • eBook Packages: Springer Book Archive

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