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Numerical simulation of the transformation of a nonlinear wave at a finite depth

  • Wave Propagation on the Sea Shelf
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Abstract

The shallow-water propagation of a nonlinear wave formed in deep water has been numerically analyzed based on the conformal model of surface waves. The lifetime of wave until its collapse is investigated. The parameters at which extreme waves may occur are found. An example of practical application of the simulation results is presented.

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References

  1. D. V. Chalikov and K. Yu. Bulgakov, “Stokes Waves at a Finite Depth,” Fundamentalnaya i Prikladnaya Gidrofizika. 7(4), 3 (2014) [in Russian].

    Google Scholar 

  2. M. S. Longuet-Higgins and E.D. Cokelet, “The Deformation of Steep SurfaceWaves onWater. I. A Numerical Method of Computations,” Proc. R. Soc. Lond. A. 350, 1 (1976).

    Article  ADS  MATH  Google Scholar 

  3. M. P. Tulin and T. Waseda, “Laboratory Observations of Wave Group Evolution, Including Breaking Effects,” J. Fluid Mech. 378, 197 (1999).

    Article  ADS  MATH  Google Scholar 

  4. C. W. Hirt and B.D. Nicholos, “Volume of Fluid (VOF) Method for the Dynamic of Free Boundaries,” J. Comp. Phys. 39(1), 201 (1981).

    Article  ADS  Google Scholar 

  5. D. Dommermuth and D. Yue, “A High-Order Spectral Method for the Study of Nonlinear Gravity Waves,” J. Fluid Mech. 184, 267 (1987).

    Article  ADS  MATH  Google Scholar 

  6. B. West, K. Brueckner, R. Janda, M. Milder, and R. Milton, “ANew Numerical Method for Surface Hydrodynamics,” J. Geophys. Res. 92(11), 803 (1987).

    Google Scholar 

  7. D. Clamond and J. Grue, “A Fast Method for Fully Nonlinear Water Wave Dynamics,” J. Fluid Mech. 447, 337 (2001).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. D. Clamond, D. Fructus, J. Grue, and O. Krisitiansen, “An Efficient Method for Three-Dimensional Surface Wave Simulations. Part II: Generation and Absorption,” J. Comp. Phys. 205, 686 (2005).

    Article  ADS  MATH  Google Scholar 

  9. D. Fructus, D. Clamond, J. Grue, and O. Krisitiansen, “An Efficient Model for Three-Dimensional Surface Wave Simulations. Part I: Free Space Problems,” J. Comp. Phys. 205, 665 (2005).

    Article  ADS  MATH  Google Scholar 

  10. S. Grilli, P. Guyenne, and F. Dias, “A Fully NonlinearModel for Three-Dimensional OverturningWaves Over Arbitrary Bottom,” Int. J. Num. Meth. Fluids. 35, 829 (2001).

    Article  MATH  Google Scholar 

  11. D. Chalikov and D. Sheinin, “Numerical Modeling of Surface Waves Based on Principal Equations of Potential Wave Dynamics,” in Technical Note (NOAA/NCEP/OMB, 1996).

    Google Scholar 

  12. D. Chalikov and D. Sheinin, “Direct Modeling of One-dimensional Nonlinear Potential Waves,” Adv. Fluid Mech. 17, 207 (1998).

    Google Scholar 

  13. D. Chalikov and D. Sheinin, “Modeling of Extreme Waves Based on Equations of Potential Flow with a Free Surface,” J. Comp. Phys. 210, 247 (2005).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. D. Sheinin and D. Chalikov, “Hydrodynamical Modeling of Potential Surface Waves,” in Proceedings of International Theoretical Conference “Problems of Hydrometeorology and Environment on the Eve of XXI Century” (24-25 June, 1999, St. Petersburg) (Hydrometeoizdat, St.Petersburg, 2000), pp. 305–337 [in Russian].

    Google Scholar 

  15. D. Chalikov, “Statistical Properties of Nonlinear One-Dimensional Wave Fields,” Nonlin. Proc. Geophys. 12, 1 (2005).

    Article  Google Scholar 

  16. J. C. Whitney, “The Numerical Solution of Unsteady Free-Surface Flows by Conformal Mapping,” in Proceedings of the 2nd International Conference on Numerical Methods in Fluid Dynamics (Springer-Verlag, 1971), pp. 458–462.

    Chapter  Google Scholar 

  17. E. A. Kuznetsov, M. D. Spector, and V.E. Zakharov, “Formulation of Singularities on the Free Surface of an Ideal Fluid,” Phys. Rev. E. 49(2), 1283 (1994).

    Article  ADS  MathSciNet  Google Scholar 

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Bulgakov, K.Y. Numerical simulation of the transformation of a nonlinear wave at a finite depth. Phys. Wave Phen. 25, 78–82 (2017). https://doi.org/10.3103/S1541308X17010137

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  • DOI: https://doi.org/10.3103/S1541308X17010137

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