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
D. V. Chalikov and K. Yu. Bulgakov, “Stokes Waves at a Finite Depth,” Fundamentalnaya i Prikladnaya Gidrofizika. 7(4), 3 (2014) [in Russian].
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).
M. P. Tulin and T. Waseda, “Laboratory Observations of Wave Group Evolution, Including Breaking Effects,” J. Fluid Mech. 378, 197 (1999).
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).
D. Dommermuth and D. Yue, “A High-Order Spectral Method for the Study of Nonlinear Gravity Waves,” J. Fluid Mech. 184, 267 (1987).
B. West, K. Brueckner, R. Janda, M. Milder, and R. Milton, “ANew Numerical Method for Surface Hydrodynamics,” J. Geophys. Res. 92(11), 803 (1987).
D. Clamond and J. Grue, “A Fast Method for Fully Nonlinear Water Wave Dynamics,” J. Fluid Mech. 447, 337 (2001).
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).
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).
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).
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).
D. Chalikov and D. Sheinin, “Direct Modeling of One-dimensional Nonlinear Potential Waves,” Adv. Fluid Mech. 17, 207 (1998).
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).
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].
D. Chalikov, “Statistical Properties of Nonlinear One-Dimensional Wave Fields,” Nonlin. Proc. Geophys. 12, 1 (2005).
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.
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).
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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