Processes of concentration of energy in the formation of rogue waves
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 1, pp. 49-58.

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We study the processes of concentration of energy in the formation of anomalously large surface waves. We got quantitative characteristics of energy processes in the formation of freak waves using numerical experiments which is based on the full nonlinear equations of hydrodynamics of ideal liquid. The results can be used to assess the risk of dangerous effects of rogue waves in the ocean.
Keywords: abnormally large surface waves, numerical experiment, hydrodynamics of ideal liquid.
Mots-clés : rogue waves
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Roman V. Shamin; Alexander V. Yudin. Processes of concentration of energy in the formation of rogue waves. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 1, pp. 49-58. http://geodesic.mathdoc.fr/item/ND_2014_10_1_a3/

[1] Kharif C., Pelinovsky E., Slunyaev A., Rogue waves in the ocean, Springer, Berlin, 2009, 216 pp. | MR | Zbl

[2] Nikolkina I., Didenkulova I., “Rogue waves in 2006–2010”, Nat. Hazards Earth Syst. Sci., 11 (2011), 2913–2924 | DOI | MR

[3] Henderson K. L., Pelegrine D. H., Dold J. W., “Unsteady water wave modulations: Fully nonlinear solutions and comparison with the nonlinear Schrödinger equation”, Wave Motion, 29:4 (1999), 341–361 | DOI | MR | Zbl

[4] Baterman W. J. D., Swan C., Taylor P. H., “On the efficient numerical simulation of directionally spread surface water waves”, J. Comput. Phys., 174:1 (2001), 277–305 | DOI | MR

[5] Dyachenko A. I., Zakharov V. E., “On the formation of freak waves on the surface of deep water”, Pisma v ZhETF, 88:5 (2008), 356–359 | MR

[6] Zakharov V. E., Dyachenko A. I., Shamin R. V., “How probability for freak wave formation can be found”, Eur. Phys. J. Spec. Top., 185:1 (2010), 113–124 | DOI

[7] Chalikov D., “Freak waves: Their occurrence and probability”, Phys. Fluids, 21:7 (2009), 076602, 18 pp. | DOI | Zbl

[8] Fochesato C., Grilli S., Dias F., “Numerical modeling of extreme rogue waves generated by directional energy focusing”, Wave Motion, 44:5 (2007), 395–416 | DOI | MR | Zbl

[9] Xiao W., Liu Y., Wu G., Yue D. K. P., “Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution”, J. Fluid Mech., 720 (2013), 357–392 | DOI | MR | Zbl

[10] Zakharov V. E., Shamin R. V., “O veroyatnosti vozniknoveniya voln-ubiits”, Pisma v ZhETF, 91:2 (2010), 68–71

[11] Zakharov V. E., Shamin R. V., “Statistika voln-ubiits v vychislitelnykh eksperimentakh”, Pisma v ZhETF, 96:1 (2012), 68–71

[12] Dyachenko A. I., Zakharov V. E., Kuznetsov E. A., “Nelineinaya dinamika svobodnoi poverkhnosti idealnoi zhidkosti”, Fizika plazmy, 1999, no. 10, 916–928

[13] Zakharov V. E., “Ustoichivost periodicheskikh voln na poverkhnosti glubokoi zhidkosti”, Prikl. mekhan. i tekhn. fiz., 1968, no. 2, 86–94

[14] Whitney J. C., “The numerical solution of unsteady free-surface flows by conformal mapping”, Proc. of the 2nd Internat. Conf. on Numerical Methods in Fluid Dynamics (University of California, Berkeley, CA, Sept. 15–19, 1970), Lecture Notes in Phys., 8, ed. M. Holt, Springer, Berlin, 1971, 458–462 | DOI

[15] Ovsyannikov L. V., “K obosnovaniyu teorii melkoi vody”, Sb. nauch. tr./Akad. nauk SSSR, Sib. otd-nie, In-t gidrodinamiki, Dinamika sploshnoi sredy, 15, AN SSSR, Novosibirsk, 1973, 104–125

[16] Chalikov D., Sheinin D., “Modeling of extreme waves based on equations of potential flow with a free surface”, J. Comput. Phys., 210:1 (2005), 247–273 | DOI | MR | Zbl

[17] Zakharov V. E., Dyachenko A. I., Vasilyev O. A., “New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface”, Eur. J. Mech. B Fluids, 21:3 (2002), 283–291 | DOI | MR | Zbl

[18] Shamin R. V., “Dynamics of an ideal liquid with a free surface in conformal variables”, J. Math. Sci., 160:5 (2009), 537–678 | DOI | MR | Zbl

[19] Shamin R. V., “O suschestvovanii gladkikh reshenii uravnenii Dyachenko, opisyvayuschikh neustanovivshiesya techeniya idealnoi zhidkosti so svobodnoi poverkhnostyu”, Dokl. RAN, 406:5 (2006), 112–113 | MR | Zbl

[20] Shamin R. V., “Ob odnom chislennom metode v zadache o dvizhenii idealnoi zhidkosti so svobodnoi poverkhnostyu”, Sib. zhurn. vychisl. matem., 9:4 (2006), 379–389 | Zbl