Mechanism of the Emergence of Rogue Waves As a Result of the Interaction between Internal Solitary Waves in a Stratified Basin
The features of the interaction between internal solitary waves are investigated within the framework of the completely integrable Gardner equation with positive cubic nonlinearity. It is shown that the soliton polarity affects radically the result of the interaction between the solitons. The role of the pair interactions between solitons of different polarities proceeding when rogue waves emerge in the soliton fields in a stratified basin is demonstrated. The effect of such interactions on the higher-order moments of the wave field is studied.
Key wordsinternal waves soliton Gardner equation rogue waves coastal area
Unable to display preview. Download preview PDF.
- 1.Yu. Z. Miropol’skii, Dynamics of Internal GravityWaves in the Ocean (Gidrometeoizdat, Leningrad, 1981) [in Russian].Google Scholar
- 4.P. Guyenne, “Large-Amplitude Internal Solitary Waves in a Two-Fluid Model,” C.R. Mecanique, 334–341 (2006).Google Scholar
- 7.J. A. Knauss, Introduction to Physical Oceanography (Prentice Hall, 1996).Google Scholar
- 10.E. N. Pelinovsky and A. V. Slunyaev, “Generation and Interaction of Large-Amplitude Solitons,” Pis’ma v Zh. Eksp. Teor. Fiz. 67, 628–633 (1998).Google Scholar
- 11.A. V. Slunyaev and E. N. Pelinovsky, “Dynamics of Large-Amplitude Solitons,” Zh. Eksp. Teor. Fiz. 116, 318–335 (1999).Google Scholar
- 12.A. V. Slunyaev, “Dynamics of Large-Amplitude Localized Waves in a Weakly Dispersive Medium with Quadratic and Cubic Nonlinearity,” Zh. Eksp. Teor. Fiz. 119, 606–612 (2001).Google Scholar
- 15.R. Grimshaw, “Internal Solitary Waves (Chapter 1),” in: R. Grimshaw (Ed.), Environmental Stratified Flows (Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001), pp. 1–28.Google Scholar
- 16.E. N. Pelinovsky, O. E. Polukhina, and K. Lamb, “Nonlinear Internal Waves in Ocean Stratified in Density and Flow,” Okeanologiya 40 (6), 805–815 (2000).Google Scholar
- 17.T. G. Talipova, E. N. Pelinovsky, K. Lamb, R. Grimshaw, and P. Holloway, “Effects of Cubic Nonlinearity in Propagation of Intense InternalWaves,” Dokl. Akad. Nauk SSSR 364 (6), 824–827 (1996).Google Scholar
- 19.E. N. Pelinovsky and E. G. Shurgalina, “Two-Soliton Interaction within the Framework of the Modified Korteweg-de Vries Equation,” Izv. Vuzov. Radiofizika 57 (10), 825–833 (2014).Google Scholar