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Interactions of Coherent Structures on the Surface of Deep Water

1
Novosibirsk State University, 630090 Novosibirsk, Russia
2
Landau Institute for Theoretical Physics RAS, 142432 Chernogolovka, Russia
*
Authors to whom correspondence should be addressed.
Fluids 2019, 4(2), 83; https://doi.org/10.3390/fluids4020083
Received: 22 March 2019 / Revised: 16 April 2019 / Accepted: 28 April 2019 / Published: 2 May 2019
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
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Abstract

We numerically investigate pairwise collisions of solitary wave structures on the surface of deep water—breathers. These breathers are spatially localised coherent groups of surface gravity waves which propagate so that their envelopes are stable and demonstrate weak oscillations. We perform numerical simulations of breather mutual collisions by using fully nonlinear equations for the potential flow of ideal incompressible fluid with a free surface written in conformal variables. The breather collisions are inelastic. However, the breathers can still propagate as stable localised wave groups after the interaction. To generate initial conditions in the form of separate breathers we use the reduced model—the Zakharov equation. We present an explicit expression for the four-wave interaction coefficient and third order accuracy formulas to recover physical variables in the Zakharov model. The suggested procedure allows the generation of breathers of controlled phase which propagate stably in the fully nonlinear model, demonstrating only minor radiation of incoherent waves. We perform a detailed study of breather collision dynamics depending on their relative phase. In 2018 Kachulin and Gelash predicted new effects of breather interactions using the Dyachenko–Zakharov equation. Here we show that all these effects can be observed in the fully nonlinear model. Namely, we report that the relative phase controls the process of energy exchange between breathers, level of energy loses, and space positions of breathers after the collision. View Full-Text
Keywords: breathers; solitons; freak waves; nonlinear waves; surface gravity waves; Dyachenko equations; Zakharov equation breathers; solitons; freak waves; nonlinear waves; surface gravity waves; Dyachenko equations; Zakharov equation
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Kachulin, D.; Dyachenko, A.; Gelash, A. Interactions of Coherent Structures on the Surface of Deep Water. Fluids 2019, 4, 83.

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