scholarly journals Interactions of Coherent Structures on the Surface of Deep Water

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 83 ◽  
Author(s):  
Dmitry Kachulin ◽  
Alexander Dyachenko ◽  
Andrey Gelash
Keyword(s):  
Nonlinear Model ◽  
Deep Water ◽  
Relative Phase ◽  
Initial Conditions ◽  
Wave Interaction ◽  
Ideal Incompressible Fluid ◽  
Interaction Coefficient ◽  
Collision Dynamics ◽  
Zakharov Equation ◽  
Fully Nonlinear

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.

Bound Coherent Structures Propagating on the Free Surface of Deep Water

2021 ◽  
Author(s):  
Sergey Dremov ◽  
Dmitry Kachulin ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Initial Conditions ◽  
Soliton Solutions ◽  
Ideal Incompressible Fluid ◽  
System Of Nonlinear Equations ◽  
Computational Domain

<p><span>               The work presents the results of studying the bound coherent structures propagating on the free surface of ideal incompressible fluid of infinite depth. Examples of such structures are bi-solitons which are exact solutions of the known approximate model for deep water waves — the nonlinear Schrödinger equation (NLSE). Recently, when studying multiple breathers collisions, the occurrence of such objects was found in a more accurate model of the supercompact equation for unidirectional water waves [1]. The aim of this work is obtaining and further studying such structures with different parameters in the supercompact equation and in the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. </span><span>The algorithm used for finding the bound coherent objects was similar to the one described in [2]. As the initial conditions for obtaining such structures in the framework of the above models, the NLSE bi-soliton solutions were used, as well as two single breathers numerically found by the Petviashvili method and placed in a same point of the computational domain. During the evolution calculation the initial structures emitted incoherent waves which were filtered at the boundaries of the domain using the damping procedure. It is shown that after switching off the filtering of radiation, periodically oscillating coherent objects remain on the surface of the liquid, propagate stably during one hundred thousand characteristic wave periods and do not lose energy. The profiles of such structures at different parameters are compared.</span></p><p><span>This work was supported by RSF grant </span><span>19-72-30028</span><span> and </span><span>RFBR grant </span><span>20-31-90093</span><span>.</span></p><p><span>[1] Kachulin D., Dyachenko A., Dremov S. Multiple Soliton Interactions on the Surface of Deep Water //Fluids. – 2020. – Т. 5. – №. 2. – С. 65.</span></p><p><span>[2] Dyachenko A. I., Zakharov V. E. On the formation of freak waves on the surface of deep water //JETP letters. – 2008. – Т. 88. – №. 5. – С. 307.</span></p>

scholarly journals Collisions of two breathers at the surface of deep water

2013 ◽  
Vol 13 (12) ◽  
pp. 3205-3210 ◽  
Author(s):  
A. I. Dyachenko ◽  
D. I. Kachulin ◽  
V. E. Zakharov
Keyword(s):  
Numerical Experiment ◽  
Deep Water ◽  
Numerical Experiments ◽  
Wave Interaction ◽  
Zakharov Equation ◽  
Envelope Solitons ◽  
Term Evolution ◽  
Refined Version ◽  
Exact Cancellation

Abstract. We present results of numerical experiments on long-term evolution and collisions of breathers (which correspond to envelope solitons in the NLSE approximation) at the surface of deep ideal fluid. The collisions happen to be nonelastic. In the numerical experiment it can be observed only after many acts of interactions. This supports the hypothesis of "deep water nonintegrability". The experiments were performed in the framework of the new and refined version of the Zakharov equation free of nonessential terms in the quartic Hamiltonian. Simplification is possible due to exact cancellation of nonelastic four-wave interaction.

scholarly journals Collisions of two breathers at the surface of deep water

2013 ◽  
Vol 1 (3) ◽  
pp. 3023-3043
Author(s):  
A. I. Dyachenko ◽  
D. I. Kachulin ◽  
V. E. Zakharov
Keyword(s):  
Numerical Experiment ◽  
Deep Water ◽  
Ideal Fluid ◽  
Numerical Experiments ◽  
Wave Interaction ◽  
Zakharov Equation ◽  
Envelope Solitons ◽  
Long Time ◽  
Refined Version ◽  
Exact Cancellation

Abstract. We present results of numerical experiments on long time evolution and collisions of breathers (which correspond to envelope solitons in the NLSE approximation) at the surface of deep ideal fluid. The collision happens to be nonelastic. In the numerical experiment it can be observed only after many acts of interactions. This supports the hypothesis of "deep water nonintegrability". The experiments were performed in the framework of the new and refined version of the Zakharov equation free of nonessential terms in the quartic Hamiltonian. Simplification is possible due to exact cancellation of nonelastic four-wave interaction.

scholarly journals Phase-dependent dynamics of breather collisions in the compact Zakharov equation for envelope

2018 ◽  
Author(s):  
Dmitry Kachulin ◽  
Andrey Gelash
Keyword(s):  
Energy Loss ◽  
Gravity Waves ◽  
Deep Water ◽  
Relative Phase ◽  
Soliton Solutions ◽  
Wave Steepness ◽  
Zakharov Equation ◽  
Coherent Wave ◽  
Amplitude Amplification ◽  
Key Parameter

Abstract. We study collisions of the solitary type coherent wave structures – breathers in the nonintegrable Zakharov equation for envelope describing gravity waves on the surface of deep water. The numerical simulations of breather interactions revealed several fundamentally different effects when compared to analytical two-soliton solutions of the nonlinear Schrodinger equation. The relative phase of the breathers is shown to be the key parameter determining the dynamics of the interaction. We show that the maximum of the amplitude amplification can significantly exceed the sum of the breather amplitudes. The breathers lose up to a few percent of their energy during the collisions due to radiation of incoherent waves and in addition exchange energy with each other. The level of the energy loss increases with large values of the wave steepness, and also with certain synchronisation of breather phases. Each of the breathers can gain or lose the energy after collision resulting in the increase or decrease of the amplitude. The magnitude of the space shifts that breathers acquire after collisions depends on the relative phase and can be either positive or negative.

scholarly journals Bound Coherent Structures Propagating on the Free Surface of Deep Water

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 115
Author(s):  
Dmitry Kachulin ◽  
Sergey Dremov ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Nonlinear Models ◽  
Ideal Incompressible Fluid ◽  
Equation Model ◽  
System Of Nonlinear Equations ◽  
Potential Flows ◽  
Deep Water Waves

This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The special numerical algorithm that includes a damping procedure of radiation and velocity adjusting was used for obtaining such bound structures. The results showed that in both nonlinear models for deep water waves after the damping is turned off, a periodically oscillating bound structure remains on the fluid surface and propagates stably over hundreds of thousands of characteristic wave periods without losing energy.

Fully Nonlinear Potential/RANSE Simulation of Wave Interaction With Ships and Marine Structures

2008 ◽  
Author(s):  
Pierre Ferrant ◽  
Lionel Gentaz ◽  
Bertrand Alessandrini ◽  
Romain Luquet ◽  
Charles Monroy ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Irregular Waves ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Fully Nonlinear ◽  
Nonlinear Potential ◽  
6 Degrees Of Freedom

This paper documents recent advances of the SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach, a method for simulating fully nonlinear wave-body interactions including viscous effects. The methods efficiently combines a fully nonlinear potential flow description of undisturbed wave systems with a modified set of RANS with free surface equations accounting for the interaction with a ship or marine structure. Arbitrary incident wave systems may be described, including regular, irregular waves, multidirectional waves, focused wave events, etc. The model may be fixed or moving with arbitrary speed and 6 degrees of freedom motion. The extension of the SWENSE method to 6 DOF simulations in irregular waves as well as to manoeuvring simulations in waves are discussed in this paper. Different illlustative simulations are presented and discussed. Results of the present approach compare favorably with available reference results.

Fully nonlinear solution of bi-chromatic deep-water waves

2014 ◽  
Vol 91 ◽  
pp. 290-299 ◽  
Author(s):  
Zhiliang Lin ◽  
Longbin Tao ◽  
Yongchang Pu ◽  
Alan J. Murphy
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Fully Nonlinear ◽  
Nonlinear Solution ◽  
Deep Water Waves

Richtmyer–Meshkov instability on two-dimensional multi-mode interfaces

2021 ◽  
Vol 928 ◽  
Author(s):  
Yu Liang ◽  
Lili Liu ◽  
Zhigang Zhai ◽  
Juchun Ding ◽  
Ting Si ◽  
...  
Keyword(s):  
Nonlinear Model ◽  
Initial Conditions ◽  
Superposition Principle ◽  
Mode Competition ◽  
Two Dimensional ◽  
Competition Effect ◽  
Density Ratios ◽  
Multi Mode ◽  
Amplitude Growth ◽  
Perturbation Growth

Shock-tube experiments on eight kinds of two-dimensional multi-mode air–SF $_6$ interface with controllable initial conditions are performed to examine the dependence of perturbation growth on initial spectra. We deduce and demonstrate experimentally that the amplitude development of each mode is influenced by the mode-competition effect from quasi-linear stages. It is confirmed that the mode-competition effect is closely related to initial spectra, including the wavenumber, the phase and the initial amplitude of constituent modes. By considering both the mode-competition effect and the high-order harmonics effect, a nonlinear model is established based on initial spectra to predict the amplitude growth of each individual mode. The nonlinear model is validated by the present experiments and data in the literature by considering diverse initial spectra, shock intensities and density ratios. Moreover, the nonlinear model is successfully extended based on the superposition principle to predict the growths of the total perturbation width and the bubble/spike width from quasi-linear to nonlinear stages.

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