TY - JOUR

T1 - Bound coherent structures propagating on the free surface of deep water

AU - Kachulin, Dmitry

AU - Dremov, Sergey

AU - Dyachenko, Alexander

N1 - Funding Information: Funding: The Russian Science Foundation Grant No. 19-72-30028 and The Russian Foundation for Basic Research Grant No. 20-31-90093. Funding Information: Acknowledgments: The study reported in Section 4 was supported by the Russian Science Foundation (Grant No. 19-72-30028 to D.K., S.D.). The study reported in Section 3 was funded by RFBR according to the research project No. 20-31-90093 (D.K., S.D.). Simulations were performed at the Novosibirsk Supercomputer Center of Novosibirsk State University. Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/3

Y1 - 2021/3

N2 - 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.

AB - 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.

KW - Bi-soliton

KW - Breather

KW - Dyachenko equations

KW - Nonlinear schrödinger equation

KW - Soliton

KW - Super-compact dyachenko-zakharov equation

KW - Surface gravity waves

UR - http://www.scopus.com/inward/record.url?scp=85107953640&partnerID=8YFLogxK

U2 - 10.3390/fluids6030115

DO - 10.3390/fluids6030115

M3 - Article

AN - SCOPUS:85107953640

VL - 6

JO - Fluids

JF - Fluids

SN - 2311-5521

IS - 3

M1 - 115

ER -