Research output: Contribution to journal › Article › peer-review
Bound coherent structures propagating on the free surface of deep water. / Kachulin, Dmitry; Dremov, Sergey; Dyachenko, Alexander.
In: Fluids, Vol. 6, No. 3, 115, 03.2021.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 34126478