The dynamic conformal transformation method has been generalized for the first time to numerically simulate the capillary wave turbulence of a liquid surface in the plane symmetric anisotropic geometry. The model is strongly nonlinear and involves effects of surface tension, as well as energy dissipation and pumping. Simulation results have shown that the system of nonlinear capillary waves can pass to the quasistationary chaotic motion regime (wave turbulence). The calculated exponents of spectra do not coincide with those for the classical Zakharov–Filonenko spectrum for isotropic capillary turbulence but are in good agreement with the estimate obtained under the assumption of the dominant effect of five-wave resonant interactions.
REFERENCES
V. E. Zakharov, G. Falkovich, and V. S. L’vov, Kolmogorov Spectra of Turbulence I: Wave Turbulence (Springer, Berlin, 1992).
A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, Phys. Rep. 542, 1 (2014).
S. Galtier, J. Phys. A: Math. Theor. 51, 293001 (2018).
S. Galtier, S. V. Nazarenko, A. C. Newell, and A. Pouquet, J. Plasma Phys. 63, 447 (2000).
E. Kochurin, G. Ricard, N. Zubarev, and E. Falcon, Phys. Rev. E 105, L063101 (2022).
S. Dorbolo and E. Falcon, Phys. Rev. E 83, 046303 (2011).
I. A. Dmitriev, E. A. Kochurin, and N. M. Zubarev, IEEE Trans. Dielectr. Electr. Insul. 304, 1408 (2023).
V. E. Zakharov and R. Z. Sagdeev, Sov. Phys. Dokl. 15, 439 (1970).
A. Griffin, G. Krstulovic, V. S. L’vov, and S. Nazarenko, Phys. Rev. Lett. 128, 224501 (2022).
E. A. Kochurin and E. A. Kuznetsov, JETP Lett. 116, 863 (2022).
V. E. Zakharov and N. N. Filonenko, J. Appl. Mech. Tech. Phys. 8, 37 (1967).
A. O. Korotkevich, Phys. Rev. Lett. 130, 264002 (2023).
Z. Zhang and Y. Pan, Phys. Rev. E 106, 044213 (2022).
G. V. Kolmakov, M. Y. Brazhnikov, A. A. Levchenko, L. V. Abdurakhimov, P. V. E. McClintock, and L. P. Mezhov-Deglin, Prog. Low Temp. Phys. 16, 305 (2009).
E. Falcon and N. Mordant, Ann. Rev. Fluid Mech. 54, 1 (2022).
A. N. Pushkarev and V. E. Zakharov, Phys. Rev. Lett. 76, 3320 (1996).
L. Deike, D. Fuster, M. Berhanu, and E. Falcon, Phys. Rev. Lett. 112, 234501 (2014).
Y. Pan and D. K. P. Yue, Phys. Rev. Lett. 113, 094501 (2014).
E. Kochurin, G. Ricard, N. Zubarev, and E. Falcon, JETP Lett. 112, 757 (2020).
G. Ricard and E. Falcon, Europhys. Lett. 135, 64001 (2021).
S. Nazarenko, Wave Turbulence, Vol. 825 of Lecture Notes in Physics (Springer, Berlin, 2011).
A. Dyachenko, Y. Lvov, and V. E. Zakharov, Phys. D (Amsterdam, Neth.) 87, 233 (1995).
A. O. Korotkevich, A. I. Dyachenko, and V. E. Zakharov, Phys. D (Amsterdam, Neth.) 321, 51 (2016).
A. C. Newell and B. Rumpf, Ann. Rev. Fluid Mech. 43, 59 (2011).
S. Walton and M. B. Tran, SIAM J. Sci. Comput. 45, B467 (2023).
L. V. Ovsjannikov, Arch. Mech. 26, 6 (1974).
A. I. Dyachenko, E. A. Kuznetsov, M. Spector, and V. E. Zakharov, Phys. Lett. A 221, 736 (1996).
V. E. Zakharov, A. I. Dyachenko, and O. A. Vasilyev, Eur. J. Mech. B: Fluids 21, 283 (2002).
S. Tanveer, Proc. R. Soc. London, Ser. A 435 (1893), 137 (1991).
S. Tanveer, Proc. R. Soc. London, Ser. A 441 (1913), 501 (1993).
S. A. Dyachenko, Stud. Appl. Math. 148, 125 (2022).
V. P. Ruban, J. Exp. Theor. Phys. 130, 797 (2020).
S. Dyachenko and A. C. Newell, Stud. Appl. Math. 137, 199 (2016).
A. O. Korotkevich, A. Prokofiev, and V. E. Zakharov, JETP Lett. 109, 309 (2019).
A. Nachbin, Phys. D (Amsterdam, Neth.) 445, 133646 (2023).
T. Gao, A. Doak, J. M. Vanden-Broeck, and Z. Wang, Eur. J. Mech. B: Fluids 77, 98 (2019).
M. V. Flamarion, T. Gao, R. Ribeiro, Jr., and A. Doak, Phys. Fluids 34, 127119 (2022).
E. A. Kochurin, J. Appl. Mech. Tech. Phys. 59, 79 (2018).
S. Murashige and W. Choi, J. Comput. Phys. 328, 234 (2017).
J. Shelton, P. Milewski, and P. H. Trinh, J. Fluid Mech. 972, R6 (2023).
L. Kayal, S. Basak, and R. Dasgupta, J. Fluid Mech. 951, A26 (2022).
E. Herbert, N. Mordant, and E. Falcon, Phys. Rev. Lett. 105, 144502 (2010).
Funding
This work was supported by the Russian Science Foundation, project no. 19-72-30028.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author of this work declares that he has no conflicts of interest.
Additional information
Translated by R. Tyapaev
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kochurin, E.A. Simulation of the Wave Turbulence of a Liquid Surface Using the Dynamic Conformal Transformation Method. Jetp Lett. 118, 893–898 (2023). https://doi.org/10.1134/S0021364023603640
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364023603640