Abstract
We report on direct numerical simulation of quasi-one-dimensional bidirectional capillary-wave turbulence. Although nontrivial three-wave and four-wave resonant interactions are absent in this peculiar geometry, we show that an energy transfer between scales still occurs concentrated around the linear dispersion relation that is broadened by nonlinearity. The wave spectrum displays a clear wavenumber power-law scaling that is found to be in good agreement with the dimensionally prediction for capillary-wave turbulence involving four-wave interactions. The carried out high-order correlation analysis (bicoherence and tricoherence) confirms quantitatively the dominant role of four-wave quasi-resonant interactions. The Kolmogorov-Zakharov spectrum constant is also estimated numerically. We interpret our results as the first numerical observation of anisotropic capillary-wave turbulence in which four-wave interactions play a dominant role.
Similar content being viewed by others
References
V. E. Zakharov, G. Falkovitch, and V. S. L’vov, Kolmogorov Spectra of Turbulence I: Wave Turbulence (Springer, Berlin, 1992).
S. Nazarenko, Lect. Notes Phys. 825, 1 (2011).
V. E. Zakharov and N. N. Filonenko, J. Appl. Mech. Tech. Phys. 8, 37 (1967).
V. E. Zakharov, J. Appl. Mech. Tech. Phys. 9, 190 (1968).
V. E. Zakharov and R. Z. Sagdeev, Sov. Phys. Dokl. 15, 439 (1970).
C. Connaughton, S. Nazarenko, and A. C. Newell, Phys. D (Amsterdam, Neth.) 184, 86 (2003).
E. A. Kochurin and N. M. Zubarev, IEEE Trans. Dielectr. Electr. Insul. 25, 1723 (2018).
E. A. Kochurin, JETP Lett. 109, 303 (2019).
F. Boyer and E. Falcon, Phys. Rev. Lett. 101, 244502 (2008).
S. Dorbolo and E. Falcon, Phys. Rev. E 83, 046303 (2011).
E. A. Kochurin, J. Magn. Magn. Mater. 503, 166607 (2020).
L. Deike, J.-C. Bacri, and E. Falcon, J. Fluid Mech. 733, 394 (2013).
L. Deike, M. Berhanu, and E. Falcon, Phys. Rev. Fluids 2, 064803 (2017).
E. Falcon, Discrete Contin. Dyn. Syst. B 13, 819 (2010).
A. C. Newell and B. Rumpf, Ann. Rev. Fluid Mech. 43, 59 (2011).
V. E. Zakharov, S. I. Badulin, V. V. Geogjaev, and A. N. Pushkarev, Earth Space Sci. 6, 540 (2019).
S. Galtier, Geophys. Astrophys. Fluid Dyn. (2020). https://www.tandfonline.com/doi/full/10.1080/03091929.2020.1715966.
A. N. Pushkarev and V. E. Zakharov, Phys. Rev. Lett. 76, 3320 (1996).
A. N. Pushkarev and V. E. Zakharov, Phys. D (Amsterdam, Neth.) 135, 98 (2000).
A. I. Dyachenko, A. O. Korotkevich, and V. E. Zakharov, JETP Lett. 77, 546 (2003).
A. I. Dyachenko, A. O. Korotkevich, and V. E. Zakharov, Phys. Rev. Lett. 92, 134501 (2004).
Y. Pan and D. K. P. Yue, Phys. Rev. Lett. 113, 094501 (2014).
L. Deike, D. Fuster, M. Berhanu, and E. Falcon, Phys. Rev. Lett. 112, 234501 (2014).
Y. Pan and D. K. P. Yue, J. Fluid Mech. 780, R1 (2015).
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).
V. Zakharov, F. Dias, and A. Pushkarev, Phys. Rep. 398, 1 (2004).
S. Chibbaro, F. de Lillo, and M. Onorato, Phys. Rev. Fluids 2, 052603 (2017).
B. Rumpf and T. Y. Sheffield, Phys. Rev. E 92, 022927 (2015).
A. I. Dyachenko, Y. V. Lvov, and V. E. Zakharov, Phys. D (Amsterdam, Neth.) 87, 233 (1995).
G. Düring and C. Falcón, Phys. Rev. Lett. 103, 174503 (2009).
C. Falcón, E. Falcon, U. Bortolozzo, and S. Fauve, Europhys. Lett. 86, 14002 (2009).
B. Issenmann, C. Laroche, and E. Falcon, Europhys. Lett. 116, 64005 (2016).
A. O. Korotkevich, A. I. Dyachenko, and V. E. Zakharov, Phys. D (Amsterdam, Neth.) 321, 51 (2016).
E. Herbert, N. Mordant, and E. Falcon, Phys. Rev. Lett. 105, 144502 (2010).
M. Berhanu and E. Falcon, Phys. Rev. E 87, 033003 (2013).
A. Campagne, R. Hassaini, I. Redor, T. Valran, S. Viboud, J. Sommeria, and N. Mordant, Phys. Rev. Fluids 7, 074801 (2019).
G. D. Crapper, J. Fluids Mech. 2, 532 (1957).
H. Punzmann, M. G. Shats, and H. Xia, Phys. Rev. Lett. 103, 064502 (2009).
Q. Aubourg and N. Mordant, Phys. Rev. Fluids 1, 023701 (2016).
Q. Aubourg, A. Campagne, C. Peureux, F. Ardhuin, J. Sommeria, S. Viboud, and N. Mordant, Phys. Rev. Fluids 2, 114802 (2017).
Funding
The work of E. Kochurin on the dimensional analysis of turbulence spectra was supported by the Russian Science Foundation, project no. 19-71-00003. E. Falcon acknowledges the partial support of the French National Research Agency (ANR Dysturb, project no. ANR-17-CE30-0004) and of the Simons Foundation/MPS no. 651463-Wave Turbulence notably for the mission of E. Kochurin in Paris, France. Software tool development for numerical simulation was partially supported by the Russian Foundation for Basic Research, project no. 20-38-70022.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kochurin, E., Ricard, G., Zubarev, N. et al. Numerical Simulation of Collinear Capillary-Wave Turbulence. Jetp Lett. 112, 757–763 (2020). https://doi.org/10.1134/S0021364020240030
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364020240030