Skip to main content
Log in

Numerical Simulation of Collinear Capillary-Wave Turbulence

  • Plasma, Hydro- and Gas Dynamics
  • Published:
JETP Letters Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. E. Zakharov, G. Falkovitch, and V. S. L’vov, Kolmogorov Spectra of Turbulence I: Wave Turbulence (Springer, Berlin, 1992).

    Book  Google Scholar 

  2. S. Nazarenko, Lect. Notes Phys. 825, 1 (2011).

    Article  Google Scholar 

  3. V. E. Zakharov and N. N. Filonenko, J. Appl. Mech. Tech. Phys. 8, 37 (1967).

    Article  ADS  Google Scholar 

  4. V. E. Zakharov, J. Appl. Mech. Tech. Phys. 9, 190 (1968).

    Article  ADS  Google Scholar 

  5. V. E. Zakharov and R. Z. Sagdeev, Sov. Phys. Dokl. 15, 439 (1970).

    ADS  Google Scholar 

  6. C. Connaughton, S. Nazarenko, and A. C. Newell, Phys. D (Amsterdam, Neth.) 184, 86 (2003).

    Article  ADS  Google Scholar 

  7. E. A. Kochurin and N. M. Zubarev, IEEE Trans. Dielectr. Electr. Insul. 25, 1723 (2018).

    Article  Google Scholar 

  8. E. A. Kochurin, JETP Lett. 109, 303 (2019).

    Article  ADS  Google Scholar 

  9. F. Boyer and E. Falcon, Phys. Rev. Lett. 101, 244502 (2008).

    Article  ADS  Google Scholar 

  10. S. Dorbolo and E. Falcon, Phys. Rev. E 83, 046303 (2011).

    Article  ADS  Google Scholar 

  11. E. A. Kochurin, J. Magn. Magn. Mater. 503, 166607 (2020).

    Article  Google Scholar 

  12. L. Deike, J.-C. Bacri, and E. Falcon, J. Fluid Mech. 733, 394 (2013).

    Article  ADS  Google Scholar 

  13. L. Deike, M. Berhanu, and E. Falcon, Phys. Rev. Fluids 2, 064803 (2017).

    Article  ADS  Google Scholar 

  14. E. Falcon, Discrete Contin. Dyn. Syst. B 13, 819 (2010).

    Article  MathSciNet  Google Scholar 

  15. A. C. Newell and B. Rumpf, Ann. Rev. Fluid Mech. 43, 59 (2011).

    Article  ADS  Google Scholar 

  16. V. E. Zakharov, S. I. Badulin, V. V. Geogjaev, and A. N. Pushkarev, Earth Space Sci. 6, 540 (2019).

    Article  ADS  Google Scholar 

  17. S. Galtier, Geophys. Astrophys. Fluid Dyn. (2020). https://www.tandfonline.com/doi/full/10.1080/03091929.2020.1715966.

  18. A. N. Pushkarev and V. E. Zakharov, Phys. Rev. Lett. 76, 3320 (1996).

    Article  ADS  Google Scholar 

  19. A. N. Pushkarev and V. E. Zakharov, Phys. D (Amsterdam, Neth.) 135, 98 (2000).

    Article  ADS  Google Scholar 

  20. A. I. Dyachenko, A. O. Korotkevich, and V. E. Zakharov, JETP Lett. 77, 546 (2003).

    Article  ADS  Google Scholar 

  21. A. I. Dyachenko, A. O. Korotkevich, and V. E. Zakharov, Phys. Rev. Lett. 92, 134501 (2004).

    Article  ADS  Google Scholar 

  22. Y. Pan and D. K. P. Yue, Phys. Rev. Lett. 113, 094501 (2014).

    Article  ADS  Google Scholar 

  23. L. Deike, D. Fuster, M. Berhanu, and E. Falcon, Phys. Rev. Lett. 112, 234501 (2014).

    Article  ADS  Google Scholar 

  24. Y. Pan and D. K. P. Yue, J. Fluid Mech. 780, R1 (2015).

    Article  ADS  Google Scholar 

  25. 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).

    Article  Google Scholar 

  26. V. Zakharov, F. Dias, and A. Pushkarev, Phys. Rep. 398, 1 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  27. S. Chibbaro, F. de Lillo, and M. Onorato, Phys. Rev. Fluids 2, 052603 (2017).

    Article  ADS  Google Scholar 

  28. B. Rumpf and T. Y. Sheffield, Phys. Rev. E 92, 022927 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  29. A. I. Dyachenko, Y. V. Lvov, and V. E. Zakharov, Phys. D (Amsterdam, Neth.) 87, 233 (1995).

    Article  ADS  Google Scholar 

  30. G. Düring and C. Falcón, Phys. Rev. Lett. 103, 174503 (2009).

    Article  ADS  Google Scholar 

  31. C. Falcón, E. Falcon, U. Bortolozzo, and S. Fauve, Europhys. Lett. 86, 14002 (2009).

    Article  ADS  Google Scholar 

  32. B. Issenmann, C. Laroche, and E. Falcon, Europhys. Lett. 116, 64005 (2016).

    Article  ADS  Google Scholar 

  33. A. O. Korotkevich, A. I. Dyachenko, and V. E. Zakharov, Phys. D (Amsterdam, Neth.) 321, 51 (2016).

    Article  ADS  Google Scholar 

  34. E. Herbert, N. Mordant, and E. Falcon, Phys. Rev. Lett. 105, 144502 (2010).

    Article  ADS  Google Scholar 

  35. M. Berhanu and E. Falcon, Phys. Rev. E 87, 033003 (2013).

    Article  ADS  Google Scholar 

  36. A. Campagne, R. Hassaini, I. Redor, T. Valran, S. Viboud, J. Sommeria, and N. Mordant, Phys. Rev. Fluids 7, 074801 (2019).

    Article  ADS  Google Scholar 

  37. G. D. Crapper, J. Fluids Mech. 2, 532 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  38. H. Punzmann, M. G. Shats, and H. Xia, Phys. Rev. Lett. 103, 064502 (2009).

    Article  ADS  Google Scholar 

  39. Q. Aubourg and N. Mordant, Phys. Rev. Fluids 1, 023701 (2016).

    Article  ADS  Google Scholar 

  40. Q. Aubourg, A. Campagne, C. Peureux, F. Ardhuin, J. Sommeria, S. Viboud, and N. Mordant, Phys. Rev. Fluids 2, 114802 (2017).

    Article  ADS  Google Scholar 

Download references

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

Authors

Corresponding author

Correspondence to E. Kochurin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021364020240030

Navigation