- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Three-wave and four-wave interactions in gravity wave turbulence

Quentin Aubourg1, Antoine Campagne1, Charles Peureux2, Fabrice Ardhuin2, Joel Sommeria1, Samuel Viboud1, and Nicolas Mordant1,*

  • 1Laboratoire des Ecoulements Géophysiques et Industriels, Université Grenoble Alpes, CNRS, 38000 Grenoble, France
  • 2Laboratoire d'Océanographie Physique et Spatiale, Université Brest, CNRS, IFREMER, IRD, 29200 Plouzané, France

  • *nicolas.mordant@univ-grenoble-alpes.fr
PDF

Phys. Rev. Fluids 2, 114802 – Published 17 November, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.114802

Abstract

Weak-turbulence theory is a statistical framework to describe a large ensemble of nonlinearly interacting waves. The archetypal example of such system is the ocean surface that is made of interacting surface gravity waves. Here we describe a laboratory experiment dedicated to probe the statistical properties of turbulent gravity waves. We set up an isotropic state of interacting gravity waves in the Coriolis facility (13-m-diam circular wave tank) by exciting waves at 1 Hz by wedge wave makers. We implement a stereoscopic technique to obtain a measurement of the surface elevation that is resolved in both space and time. Fourier analysis shows that the laboratory spectra are systematically steeper than the theoretical predictions and the field observations in the Black Sea by Leckler et al. [F. Leckler et al., J. Phys. Oceanogr. 45, 2484 (2015)]. We identify a strong impact of surface dissipation on the scaling of the Fourier spectrum at the scales that are accessible in the experiments. We use bicoherence and tricoherence statistical tools in frequency and/or wave-vector space to identify the active nonlinear coupling. These analyses are also performed on the field data by Leckler et al. for comparison with the laboratory data. Three-wave coupling is characterized by and shown to involve mostly quasiresonances of waves with second- or higher-order harmonics. Four-wave coupling is not observed in the laboratory but is evidenced in the field data. We discuss temporal scale separation to explain our observations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (34)

  1. V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence (Springer, Berlin, 1992).
  2. S. Nazarenko, Wave Turbulence (Springer, Berlin, 2011).
  3. A. C. Newell and B. Rumpf, Wave turbulence, Annu. Rev. Fluid Mech. 43, 59 (2011).
  4. V. E. Zakharov, in Basic Plasma Physics: Selected Chapters, Handbook of Plasma Physics, edited by A. A. Galeev and R. N. Sudan (Elsevier, Amsterdam, 1984), Vol. 1, p. 3.
  5. K. Hasselmann, On the non-linear energy transfer in gravity-wave spectrum. Part 1. General theory, J. Fluid Mech. 12, 481 (1962).
  6. M. Berhanu and E. Falcon, Space-time-resolved capillary wave turbulence, Phys. Rev. E 87, 033003 (2013).
  7. E. Falcon, C. Laroche, and S. Fauve, Observation of Gravity-Capillary Wave Turbulence, Phys. Rev. Lett. 98, 094503 (2007).
  8. E. Falcon, U. Bortolozzo, and S. Fauve, Capillary wave turbulence on a spherical fluid surface in low gravity, Europhys. Lett. 86, 14002 (2009).
  9. L. Deike, D. Fuster, M. Berhanu, and E. Falcon, Direct Numerical Simulations of Capillary Wave Turbulence, Phys. Rev. Lett. 112, 234501 (2014).
  10. P. Cobelli, A. Przadka, P. Petitjeans, G. Lagubeau, V. Pagneux, and A. Maurel, Different Regimes for Water Wave Turbulence, Phys. Rev. Lett. 107, 214503 (2011).
  11. S. Nazarenko, S. Lukaschuk, S. McLelland, and P. Denissenko, Statistics of surface gravity wave turbulence in the space and time domains, J. Fluid Mech. 642, 395 (2009).
  12. L. Deike, B. Miquel, T. Jamin, B. Semin, M. Berhanu, E. Falcon, and F. Bonnefoy, Role of the basin boundary conditions in gravity wave turbulence, J. Fluid Mech. 781, 196 (2015).
  13. P. Denissenko, S. Lukaschuk, and S. Nazarenko, Gravity Wave Turbulence in a Laboratory Flume, Phys. Rev. Lett. 99, 014501 (2007).
  14. E. Kartashova, in Nonlinear Waves and Weak Turbulence, edited by V. E. Zakharov (Springer, Berlin, 1998), p. 95.
  15. A. Pushkarev, On the Kolmogorov and frozen turbulence in numerical simulation of capillary waves, Eur. J. Mech. B 18, 345 (1999).
  16. S. Nazarenko, Sandpile behaviour in discrete water-wave turbulence, J. Stat. Mech. (2006) L02002.
  17. B. Miquel, A. Alexakis, and N. Mordant, Role of dissipation in flexural wave turbulence: From experimental spectrum to Kolmogorov-Zakharov spectrum, Phys. Rev. E 89, 062925 (2014).
  18. T. Humbert, O. Cadot, G. Düring, C. Josserand, S. Rica, and C. Touzé, Wave turbulence in vibrating plates: The effect of damping, Europhys. Lett. 102, 30002 (2013).
  19. W. Alpers and H. Hühnerfuss, The damping of ocean waves by surface films: A new look at an old problem, J. Geophys. Res. 94, 6251 (1989).
  20. F. Behroozi, K. Cordray, and W. Griffin, The calming effect of oil on water, Am. J. Phys. 75, 407 (2007).
  21. A. Przadka, B. Cabane, V. Pagneux, A. Maurel, and P. Petitjeans, Fourier transform profilometry for water waves: How to achieve clean water attenuation with diffusive reflection at the water surface? Exp. Fluids 52, 519 (2011).
  22. Q. Aubourg and N. Mordant, Nonlocal Resonances in Weak Turbulence of Gravity-Capillary Waves, Phys. Rev. Lett. 114, 144501 (2015).
  23. Q. Aubourg and N. Mordant, Investigation of resonances in gravity-capillary wave turbulence, Phys. Rev. Fluids 1, 023701 (2016).
  24. Q. Aubourg, Etude expérimentale de la turbulence d'ondes à la surface d'un fluide. La théorie de la turbulence faible à l'épreuve de la réalité pour les ondes de capillarité et gravité, Ph.D. thesis, Université Grenoble Alpes, 2016.
  25. P. A. Kralchevsky and K. Nagayama, Capillary interactions between particles bound to interfaces, liquid films and biomembranes, Adv. Colloid Interface Sci. 85, 145 (2000).
  26. W. A. Gifford and L. E. Scriven, On the attraction of floating particles, Chem. Eng. Sci. 26, 287 (1971).
  27. M. A. Tayfun, Narrow-band nonlinear sea waves, J. Geophys. Res. 85, 1548 (1980).
  28. H. Socquet-Juglard, K. B. Dysthe, K. Trulsen, H. E. Krogstad, and J. Liu, Probability distributions of surface gravity waves during spectral changes, J. Fluid Mech. 542, 195 (2005).
  29. M. Onorato, L. Cavaleri, S. Fouques, O. Gramstad, P. A. E. M. Janssen, J. Monbaliu, A. R. Osborne, C. Pakozdi, M. Serio, C. T. Stansberg, A. Toffoli, and K. Trulsen, Statistical properties of mechanically generated surface gravity waves: A laboratory experiment in a three-dimensional wave basin, J. Fluid Mech. 627, 235 (2009).
  30. F. Leckler, F. Ardhuin, C. Peureux, A. Benetazzo, F. Bergamasco, and V. Dulov, Analysis and interpretation of frequency-wavenumber spectra of young wind waves, J. Phys. Oceanogr. 45, 2484 (2015).
  31. T. M. A Taklo, K. Trulsen, O. Gramstad, H. E. Krogstad, and A. Jensen, Measurement of the dispersion relation for random surface gravity waves, J. Fluid Mech. 766, 326 (2015).
  32. T. M. A. Taklo, K. Trulsen, H. E. Krogstad, and J. C. Nieto Borge, On dispersion of directional surface gravity waves, J. Fluid Mech. 812, 681 (2017).
  33. W. B. Collis, P. R. White, and J. K. Hammond, Higher-order spectra: The bispectrum and trispectrum, Mech. Syst. Signal Process. 12, 375 (1998).
  34. V. P. Krasitskii, On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves, J. Fluid Mech. 272, 1 (1994).

Outline

Information

Phys. Rev. Fluids 2, 114802– Published 17 November, 2017
  • Received 26 June 2017

©2017 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation