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Forced three-wave interactions of capillary-gravity surface waves

Annette Cazaubiel, Florence Haudin, Eric Falcon, and Michael Berhanu*

  • MSC, University of Paris Diderot, CNRS (UMR 7057), 75013 Paris, France

  • *michael.berhanu@univ-paris-diderot.fr
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Phys. Rev. Fluids 4, 074803 – Published 9 July, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.074803

Abstract

Three-wave resonant interactions constitute an essential nonlinear mechanism coupling capillary surface waves. In a previous work [Haudin et al. Phys. Rev. E 93, 043110 (2016)], we characterized experimentally the generation by this mechanism of a daughter wave, whose amplitude saturates due to the viscous dissipation. Here, we show experimentally the generation of a daughter wave verifying the resonant conditions, but not the dispersion relation. By modeling the response of the free surface at the lowest nonlinear order, we explain this observation as a forced interaction. The bandwidth of the linear transfer function of the free surface is indeed increased by the significant viscous dissipation. The observation of free surface excitations not following the linear dispersion relation then becomes possible. This forced three-wave interaction mechanism could have important consequences for wave turbulence in experimental or natural systems with nonnegligible dissipation.

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References (44)

  1. L. F. McGoldrick, Resonant interactions among capillary-gravity waves, J. Fluid Mech. 21, 305 (1965).
  2. W. F. Simmons, A variational method for week resonant wave interactions, Proc. Roy. Soc. A 309, 551 (1969).
  3. A. D. D. Craik, Wave Interactions and Fluid Flows (Cambridge University Press, Cambridge, 1988).
  4. J. L. Hammack and D. M. Henderson, Resonant interactions among surface water waves, Annu. Rev. Fluid Mech 25, 55 (1993).
  5. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 2004).
  6. F. P. Bretherton, Resonant interactions between waves. the case of discrete oscillations, J. Fluid Mech. 20, 457 (1964).
  7. V. E. Zakharov, V. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence (Springer-Verlag, Berlin, 1992).
  8. S. Nazarenko, Wave Turbulence (Springer-Verlag, Berlin, 2011).
  9. V. E. Zakharov and N. N. Filonenko, Weak turbulence of capillary waves, J. Appl. Mech. Tech. Phys. 8, 37 (1967).
  10. M. Berhanu and E. Falcon, Space-time resolved capillary wave turbulence, Phys. Rev. E 87, 033003 (2013).
  11. M. Berhanu, E. Falcon, and L. Deike, Turbulence of capillary waves forced by steep gravity waves, J. Fluid Mech. 850, 803 (2018).
  12. F. Haudin, A. Cazaubiel, L. Deike, T. Jamin, E. Falcon, and M. Berhanu, Experimental study of three-wave interactions among capillary-gravity surface waves, Phys. Rev. E 93, 043110 (2016).
  13. L. F. McGoldrick, An experiment on second-order capillary gravity resonant wave interactions, J. Fluid Mech. 40, 251 (1970).
  14. D. M. Henderson and J. L. Hammack, Experiments on ripple instabilities, part 1. Resonant triads, J. Fluid Mech 184, 15 (1987).
  15. H. Lamb, Hydrodynamics (Springer-Verlag, Berlin, 1932).
  16. W. G. van Dorn, Boundary dissipation of oscillatory waves, J. Fluids Mech. 24, 769 (1966).
  17. W. B. Wright, R. Budakian, and S. J. Putterman, Diffusing Light Photography of Fully Developed Isotropic Ripple Turbulence, Phys. Rev. Lett. 76, 4528 (1996).
  18. W. B. Wright, R. Budakian, D. J. Pine, and S. J. Putterman, Imaging of intermittency in ripple-wave turbulence, Science 278, 1609 (1997).
  19. 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 (2012).
  20. L. Deike, M. Berhanu, and E. Falcon, Experimental observation of hydroelastic three-wave interactions, Phys. Rev. Fluids 2, 064803 (2017).
  21. F. Moisy, M. Rabaud, and K. Salsac, Measurement by digital image correlation of the topography of a liquid surface, Exp. Fluids. 46, 1021 (2009).
  22. A. P. Abella and M. N. Soriano, Detection and visualization of water surface three-wave resonance via a synthetic schlieren method, Phys. Scr. 94, 034006 (2019).
  23. P. Cobelli, A. Maurel, V. Pagneux, and P. Petitjeans, Global measurement of water waves by fourier transform profilometry, Exp. Fluids. 46, 1037 (2009).
  24. K. M. Case and S. C. Chiu, Three-wave resonant interactions of gravity-capillary waves, Phys. Fluids 20, 742 (1977).
  25. M. Chabane and W. Choi, On resonant interactions of gravity-capillary waves without energy exchange, Stud. Appl. Math. 142, 528 (2019).
  26. W. Alpers and H. Hühnerfuss, Damping of ocean waves by surface films: A new look at an old problem, J. Geophys. Res. 94, 6251 (1989).
  27. D. M. Henderson and H. Segur, The role of dissipation in the evolution of ocean swell, J. Geophys. Res.: Oceans 118, 5074 (2013).
  28. L. Deike, M. Berhanu, and E. Falcon, Decay of capillary wave turbulence, Phys. Rev. E 85, 066311 (2012).
  29. F. Bonnefoy, F. Haudin, G. Michel, B. Semin, T. Humbert, S. Aumaître, M. Berhanu, and E. Falcon, Observation of resonant interactions among surface gravity waves, J. Fluid Mech. 805, R3 (2016).
  30. R. A. Ibrahim, Liquid Sloshing Dynamics (Cambridge University Press, New York, 2005).
  31. G. Michel, F. Petrelis, and S. Fauve, Acoustic Measurement of Surface Wave Damping by a Meniscus, Phys. Rev. Lett. 116, 174301 (2016).
  32. P. Janssen, The Interaction of Ocean Waves and Wind (Cambridge University Press, New York, 2004).
  33. G. Michel, Three-wave interactions among surface gravity waves in a cylindrical container, Phys. Rev. Fluids. 4, 012801(R) (2019).
  34. A. V. Slunyaev, Group-wave resonances in nonlinear dispersive media: The case of gravity water waves, Phys. Rev. E 97, 010202(R) (2018).
  35. C. P. Ritz, E. J. Powers, and R. D. Bengtson, Experimental measurement of three-wave coupling and energy cascading, Phys. Fluids B 1, 153 (1988).
  36. V. Sokolov and A. K. Sen, Analogous Saturation Mechanisms of the Ion and Electron Temperature Gradient Drift Wave Turbulence, Phys. Rev. Lett. 113, 095001 (2014).
  37. G. Bordes, F. Moisy, T. Dauxois, and P.-P. Cortet, Experimental evidence of a triadic resonance of plane inertial waves in a rotating fluid, Phys. Fluids 24, 014105 (2012).
  38. S. Joubaud, J. Munroe, P. Odier, and T. Dauxois, Experimental parametric subharmonic instability in stratified fluids, Phys. Fluids 24, 041703 (2012).
  39. F. Moisy, G.-J. Michon, M. Rabaud, and E. Sultan, Cross-waves induced by the vertical oscillation of a fully immersed vertical plate, Phys. Fluids 24, 022110 (2012).
  40. S. Perrard, A. Lozano-Durán, M. Rabaud, M. Benzaquen, and F. Moisy, Turbulent windprint on a liquid surface, J. Fluid Mech. 873, 1020 (2019).
  41. Q. Aubourg and N. Mordant, Nonlocal Resonances in Weak Turbulence of Gravity-Capillary Waves, Phys. Rev. Lett. 114, 144501 (2015).
  42. Q. Aubourg and N. Mordant, Investigation of resonances in gravity-capillary wave turbulence, Phys. Rev. Fluids. 1, 023701 (2016).
  43. R. W. Boyd, Nonlinear Optics (Academic Press, Berlin, 2008).
  44. F. Bonnefoy, F. Haudin, G. Michel, B. Semin, T. Humbert, S. Aumaître, M. Berhanu, and E. Falcon, Observation expérimentale en bassin à vagues des interactions résonantes à quatre ondes, La Houille Blanche 5, 56 (2017).

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Phys. Rev. Fluids 4, 074803– Published 9 July, 2019
  • Received 25 February 2019
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