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Investigation of resonances in gravity-capillary wave turbulence
Phys. Rev. Fluids 1, 023701 – Published 7 June, 2016
DOI: https://doi.org/10.1103/PhysRevFluids.1.023701
Abstract
We report experimental results on nonlinear wave coupling in surface wave turbulence on water at scales close to the crossover between surface gravity waves and capillary waves. We study three-wave correlations either in the frequency domain or in the wave-vector domain. We observe that in a weakly nonlinear regime, the dominant nonlinear interactions correspond to waves that are collinear or close to collinear. Although the resonant coupling of pure gravity waves is supposed to involve four waves, at the capillary crossover we observe a nonlocal coupling between a gravity wave and two capillary waves. Furthermore, nonlinear spectral spreading permits three-gravity wave coupling. These observations raise the question of the relevance of these processes in the oceanographic context and in particular the range of frequencies of gravity waves that may be impacted.
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References (25)
- V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence (Springer, Berlin, 1992).
- S. Nazarenko, Wave Turbulence (Springer, Berlin, 2011).
- A. C. Newell and B. Rumpf, Wave turbulence, Annu. Rev. Fluid Mech. 43, 59 (2011).
- E. A. Kartashova, Weakly Nonlinear Theory of Finite-Size Effects in Resonators, Phys. Rev. Lett. 72, 2013 (1994).
- E. Kartashova, Model of laminated wave turbulence, JETP Lett. 83, 283 (2006).
- E. Kartashova, Discrete wave turbulence, Europhys. Lett. 87, 44001 (2009).
- Y. V. Lvov, S. Nazarenko, and B. Pokorni, Discreteness and its effect on water-wave turbulence, Physica D 218, 24 (2006).
- L. F. Mcgoldrick, Resonant interactions among capillary-gravity waves, J. Fluid Mech. 21, 305 (1965).
- W. F. Simmons, A variational method for weak resonant wave interactions, Proc. R. Soc. London Ser. A 309, 551 (1969).
- Q. Aubourg and N. Mordant, Nonlocal Resonances in Weak Turbulence of Gravity-Capillary Waves, Phys. Rev. Lett. 114, 144501 (2015).
- P. J. Cobelli, A. Maurel, V. Pagneux, and P. Petitjeans, Global measurement of water waves by Fourier transform profilometry, Exp. Fluids 46, 1037 (2009).
- 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).
- 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).
- 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).
- B. Issenmann and E. Falcon, Gravity wave turbulence revealed by horizontal vibrations of the container, Phys. Rev. E 87, 011001 (2013).
- L. Deike, B. Miquel, P. Gutierrez, 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).
- N. Mordant, Fourier analysis of wave turbulence in a thin elastic plate, Eur. Phys. J. B 76, 537 (2010).
- E. Herbert, N. Mordant, and E. Falcon, Observation of Nonlinear Dispersion Relation and Spatial Statistics of Wave Turbulence on the Surface of a Fluid, Phys. Rev. Lett. 105, 144502 (2010).
- P. Clark di Leoni, P. Cobelli, and P. D. Mininni, The spatio-temporal spectrum of turbulent flows, Eur. Phys. J. E 38, 1 (2015).
- P. Clark di Leoni, P. D. Mininni, and M. E. Brachet, Spatiotemporal detection of Kelvin waves in quantum turbulence simulations, Phys. Rev. A 92, 063632 (2015).
- 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).
- B. Miquel and N. Mordant, Nonlinear dynamics of flexural wave turbulence, Phys. Rev. E 84, 066607 (2011).
- M. Berhanu and E. Falcon, Space-time-resolved capillary wave turbulence, Phys. Rev. E 87, 033003 (2013).
- J. Wilton, LXXII. On ripples, London Edinburgh Dublin Philos. Mag. J. Sci. 29, 688 (1915).
- D. Henderson and J. Hammack, Experiments on ripple instabilities. Part 1. Resonant triads, J. Fluid Mech. 184, 15 (1987).