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Turbulence of capillary waves forced by steep gravity waves

Published online by Cambridge University Press:  10 July 2018

M. Berhanu Open the ORCID record for M. Berhanu [Opens in a new window] ,
E. Falcon  and
L. Deike Open the ORCID record for L. Deike [Opens in a new window]
M. Berhanu*
Affiliation:
Matière et Systèmes Complexes (MSC), Université Paris Diderot, CNRS (UMR 7057), 75013 Paris, France
E. Falcon
Affiliation:
Matière et Systèmes Complexes (MSC), Université Paris Diderot, CNRS (UMR 7057), 75013 Paris, France
L. Deike
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, NJ 08544, USA Princeton Environmental Institute, Princeton University, NJ 08544, USA
*
†Email address for correspondence: [email protected]
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Abstract

We study experimentally the dynamics and statistics of capillary waves forced by random steep gravity waves mechanically generated in the laboratory. Capillary waves are produced here by gravity waves from nonlinear wave interactions. Using a spatio-temporal measurement of the free surface, we characterize statistically the random regimes of capillary waves in the spatial and temporal Fourier spaces. For a significant wave steepness (0.2–0.3), power-law spectra are observed both in space and time, defining a turbulent regime of capillary waves transferring energy from the large scale to the small scale. Analysis of temporal fluctuations of the spatial spectrum demonstrates that the capillary power-law spectra result from the temporal averaging over intermittent and strong nonlinear events transferring energy to the small scale in a fast time scale, when capillary wave trains are generated in a way similar to the parasitic capillary wave generation mechanism. The frequency and wavenumber power-law exponents of the wave spectra are found to be in agreement with those of the weakly nonlinear wave turbulence theory. However, the energy flux is not constant through the scales and the wave spectrum scaling with this flux is not in good agreement with wave turbulence theory. These results suggest that theoretical developments beyond the classic wave turbulence theory are necessary to describe the dynamics and statistics of capillary waves in a natural environment. In particular, in the presence of broad-scale viscous dissipation and strong nonlinearity, the role of non-local and non-resonant interactions should be reconsidered.

JFM classification

Waves/Free-surface Flows: Capillary waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 850 , 10 September 2018 , pp. 803 - 843
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Copyright
© 2018 Cambridge University Press 

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Berhanu et al. supplementary movie 1

3D Free-surface reconstruction for the highest forcing amplitude σ_h =3.6 mm. The animation corresponds to 2.5 s in real time. Steep gravity waves generate smaller capillary waves.

Download Berhanu et al. supplementary movie 1(Video)
Video 16.8 MB

Berhanu et al. supplementary movie 2

Simultaneous plot of wave-field gradient map and spatial spectrum f wave elevation. σ_h =3.6 mm. The animation corresponds to 2.5 s in real time. Transient generations of capillary wave train are associated with sudden increases of spatial spectrum at small scale.

Download Berhanu et al. supplementary movie 2(Video)
Video 36.2 MB