Wave turbulence of surface waves

Non linear interactions between waves can produce out of equilibrium stationary regimes, which can be said to be turbulent. Provided energy to the system, is transferred by a cascade phenomenon to a dissipative scale. Contrary to turbulence of Navier-Stokes equation, Weak turbulence theory predicts statistical properties of these stationary regime of interacting waves (under important assumptions like small non linearity and infinite system). Waves at the surface of a liquid are the most common example. Members of our group develop experiments to measure the deformation of a liquid surface in presence of gravity and capillary waves. We compare our results with theory in order to better understand occurrence of turbulent regimes.

Work in progress ...

Recent presentation (2014)

Spatio temporal investigation of capillary wave turbulence using Diffusing Light Photography

The Diffusing Light Photography (DLP) is an optical method to reconstruct in space and time the wave field experiencing high amplitude motion. In contrast to other methods relying on surface slope measurement, the DLP method is not limited to small waves steepness. Using this method, we were able to characterize capillary wave turbulence excited by gravity waves. Analysis in Fourier space shows power law spectra both in time and space, inside the capillary range scale. Exponents of the power laws, are in good agreement with predictions given by the weak turbulence theory.

Related publication:

"Space-Time-Resolved Capillary Wave Turbulence" (Phys. Rev. E 87, 033003 (2013)).

Supplemental material: Typical movies of wave elevation and wave steepness (norm of local wave gradient) , for a random excitation band pass filtered around 5 Hz.
Wave field High amplitude (σ h = 3.6 mm)
Wave steepness High amplitude (σ h = 3.6 mm)
Wave field Low amplitude (σ h = 1.3 mm)
Wave steepness Low amplitude (σ h = 1.3 mm)

Work in progress ...

Movies of water waves reconstruction :

Capillary wave turbulence, excitation : noise between 4 and 6 Hz

Steep stationary waves, sinusoidal excitation 5 Hz