### 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__