Gravity capillary wave turbulence
Gravity-capillary waves are water surface waves for which capillarity and gravity act simultaneously. At the surface of water it means frequencies close to 10 Hz and wavelengths around the centimeter. Such experiments are easier to handle as the wave tank about half a meter in size (as compared to 13m for the Coriolis facility). The interplay of capillarity and gravity makes this range of scales quite specific.
In order to obtain a space and time resolved measurement of the surface elevation, we use the so-called Fourier transform profilometry following the efficient scheme proposed by P. Cobelli, A. Maurel and P. Petitjeans. A line pattern is projected on the water surface (made optically diffusive by adding Titanium oxyde). The deformation of the pattern is then recorded by a high speed camera and subsequently inverted to obtain the deformation of the surface.
The surface is measured using the Fourier transform profilometry method
(deformation of a projected pattern at the water surface)
optimized by Cobelli, Maurel and Petitjeans in Paris.
movie of the water surface deformation using the above technique over 20cm x 20cm
During the PhDs of Quentin Aubourg and Roumaissa Hassaini, we used this technique to perform statistical analyses of various aspects of gravity-capillary wave turbulence:
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1. the 3-wave nonlinear coupling that show the strong predominance of unidirectional nonlinear coupling which is quite exotic in wave turbulence studies
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2. the transition from weak turbulence to integrable turbulence when decreasing the water depth to go from deep water (weak turbulence) to shallow water (integrable turbulence with solitons). This transition occurs for a finite depth and a finite level on nonlinearity
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3. the effect of confinement on the properties of wave turbulence. We use a channel which is narrow along one axis and much longer along the other. Because of the peculiarity that unidirectional nonlinear coupling can occur for gravity-capillarity waves, a continuous weak turbulence develops in the long axis and discrete turbulence is present along the short axis.
