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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - WATU (Wave turbulence: beyond weak turbulence)

Teaser

Summary

\"The sea surface is deformed by waves induced by the wind. These waves may have many socio-economic impact on transportation or impact on the shore. Prediction of sea states (\"\"wave meteorology\"\") requires an accurate knowledge of the wave coupling and dissipation. On a global scale the roughness of the sea impacts the exchanges between atmosphere and ocean. The complex distribution of waves at the surface of the sea share the same phenomenology with many other nonlinear waves systems in vibrating structures, plasmas or optics in fibers as well as other geophysical waves. It can be described generically as wave turbulence.

Wave turbulence and fluid turbulence belong to the same class of turbulent states made of a large number of nonlinearly coupled degrees of freedom driven far from equilibrium. The Weak Turbulence Theory is a statistical theory of low amplitude turbulent waves. The predicted phenomenology (energy cascade) is very similar to that of fluid turbulence, which badly lacks such a statistical theory. Weak Turbulence is thus a promising mathematical framework for turbulence in general. It is observed in many systems such as planetary atmospheres, astrophysical plasmas, tokomak fusion plasmas, superfluid turbulence or Bose- Einstein condensates for example. The theory is much less advanced in the strong wave turbulence case for which a richer phenomenology appears due to the generation of coherent structures. Furthermore, to a large extent the theory lacks experimental validation.
My project aims at studying several physical systems (vibrating elastic plate, 1D and 2D water surface waves, 3D internal waves in a stratified fluid) specifically chosen to highlight various features of wave turbulence both in the weak and strong regimes. Under strong forcing, coherent structures will appear such as developable cones (elastic plates), solitons and sharp water wave ridges (water surface waves) or even fluid turbulence for overturning 3D internal waves. I will specifically use two unique large-scale facilities available in LEGI (Grenoble, France): the 30 m 1D wave flume for surface water waves and the 13m- diameter Coriolis turntable for water surface waves and internal waves. I will setup advanced space-time resolved profilometry and velocimetry techniques adapted to the dimensionality and size of each one of these systems. Advanced statistical tools on massive datasets will provide a profound insight into the coupling between waves and structures in the various regimes of wave turbulence.
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Work performed

We are currently studying several wave configurations: elastic waves in a vibrating plate (task1), capillary waves at the surface of water in small wave tanks (half a meter size, task 2) and gravity waves in a large pool (13m in diameter, task 3) and a linear wave tank (36m long, task 3). In all these systems we have developed an imaging system that can record the deformation of the surface with both spatial resolution in 2D and good temporal resolutions so that to obtain movies of the wave field. For the elastic plate and capillary waves we use a profilometry technique and a high speed camera (250 frames/s for capillary waves, 10000 frames/s for the vibrating plate). For the gravity waves in the 13m wave tank we developed a stereoscopic technique using 3 cameras and in the 36 m 1D wave flume we use a set of 8 cameras to record the wave elevation over 16m. A part of the work was also to develop schemes to excite the waves. Databases are currently being built in each of these experiments. In parallel to these experiments, we are also developing a 3D measurement of stratified turbulence in order to obtain similar measurements but resolved in 3D and time (task 4).

We use high order statistical analysis to identify the wave coupling in these turbulent waves and compare them to the theoretical predictions. We investigate the effect of altering the physical conditions such as changing the water depth or adding stress to the vibrating plate. For instance, for capillary waves, we observed a clear transition from a wave turbulence state to a solitonic regime at low depth (article submitted to Physical Review Fluids). In contrast, applying stress to the vibrating plate does not lead to such a change although the main effect is also to reduce the dispersion of the waves. For gravity waves we are also working on the distinction between 3-wave or 4-wave coupling (article in preparation).

These results led also to communications in international conferences.

Final results

The main progresses beyond the state of the art are the following:
- capillary waves: identification of the impact of decreasing the dispersivity of the waves by lowering the water depth. Observation of a strong change of the angular transfer among waves and a transition to a solitonic regime (one article under revision). Identification of nonlinear coupling among waves in the deep water case (article published in Physical Review Fluids)
- gravity waves in 2D: observation of a true isotropic regime of wave turbulence in the laboratory. Observation of 3- and 4-wave coupling and importance of coupling with bound harmonics (one article in preparation)
- gravity waves in 1D: observation of weak wave turbulence and impact of strong nonlinearities.
- internal waves: observation of regimes of strongly stratified turbulence (publication of an international conference proceedings).