Nicolas MORDANT

A thin elastic sheet (in our case a 2mx1mx0.5mm steel plate) can sustain bending waves. These waves can interact nonlinearly and develop wave turbulence. Due to the thunder noise generated in the air by the vibrations of the plate, such shaken plates were used in theaters for centuries to mimic thunderstorms. The physics is similar to that of gongs. This system is very interesting as a physical model as experimental setups are relatively simple but the physics is rich nonetheless.

«the sound of the Kolmogorov spectrum»
(title proposed by A. Newell for the original theoretical paper by Düring, Rica & Josserand)

The deformation of the plate due to the waves is measured using 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 plate surface (painted in mate white). The deformation of the pattern is then recorded by a high speed camera (at framerates up to 10,000 frames/s) and subsequently inverted to obtain the deformation of the surface.

During the PhD of Benjamin Miquel, we showed that indeed a turbulent-like behavior of waves is observed but which does not obey the predictions of the theory. By using direct numerical simulations, we showed that this is due to the fact that dissipation is active over all wavelengths so that the energy cascade is leaking. We are able to follow the non linear dynamics of a wavepacket in the turbulent wave field and to check the validity of some of the fundamental hypotheses of the weak turbulence theory applied to this system. Later we also studied the strongly nonlinear regime in which folds and D-cones appear, some sort of dynamical crumpling. We showed that these coherent structures are responsible for the development of intermittency. We also studied non stationary regimes of decay and buildup of wave turbulence.

During the PhD of Roumaissa Hassaini, in collaboration with G. Düring and G. Krstulovic, we studied experimentally and numerically, the case of a plate under tension. Tension changes the dispersion relation of the plate. A large scales it behaves as a membrane (a drum) and at small scales as a plate. When increasing the tension we observed that the stressed plated remained in a regime of weak turbulence. No transiton to chocks (as in acoustics) or to a solitonic regime (as for shallow water waves) is observed. This is due to the peculiarity that the nonlinear coupling among waves propagating in the same direction is zero which prevents self-steepening of the wave fronts. This systems shows some analogies with the case of gravitational waves in the primordial Universe that has been studied theoretically by S. Nazarenko and S. Galtier. We also observed weak turbulence on a bass drum !