Wave Turbulence
A large plate of lateral dimension (2m * 1m) and of thickness 0.5 mm is driven out of equilibrium by means of a concentrated external forcing. For large amplitude of the forcing, the system reaches a state of wave turbulence (or weak turbulence), that is characterized by a large-band Fourier spectrum. Below is shown the power spectrum of the instantaneous transverse velocity for increasing values of the injected power I (left). These spectra can be scaled on a single, universal curve, that is shown on the right.
The scaling form together with the behaviour of the cut-off frequency fc shown in the insert of the right figure implies a behaviour for the power spectrum of the velocity as I0.6. This shows that a three-wave interaction associated to the quadratic non-linearities created by the imperfection of the plate is the dominant pattern in the inertial range.
The statistics of injected power is investigated for different forcing frequency from a pure sinusoidal harmonic content (obtained for alpha = 1) to a narrow-band random noise excitation (alpha = 0). Below is shown the PDF of the mean value epsilon(tau) of the injected power computed on an intervall tau for various values of alpha. The asymmetry function rho is shown on the right. For alpha = 1 (harmonic forcing), a linear law is obtained, as predicted in the framework of the fluctuation Galavotti-Cohen theorem. For alpha = 0, a significant departure from the linear law is observed.
Related articles
- 14. A. Boudaoud, O. Cadot, B. Odille et C. Touzé : Observation of wave turbulence in vibrating plates, Physical Review Letters, vol. 100, 234504, 2008.
[PRL/APS]
- O. Cadot, A. Boudaoud et C. Touzé : Statistics of power injection in a plate set into chaotic vibration, Eur. Phys. J. B, vol. 66, pp. 399-407, 2008.
[Edpsciences/EPJB]
