Fonctionne avec Indico
v3.2.9
In fluid turbulence, energy is transferred from one scale to another by
an energy cascade that depends only on the energy dissipation rate.
Remarkably, a similar phenomenon takes place in thin elastic plates. In
the limit where the non-linearity in the equations governing the
vibrations of a plate is weak, the theory of wave turbulence (WT) can be
safely applied. Over the last ten years this cascade has been
extensively studied theoretically and numerically. This system has
revealed itself as a useful prototype to study wave interactions and
turbulence.
In this seminar, I will start by explaining how the theory of weak wave
turbulence applies to this problem, what are the corresponding
theoretical predictions and how well experimental results confirm such
predictions. Then, I will show that for this system, it is possible to
derive the analogous of the 4/5-law of hydrodynamic turbulence, which
provides an exact result concerning the energy transfers. Moreover, I
will show than in the fully non-linear regime, elastic deformations
present large “eddies” together with a myriad of small “crumpling
eddies”, such that folds, developable cones, and more complex stretching
structures, in close analogy with swirls, vortices and other structures
in hydrodynamic turbulence. This deformations lead to the same
Kolmogorov spectrum observed in hydrodynamic turbulence. To finish, if
time allows it, I will discuss the non-dispersive limit and explain what
are the mathematical difficulties of applying WT theory in this case.