Orateur
Description
Wave turbulence shares three key characteristics with hydrodynamic turbulence: multiple scales, randomness and the presence of cascades. Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. With C.-E. Bréhier, L. Chevillard, I. Gallagher, R. Grande and W. Ruffenach, we have constructed a linear equation that mimics the phenomenology of energy cascades when the external force is a statistically homogeneous and stationary stochastic process. In the Fourier variable, this equation can be seen as a wave equation, which corre- sponds to a wave operator of degree 0 in physical space. Our results give a complete characterization of the solution: it is smooth at any finite time, and, up to smaller order corrections, it converges to a fractional Gaussian field at infinite time. The proposed linear dynamics can be generalized to more general spectra, possibly non-radial, including sea wavenumber spectra such as the JONSWAP spectrum. We apply a finite volume method in the Fourier variables formulation in order to reach the invariant measure of the equation.
