Wednesday, 27 July 2022
Institute for Theoretical Physics, Philosophenweg 19, Seminar Room

Speaker: Malo Tarpin (ENS de Lyon)
Title of Talk: The stochastic Euler energy model

Abstract: We propose a diffusion model for the dynamics of the fluctuating energy spectrum of turbulent flows. Our model is inspired by the decomposition of the Euler equations into triad interactions and have the same symmetries, quadratic conserved quantities and equilibrium stationnary distribution. The model is parametrised by a typical time τ associated to each triad. We argue that when the energy of the turbulent flow is well spread out and spans a quasi-continuum of modes, the observable of our model naturally follows a path large deviation principle. We then show that the same large deviation principle can also be formally derived from a spherical model of turbulence, namely a modified version of the Markovian random coupling model which takes into account the presence of an effective eddy-damping rate 1/τ. The ensuing large deviation principle takes the form of a small-noise diffusion around the eddy-damped quasi-normal Markovian dynamics, whose noise covariance matrix is not diagonal and cannot be inferred from one-mode statistics alone.