The prediction of the evolution of coherent structures in turbulent flows by models linearised over the mean flow leads to a closure problem. We propose to go back to the conservation laws, and to consider a version of the Navier-Stokes equations submitted to a stochastic transport, referred to as « under location uncertainty ». In this framework, the displacement of a particle is caused by a resolved time-differentiable velocity field perturbed by a Brownian motion mimicking the effect of turbulent fluctuations. With these hypotheses, conservation laws show additional terms such as a stochastic diffusion induced by the Brownian motion or an effective transport velocity from high to low turbulence regions.
We propose to linearise this set of stochastic equations over the mean flow of turbulent channels at friction Reynolds numbers 180, 550 and 1000, in order to predict coherent streaks/rolls structures in the buffer and logarithmic layer. We show that for such a flow, it is required to add a non-linear forcing term, as performed in resolvent analysis, to account for non-linear interactions between time-correlated structures, active in the regeneration cycle of roll/streaks structures. We show moreover the improvements of predictions in the logarithmic layer by employing the stochastic modelling.

Bio:
Gilles Tissot est chercheur à INRIA Rennes dans l’équipe Odyssey. Il a effectué sa thèse à l’institut Pprime avec Laurent Cordier et Bernd Noack. Il a effectuer un post-doc à l’ITA (Brésil) avec André Cavalieri, un post-doc à l’institut de mathématiques de Toulouse avec Jean-Pierre Raymond et un post doc au laboratoire d’acoustique de l’université du Mans avec Gwénaël Gaba