Random Splitting of Fluid Models: Ergodicity, Convergence and Lyapunov exponents

We consider a family of processes obtained by randomly splitting the deterministic flows associated with some fluid models (e.g. Lorenz 96, 2d Galerkin-Navier-Stokes). These split dynamics conveniently separate the conservative and dissipative part of the underlying equation. We characterize some ergodic properties of these stochastic dynamical systems and prove their convergence to the original deterministic flow in the small noise regime, both in the conservative and in the dissipative setting. Finally, we show that the top Lyapunov exponent of these models is positive.

This is joint work with Jonathan Mattingly and Omar Melikechi.