Random Splitting of Fluid Models: Positive Lyapunov Exponents

. In this paper, we apply the framework of [5] to give sufficient conditions for the random splitting systems introduced in [2] to have a positive top Lyapunov exponent. We verify these conditions for the randomly split conservative Lorenz-96 equations and randomly split Galerkin approximations of the 2D Euler equations on the torus. In doing so, we highlight particular structures in the equations such as shearing. Since a positive top Lyapunov exponent is an indicator of chaos which in turn is a feature of turbulence, our results show these randomly split fluid models have important characteristics of turbulent flow.

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