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arXiv · 2210.02958

Random Splitting of Fluid Models: Positive Lyapunov Exponents

Andrea Agazzi·Jonathan C. Mattingly·Omar Melikechi
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Abstract

In this paper we give sufficient conditions for random splitting systems to have a positive top Lyapunov exponent. We verify these conditions for random splittings of two fluid models: the conservative Lorenz-96 equations and Galerkin approximations of the 2D Euler equations on the torus. In doing so, we highlight particular structures in these 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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BibTeXRIS

Andrea Agazzi, Jonathan C. Mattingly, Omar Melikechi. 2022-10-06. Random Splitting of Fluid Models: Positive Lyapunov Exponents. https://arxiv.org/abs/2210.02958

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