Random Splitting of Fluid Models: Positive Lyapunov Exponents
Dynamical Systems
2023-11-29 v2 Mathematical Physics
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.2210.02958,
title = {Random Splitting of Fluid Models: Positive Lyapunov Exponents},
author = {Andrea Agazzi and Jonathan C. Mattingly and Omar Melikechi},
journal= {arXiv preprint arXiv:2210.02958},
year = {2023}
}