Random Splitting of Fluid Models: Positive Lyapunov Exponents

TL;DR

This paper establishes conditions under which random splitting fluid models exhibit positive Lyapunov exponents, indicating chaotic behavior similar to turbulence, verified for Lorenz-96 and 2D Euler models.

Contribution

It provides new sufficient conditions for positive Lyapunov exponents in random splitting systems and applies them to specific fluid models, linking chaos to turbulence features.

Findings

Random splitting systems can have positive Lyapunov exponents.

Conditions verified for Lorenz-96 and 2D Euler models.

Positive exponents suggest chaotic, turbulent-like behavior.

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.