Nonlinear dynamical systems and bistability in linearly forced isotropic turbulence

TL;DR

This paper analyzes linearly forced isotropic turbulence, revealing it as a bistable nonlinear dynamical system described by a cubic Lienard equation, with implications for understanding turbulence behavior.

Contribution

It identifies a new parametric form of the nonlinear dynamical system governing turbulence and connects it to a Fokker-Planck framework, highlighting bistability.

Findings

The dynamical system is a cubic Lienard equation with linear damping.

The system exhibits bistability with two stable stationary densities.

New parametric choices for modeling turbulence dynamics.

Abstract

In this letter, we present an extensive study of the linearly forced isotropic turbulence. By using analytical method, we identify two parametric choices, of which they seem to be new as far as our knowledge goes. We prove that the underlying nonlinear dynamical system for linearly forced isotropic turbulence is the general case of a cubic Lienard equation with linear damping. We also discuss a Fokker-Planck approach to this new dynamical system,which is bistable and exhibits two asymmetric and asymptotically stable stationary probability densities.