Nonlinear dynamical systems and linearly forced isotropic turbulence

TL;DR

This paper analyzes linearly forced isotropic turbulence using an analytical approach, revealing new parametric choices and establishing its connection to a generalized cubic Lienard equation with linear damping.

Contribution

It introduces two new parametric choices and proves the turbulence system is a general cubic Lienard equation with linear damping.

Findings

Identified two new parametric choices for the turbulence model

Established the turbulence system as a general cubic Lienard equation

Provided analytical insights into the nonlinear dynamics of turbulence

Abstract

In this paper, we present an extensive study of linearly forced isotropic turbulence. By using an analytical method, we identified two parametric choices that are new to our knowledge. We proved that the underlying nonlinear dynamical system for linearly forced isotropic turbulence is the general case of a cubic Lienard equation with linear damping (Dumortier and Rousseau 1990).