Lyapunov Analysis for Fully Developed Homogeneous Isotropic Turbulence

TL;DR

This paper applies Lyapunov analysis to isotropic turbulence, explaining the energy cascade mechanism and providing a closure for the von Karman-Howarth equation, supported by numerical tests.

Contribution

It introduces a Lyapunov-based approach to analyze turbulence, offering new insights into the energy cascade and velocity difference statistics.

Findings

Provides a Lyapunov-based explanation for the energy cascade.

Achieves closure of the von Karman-Howarth equation.

Presents numerical validation of the theoretical results.

Abstract

The present work studies the isotropic and homogeneous turbulence for incompressible fluids through a specific Lyapunov analysis, assuming that the turbulence is due to the bifurcations associated to the velocity field. The analysis consists in the calculation of the velocity fluctuation through the Lyapunov analysis of the local deformation and the Navier-Stokes equations and in the study of the mechanism of the energy cascade from large to small scales through the finite scale Lyapunov analysis of the relative motion between two particles. The analysis provides an explanation for the mechanism of the energy cascade, leads to the closure of the von Karman-Howarth equation, and describes the statistics of the velocity difference. Several tests and numerical results are presented.