Lyapunov Analysis of Homogeneous Isotropic Turbulence

Nicola de Divitiis

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arXiv · 0905.3513

Lyapunov Analysis of Homogeneous Isotropic Turbulence

Nicola de Divitiis

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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 study of the mechanism of the energy cascade from large to small scales through the Lyapunov analysis of the relative motion between two particles and in the calculation of the velocity fluctuation through the Lyapunov analysis of the local deformation and the Navier-Stokes equations. The analysis provides an explanation for the mechanism of the energy cascade, leads to the closure of the von Kármán-Howarth equation, and describes the statistics of the velocity difference. Several tests and numerical results are presented.

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Nicola de Divitiis. 2009-08-12. Lyapunov Analysis of Homogeneous Isotropic Turbulence. https://arxiv.org/abs/0905.3513

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