Physics – Fluid Dynamics
Scientific paper
2009-05-21
Physics
Fluid Dynamics
31 pages, 14 figures, Revision of "Lyapunov Analysis of Homogeneous Isotropic Turbulence", Submitted on Phys. Rev. E
Scientific paper
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 K\'arm\'an-Howarth equation, and describes the statistics of the velocity difference. Several tests and numerical results are presented.
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