The vanishing viscosity limit for a dyadic model

Details The vanishing viscosity limit for a dyadic model The vanishing viscosity limit for a dyadic model

2008-10-21

arxiv.org/abs/0810.3718v1

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.physd.2009.01.011

A dyadic shell model for the Navier-Stokes equations is studied in the context of turbulence. The model is an infinite nonlinearly coupled system of ODEs. It is proved that the unique fixed point is a global attractor, which converges to the global attractor of the inviscid system as viscosity goes to zero. This implies that the average dissipation rate for the viscous system converges to the anomalous dissipation rate for the inviscid system (which is positive) as viscosity goes to zero. This phenomenon is called the dissipation anomaly predicted by Kolmogorov's theory for the actual Navier-Stokes equations.

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