### Abstract

We study the asymptotic behavior of the statistical solutions to the Navier-Stokes equations using the normalization map [9]. It is then applied to the study of mean energy, mean dissipation rate of energy, and mean helicity of the spatial periodic flows driven by potential body forces. The statistical distribution of the asymptotic Beltrami flows are also investigated. We connect our mathematical analysis with the empirical theory of decaying turbulence. With appropriate mathematically defined ensemble averages, the Kolmogorov universal features are shown to be transient in time. We provide an estimate for the time interval in which those features may still be present.

Original language | English |
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Pages (from-to) | 679-717 |

Number of pages | 39 |

Journal | Communications in Mathematical Physics |

Volume | 290 |

Issue number | 2 |

DOIs | |

State | Published - Jul 2009 |

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## Cite this

*Communications in Mathematical Physics*,

*290*(2), 679-717. https://doi.org/10.1007/s00220-009-0827-z