On the helicity in 3D-periodic Navier-stokes equations II: The statistical case

Ciprian Foias, Luan Hoang, Basil Nicolaenko

Research output: Contribution to journalArticle

7 Scopus citations

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 languageEnglish
Pages (from-to)679-717
Number of pages39
JournalCommunications in Mathematical Physics
Volume290
Issue number2
DOIs
StatePublished - Jul 2009

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