Exponential decay of the power spectrum of turbulence

H. Bercovici, P. Constantin, C. Foias, O. P. Manley

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


The analyticity on a strip of the solutions of Navier-Stokes equations in 2D is shown to explain the observed fast decay of the frequency power spectrum of the turbulent velocity field. Some subtleties in the application of the Wiener-Khinchine method to turbulence are resolved by showing that the frequency power spectrum of turbulent velocities is in fact a measure exponentially decaying for frequency →±∞. Our approach also shows that the conventional procedures used in analyzing data in turbulence experiments are valid even in the absence of the ergodic property in the flow.

Original languageEnglish (US)
Pages (from-to)579-602
Number of pages24
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - Aug 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Turbulence
  • analyticity
  • ergodicity
  • invariant probability measure
  • statistical power spectra
  • temporal velocity fluctuations


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