Breakdown of dynamic scaling and intermittency in a cascade model of turbulence

Omri Gat*, Itamar Procaccia, Reuven Zeitak

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We present an analytic and numerical analysis of the Gledzer-Ohkitani- Yamada (GOY) cascade model for turbulence. We concentrate on the dynamic correlations, and demonstrate both numerically and analytically, using resummed perturbation theory, that the correlations do not follow a dynamic scaling ansatz. The basic reason for this is the existence of a second quadratic invariant, in addition to energy. This implies the breakdown of the Kolmogorov-type scaling law, in a manner different from the conventional mechanisms proposed for Navier-Stokes intermittency. By modifying the model equation so as to eliminate the spurious invariant, we recover to good accuracy both dynamic scaling and the Kolmogorov exponents. We conclude that intermittency in the GOY model may be attributed to the effects of the spurious invariant which does not exist in the three-dimensional Navier-Stokes flow.

Original languageAmerican English
Pages (from-to)1148-1154
Number of pages7
JournalPhysical Review E
Issue number2
StatePublished - 1995
Externally publishedYes


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