Inverse versus direct cascades in turbulent advection

M. Chertkov, I. Kolokolov, M. Vergassola

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending onthe dimensionality d of space and the degree of compressibility of the smooth advecting velocity field, the cascade of the scalar is direct or inverse. If d > 4 the cascade is always direct. For a small enough degree of compressibility, the cascade is direct again. Otherwise it is inverse; i.e., very large scales are excited. The dynamical hint for the direction of the cascade is the sign of the Lyapunov exponent for particles separation. Positive Lyapunov exponents are associated to direct cascade and Gaussianity at small scales. Negative Lyapunov exponents lead to inverse cascade, Gaussianity at large scales, and strong intermittency at small scales.

Original languageEnglish (US)
Pages (from-to)512-515
Number of pages4
JournalPhysical review letters
Issue number3
StatePublished - 1998
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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