Turbulence in noninteger dimensions by fractal fourier decimation

Uriel Frisch, Anna Pomyalov, Itamar Procaccia, Samriddhi Sankar Ray

Research output: Contribution to journalArticlepeer-review


Fractal decimation reduces the effective dimensionality D of a flow by keeping only a (randomly chosen) set of Fourier modes whose number in a ball of radius k is proportional to kD for large k. At the critical dimension D c=4/3 there is an equilibrium Gibbs state with a k -5 /3 spectrum, as in V. L'vov et al., Phys. Rev. Lett. 89, 064501 (2002)PRLTAO0031-900710.1103/PhysRevLett.89.064501. Spectral simulations of fractally decimated two-dimensional turbulence show that the inverse cascade persists below D=2 with a rapidly rising Kolmogorov constant, likely to diverge as (D-4/3) -2 /3.

Original languageEnglish
Article number074501
JournalPhysical review letters
Issue number7
StatePublished - 13 Feb 2012

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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