title: Turbulence in noninteger dimensions by fractal Fourier decimation.
abstract: 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 k(D) 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). 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).
authors.affiliation: UNS, CNRS, OCA, Laboratoire Lagrange, Nice, France.
authors.forename: Uriel
authors.initials: U
authors.lastname: Frisch
authors.forename: Anna
authors.initials: A
authors.lastname: Pomyalov
authors.forename: Itamar
authors.initials: I
authors.lastname: Procaccia
authors.forename: Samriddhi Sankar
authors.initials: SS
authors.lastname: Ray