Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2011-08-05
Nonlinear Sciences
Chaotic Dynamics
Submitted to Phys. Rev. Lett. 4 pages, 3 figures
Scientific paper
Fractal decimation reduces the effective dimensionality 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=4/3 there is an equilibrium Gibbs state with a $k^{-5/3}$ spectrum, as in [V. L'vov {\it et al.}, Phys. Rev. Lett. {\bf 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 $(D-4/3)^{-2/3}$.
Frisch Uriel
Pomyalov Anna
Procaccia Itamar
Sankar Ray Samriddhi
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