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arXiv · 1108.1295

Turbulence in non-integer dimensions by fractal Fourier decimation

Uriel Frisch·Anna Pomyalov·Itamar Procaccia·Samriddhi Sankar Ray
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Abstract

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 $(D-4/3)^{-2/3}$.

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Uriel Frisch, Anna Pomyalov, Itamar Procaccia, Samriddhi Sankar Ray. 2011-08-05. Turbulence in non-integer dimensions by fractal Fourier decimation. https://doi.org/10.1103/physrevlett.108.074501

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