2012
DOI: 10.1103/physrevlett.108.074501
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Turbulence in Noninteger Dimensions by Fractal Fourier Decimation

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Cited by 68 publications
(90 citation statements)
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“…For example, for approaches based on Galerkin projections, we cite the idea of keeping modes in Fourier space corresponding to wavenumbers logarithmically equispaced (Grossmann et al 1996), or on a Fractal set (Frisch et al 2012). Similarly, Laval, Dubrulle & Nazarenko (2001) proposed multiscale triad pruning, in order to distinguish the role played by local and non-local Fourier interactions in the growth of intermittency.…”
Section: Discussionmentioning
confidence: 99%
“…For example, for approaches based on Galerkin projections, we cite the idea of keeping modes in Fourier space corresponding to wavenumbers logarithmically equispaced (Grossmann et al 1996), or on a Fractal set (Frisch et al 2012). Similarly, Laval, Dubrulle & Nazarenko (2001) proposed multiscale triad pruning, in order to distinguish the role played by local and non-local Fourier interactions in the growth of intermittency.…”
Section: Discussionmentioning
confidence: 99%
“…[18] we define the fractal Fourier decimation operator P D acting on a generic field u(x, t) = k e ikxû k (t) as:…”
Section: The Burgers Equation On a Fractally Decimated Fourier Setmentioning
confidence: 99%
“…In a recent work [18], the idea of fractal decimation was introduced, with the aim of studying the evolution of the Navier-Stokes equations on an effective dimension D out of an integer ddimensional embedding manifold. This is done by introducing a quenched mode-reduction in Fourier space such that in a sphere of radius k the number of modes that are involved in the dynamics scale as k D (where D < d is the effective fractal dimension of the system) for large k [18,19]. This approach allows us to decimate the number of triad interactions in Fourier space as a function of the wavenumbers involved as well as to consider the problem in non-integer, fractal dimensions D. In Ref.…”
Section: Introductionmentioning
confidence: 99%
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“…Recent work on turbulence on fractal decimated Fourier space [32,33] show the role and the importance of equipartition in reduced Fourier space and its connection to cascades. In general if a binning is used, one that contains equal number of modes per bin gives the same equipartition solution as the original system [27].…”
Section: Introductionmentioning
confidence: 99%