Intermittent Turbulence in Self-Similar Cascades¶
Mandelbrot, B. B. (1974). Intermittent Turbulence in Self-Similar Cascades: Divergence of High Moments and Dimension of the Carrier. Journal of Fluid Mechanics, 62(2), 331-358.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Fractal Geometry
- … iterated function systems (Hutchinson's (1981) collage theorem giving an existence-and-uniqueness result for self-similar attractors of contraction systems), and probability theory (fractional Brownian motion, multifractal cascades following Mandelbrot's (1974) multiplicative-cascade construction, Lévy flights).
This sourceIntroduces multifractal intermittency: turbulent dissipation concentrated on fractal subsets, with scaling exponents depending on moment order (anomalous scaling).
Supported in partVerified against the publisher's abstract
Mandelbrot (1974) backs only the cascade clause: its abstract models intermittent turbulence as a self-similar/canonical cascade with an 'intrinsic fractional dimension'; it says nothing of Hutchinson, fBm or Lévy flights.
“The second is to replace Yaglom's model by a different, less constrained one, based upon the concept of ‘canonical cascade’.”
- … iterated function systems (Hutchinson's (1981) collage theorem giving an existence-and-uniqueness result for self-similar attractors of contraction systems), and probability theory (fractional Brownian motion, multifractal cascades following Mandelbrot's (1974) multiplicative-cascade construction, Lévy flights).
- Intermittency
- Multifractal intermittency in fully developed turbulence — wherein structure functions exhibit anomalous
This sourceMandelbrot links intermittency to multifractal structure and cascades; She-Leveque proposes universal log-Poisson model predicting moment-dependent anomalous exponents ζ(p). Both establish multifractal formalism as central to intermittency theory. Cross-link with DP-04 `fractal_geometry`.
Supported in partVerified against the publisher's abstract
Mandelbrot's abstract supports intermittent turbulence modelled by cascades with divergent high moments, but not 'multifractal' or anomalous structure functions.
“In the latter two cases, high-order moments of E turn out to be infinite.”
- Multifractal intermittency in fully developed turbulence — wherein structure functions exhibit anomalous
- Turbulence
- energy spectral density decays following dimensional-analysis predictions derived from dissipation rate and wavenumber alone. Enhanced mixing and transport. Turbulence dramatically enhances the transport of momentum, heat, and scalars compared to laminar flow at the same mean velocity. Intermittency. Turbulent fluctuations are not uniform; intense bursts and quiet periods alternate, and the statistics of rare events deviate from simple Gaussian expectations.
This sourceIntroduces multifractal intermittency: turbulent dissipation is not uniformly distributed but concentrated on fractal subsets of progressively smaller Hausdorff dimension; shows that scaling exponents depend on moment order (anomalous scaling).
Supported in partVerified against the publisher's abstract
The abstract establishes non-uniform, intermittent dissipation on fractal subsets with anomalous moments; it does not state the claim's transport-enhancement or spectral-decay clauses.
“the distribution of ε differs from the lognormal distribution”
- energy spectral density decays following dimensional-analysis predictions derived from dissipation rate and wavenumber alone. Enhanced mixing and transport. Turbulence dramatically enhances the transport of momentum, heat, and scalars compared to laminar flow at the same mean velocity. Intermittency. Turbulent fluctuations are not uniform; intense bursts and quiet periods alternate, and the statistics of rare events deviate from simple Gaussian expectations.
Verification¶
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