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).
- … 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`.
- 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).
- 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.
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