Critical exponents and universality in fully developed turbulence

A new perspective on the critical phenomena aspects of fully developed turbulence (FDT) is considered. The energy (or enstrophy) dissipation rate e (or τ) is pointed out to be the suitable quantity to be identified as the order parameter for the FDT problem. Multi-fractal model has been used to provide a detailed structure for the critical exponent σ associated with this order parameter that appears to exhibit an interesting universality covering radically different FDT systems in fluid and plasma dynamics. This result also appears to provide a consistent framework for classification of dissipation field into critical, subcritical and supercritical cases. Some FDT problems that exemplify these cases are discussed. This classification is validated further by considering the probability density functions (PDF) of relevant flow-variable gradients in the FDT problems exemplifying the various cases.

• Publication year

  2004

• Venue

  Chaos Solitons & Fractals

• Publication date

  2004-04-21

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1016/J.CHAOS.2005.11.017arXiv physics/0404099
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Collisionless magnetohydrodynamic turbulence in two dimensions

  2005cited by this paper
• Anomalous scaling of a passive scalar in turbulence and in equilibrium.

  2005cited by this paper
• Erratum and addendum to “Multi-fractal scaling at the Kolmogorov microscale in fully developed compressible turbulence” [Ann. Phys. 243 (1995), 177–191]

  2005cited by this paper
• Addendum to ``Spatial intermittency in the classical two-dimensional and geostrophic turbulence'' [Ann. Phys. 270 (1998) 263-291]

  2004cited by this paper
• Fractals in geophysics

  2004cited by this paper
• Particles and fields in fluid turbulence

  2001cited by this paper
• A note on the application of non-extensive statistical mechanics to fully developed turbulence

  2001cited by this paper
• Application of generalized thermostatistics to fully developed turbulence

  2000cited by this paper
• Non-extensive statistical mechanics of compressible turbulence

  2000cited by this paper
• Scaling, Universality, and Renormalization: Three Pillars of Modern Critical Phenomena

  1999cited by this paper
• Spatial Intermittency in the Classical Two-Dimensional and Geostrophic Turbulence☆

  1998cited by this paper
• Nonperturbative renormalization group approach to turbulence

  1997cited by this paper
• Multi-Fractal Aspects of Spatial Intermittency in Fully Developed Magnetohydrodynamic Turbulence

  1997cited by this paper
• Multifractal Scaling at the Kolmogorov Microscale in Fully Developed Compressible Turbulence

  1995cited by this paper
• A career in theoretical physics

  1994cited by this paper
• Analogies between scaling in turbulence, field theory, and critical phenomena.

  1994cited by this paper
• Energy dissipation in shear driven turbulence.

  1992cited by this paper
• The multifractal nature of turbulent energy dissipation

  1991cited by this paper
• On the probability density function of velocity gradients in fully developed turbulence

  1991cited by this paper
• Multifractal scaling of velocity derivatives in turbulence.

  1990cited by this paper
• Scaling and universality in statistical physics

  1990cited by this paper
• The effects of intermittency on statistical characteristics of turbulence and scale similarity of breakdown coefficients

  1990cited by this paper
• Fractals in Geophysics

  1989cited by this paper
• Possible generalization of Boltzmann-Gibbs statistics

  1988cited by this paper
• Self-organized criticality.

  1988cited by this paper
• Singularities of the equations of fluid motion.

  1988cited by this paper
• Degrees of freedom of turbulence.

  1987cited by this paper
• Renormalization group analysis of turbulence. I. Basic theory

  1986cited by this paper
• Erratum: Fractal measures and their singularities: The characterization of strange sets

  1986cited by this paper
• Turbulence and predictability in geophysical fluid dynamics and climate dynamics

  1985cited by this paper
• On the scaling of the turbulent energy dissipation rate

  1984cited by this paper
• Characterization of Strange Attractors

  1983cited by this paper
• The renormalization group: Critical phenomena and the Kondo problem

  1975cited by this paper
• Turbulence, critical fluctuations, and intermittency

  1974cited by this paper
• Critical phenomena.

  1971cited by this paper
• Scaling laws for Ising models near T(c)

  1966cited by this paper
• The Spectrum of Turbulence

  1938cited by this paper

• Generalized fractal dimension for a dissipative multi-fractal cascade model for fully developed turbulence

  2022cites this paper
• Fractals and Multi-Fractals in Turbulence

  2014cites this paper
• Electron magnetohydrodynamic turbulence: universal features

  2011cites this paper
• Intermittency in the enstrophy cascade of two-dimensional fully developed turbulence: Universal features

  2004cites this paper