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Related Experiment Videos

Mean-field approximation and a small parameter in turbulence theory.

V Yakhot1

  • 1School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
Summary

Two-dimensional turbulence exhibits Gaussian statistics and Kolmogorov scaling for transverse velocity differences. A critical dimensionality reveals insights into energy flux and dissipation, explaining observed phenomena in fluid dynamics.

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Area of Science:

  • Fluid Dynamics
  • Statistical Mechanics
  • Turbulence Theory

Background:

  • Two-dimensional turbulence exhibits complex behaviors, with transverse velocity components often described by Gaussian statistics and Kolmogorov scaling.
  • Dissipation fluctuations are generally considered irrelevant in the limit of small viscosity for these systems.

Purpose of the Study:

  • To investigate the role of critical dimensionality in two-dimensional turbulence.
  • To derive theoretical expressions for pressure and dissipation contributions to the generating function of transverse velocity differences.
  • To explain the onset of intermittency and validate findings with experimental data.

Main Methods:

  • Numerical and physical experiments on two-dimensional turbulence.
  • Theoretical analysis assuming a critical space dimensionality d=d(c).

Related Experiment Videos

  • Derivation of exact relations between correlation functions and an equation for the generating function.

    • Main Results:

    • Transverse velocity differences in 2D turbulence follow Gaussian statistics and Kolmogorov scaling.
    • A critical dimensionality d(c) is identified where energy flux and odd-order moments change sign.
    • The derived equation accurately describes experimental data and shows intermittency onset under specific conditions.

    Conclusions:

    • The mean-field theory effectively describes 2D turbulence at d
    • The study provides a theoretical framework for understanding intermittency in turbulent flows.
    • Gaussian statistics are predicted for transverse velocity components in various 2D turbulence regimes.