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Eulerian spectral closures for isotropic turbulence using a time-ordered fluctuation-dissipation relation.

W D McComb1, K Kiyani

  • 1School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom. w.d.mccomb@ed.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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This study extends time-ordering procedures to analyze turbulence. Researchers demonstrate a local energy balance for the Kraichnan-Wyld perturbation series and confirm no infrared divergence in the response equation.

Area of Science:

  • Fluid dynamics
  • Turbulence theory
  • Statistical mechanics

Background:

  • The Kraichnan-Wyld perturbation theory is a key framework for studying turbulence.
  • Previous work established procedures for time-ordering the covariance function.

Purpose of the Study:

  • To extend time-ordering procedures for analyzing turbulence.
  • To determine the response function at second order using local energy balance.
  • To investigate the behavior of the response equation at infinite Reynolds number.

Main Methods:

  • Extension of time-ordering procedures for covariance functions.
  • Application of these procedures to the Kraichnan-Wyld perturbation series.
  • Use of exponential approximations to simplify the two-time formulation.

Related Experiment Videos

  • Derivation of single-time Markovianized closure equations.

    • Main Results:

    • The response function at second order is determined by local energy balance in wave number.
    • The response equation shows no infrared divergence at infinite Reynolds number.
    • Derived closure equations are compatible with the Kolmogorov distribution without ad hoc constants.

    Conclusions:

    • The extended time-ordering procedures provide a robust method for analyzing turbulent systems.
    • The findings confirm the validity of the Kraichnan-Wyld theory and its extensions.
    • The results offer a more fundamental understanding of turbulence closure models.