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Fluctuation-response relation in turbulent systems.

L Biferale1, I Daumont, G Lacorata

  • 1Department of Physics and INFM, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, I-00133 Roma, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
PubMed
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We developed halving-time statistics to measure time decay in Gaussian and turbulent models. This method reveals response functions in turbulence are inertial range quantities, suggesting short-range interactions in shell models.

Area of Science:

  • Physics
  • Fluid Dynamics
  • Statistical Mechanics

Background:

  • Measuring time properties of response functions is crucial in physics.
  • Existing methods face challenges in Gaussian (Orszag-McLaughlin) and non-Gaussian (shell models for turbulence) systems.
  • Quantifying time decay of high-order generalized response functions requires stable statistical tools.

Purpose of the Study:

  • To introduce a statistically stable method for measuring time decay of response functions.
  • To analyze time properties of response functions in both Gaussian and strongly non-Gaussian models.
  • To investigate the nature of response functions in shell models for three-dimensional turbulence.

Main Methods:

  • Introduction of halving-time statistics as a novel tool.

Related Experiment Videos

  • Numerical analysis of response functions and generalized response functions.
  • Application to Gaussian models (Orszag-McLaughlin) and shell models for turbulence.

    • Main Results:

    • Halving-time statistics provide a stable measure for time decay.
    • Response functions in shell models for 3D turbulence are identified as inertial range quantities.
    • Numerical results indicate short-range interactions in the invariant measure of shell-velocity fluctuations.

    Conclusions:

    • Halving-time statistics is an effective tool for analyzing time-dependent properties of response functions.
    • The findings in turbulent shell models suggest a connection between response functions and inertial range dynamics.
    • The results support the hypothesis of short-range interactions governing shell-velocity fluctuations in turbulence.