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Velocity difference statistics in turbulence.

Sunghwan Jung1, Harry L Swinney

  • 1Center for Nonlinear Dynamics and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA. sunnyjsh@chaos.utexas.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2005
PubMed
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This study unifies two turbulence theories to explain non-Gaussian velocity differences. Applying this unified approach to Couette-Taylor turbulence data provides a log-normal distribution for the intensive parameter, accurately matching observed probability distribution functions.

Area of Science:

  • Fluid Dynamics
  • Turbulence Research
  • Statistical Mechanics

Background:

  • Non-Gaussian probability distribution functions (PDFs) are observed in turbulent velocity differences.
  • Existing theories by Castaing and Beck-Cohen offer different explanations for these PDFs.

Purpose of the Study:

  • To unify the Castaing and Beck-Cohen approaches for explaining non-Gaussian PDFs in turbulence.
  • To develop a method for determining subsystem size within the Beck-Cohen framework.
  • To apply the unified approach to experimental Couette-Taylor turbulence data.

Main Methods:

  • Unification of two distinct theoretical frameworks for turbulence PDFs.
  • Development of a method to determine subsystem size based on local thermodynamic equilibrium.

Related Experiment Videos

  • Application to Couette-Taylor turbulence data at a Reynolds number of 540,000.
  • Main Results:

    • Demonstrated a relationship between the Castaing and Beck-Cohen methods.
    • Successfully determined subsystem size for the Beck-Cohen approach.
    • Observed a log-normal distribution for the intensive parameter in Couette-Taylor turbulence.
    • Achieved excellent agreement between the model's predicted PDFs and experimental data.

    Conclusions:

    • The unified approach successfully explains non-Gaussian velocity difference PDFs.
    • The method provides a robust framework for analyzing turbulence data.
    • This work advances the understanding of statistical properties in turbulent flows.