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Exact relationship for third-order structure functions in helical flows

Gomez1, Politano, Pouquet

  • 1Observatoire de la Cote d'Azur, CNRS UMR 6529, Nice, France.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 14, 2000
PubMed
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Researchers derived a new law for turbulent flows, extending Kolmogorov's "4/5 law" to account for helicity invariance. This provides a novel method for studying helical fluid dynamics and testing vorticity measurements.

Area of Science:

  • Fluid Dynamics
  • Turbulence Theory
  • Statistical Mechanics

Background:

  • Kolmogorov's
  • 4/5 law
  • describes energy dissipation in isotropic turbulence.
  • Helical flows, possessing a specific symmetry, require modified theoretical frameworks.

Purpose of the Study:

  • To derive an exact law for third-order structure functions in turbulent flows with helicity invariance.
  • To establish a relationship analogous to Kolmogorov's law but applicable to helical turbulence.
  • To introduce a new tool for analyzing helical flows and validating vorticity measurements.

Main Methods:

  • Formulation of an exact law for third-order structure functions.
  • Consideration of flow properties: homogeneity, incompressibility, isotropy, and non-invariance under reflectional symmetry.

Related Experiment Videos

  • Derivation of a Kolmogorov-type relation using mixed structure functions of velocity and vorticity fields.

    • Main Results:

    • An exact law for third-order structure functions in helical turbulent flows was established.
    • The derived law is consistent with previous work on the von Karman-Howarth equation for helical flows.
    • A linear scaling relation for the third-order velocity correlation function was obtained.

    Conclusions:

    • The new law offers an alternative to Kolmogorov's relation for helical turbulence.
    • The derived relationship can serve as a stringent test for laboratory vorticity measurements.
    • This work provides a supplementary tool for investigating the characteristics of helical flows.