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Three-point velocity correlation functions in two-dimensional forced turbulence.

D Bernard1

  • 1Service de Physique Théorique de Saclay, F-91191 Gif-sur-Yvette, France. dbernard@spht.saclay.cea.fr

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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We derived a simple formula for three-point velocity correlations in 2D turbulence, applicable across all scales. This formula bridges direct and inverse cascade regimes, showing expected universality in extreme conditions.

Area of Science:

  • Fluid Dynamics
  • Turbulence Theory
  • Statistical Mechanics

Background:

  • Two-dimensional turbulence exhibits distinct direct and inverse energy cascades.
  • Understanding multi-point velocity correlations is crucial for characterizing turbulent flows.
  • Universality in extreme regimes of turbulence remains an active area of research.

Purpose of the Study:

  • To develop an exact, scale-bridging formula for three-point velocity correlation functions in 2D turbulence.
  • To investigate the universality of these correlations in direct and inverse cascade regimes.
  • To explore the influence of anisotropy and friction on turbulent correlations.

Main Methods:

  • Derivation of an exact analytical formula for three-point velocity correlations.

Related Experiment Videos

  • Analysis of the formula's behavior across different scales.
  • Examination of limiting cases corresponding to direct and inverse cascades.

    • Main Results:

    • A simple, exact formula for three-point velocity correlation functions in 2D turbulence is presented.
    • The formula successfully interpolates between the direct and inverse cascade regimes.
    • Universality of these correlations is confirmed in the extreme regimes.

    Conclusions:

    • The derived formula provides a comprehensive tool for analyzing 2D turbulence.
    • The study confirms the universal nature of velocity correlations in extreme turbulent regimes.
    • Anisotropy and friction effects on these correlations are discussed.