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Turbulent flows transfer energy across scales. Experiments show velocity differences are Reynolds number-independent, but deviate from classical power laws, suggesting a logarithmic correction.

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Area of Science:

  • Fluid dynamics
  • Turbulence research
  • Statistical mechanics

Background:

  • Turbulent flows exhibit energy transfer from large to small scales, ultimately dissipated as heat.
  • Kolmogorov's 1941 conjecture posits inertial forces dominate energy transfer in the inertial range at high Reynolds numbers.
  • Universal power laws for velocity difference statistics in the inertial range are theoretically predicted.

Purpose of the Study:

  • To experimentally investigate the behavior of velocity difference statistics in turbulent flows.
  • To test Kolmogorov's conjecture and the universality of power laws across a wide range of Reynolds numbers.
  • To identify deviations from classical power law predictions in high Reynolds number turbulence.

Main Methods:

  • Experiments conducted in a well-controlled wind tunnel flow at the Max Planck Variable Density Turbulence Tunnel.
  • Measurement of second-order velocity difference statistics over an unprecedented range of Reynolds numbers.
  • Analysis of turbulence data to identify scaling laws and Reynolds number dependencies.

Main Results:

  • Measured second-order velocity difference statistics demonstrated independence from the Reynolds number.
  • Universal behavior was observed, consistent with decaying turbulence.
  • Classical power laws were not observed even at the highest tested Reynolds numbers.

Conclusions:

  • The findings suggest a Reynolds number-independent logarithmic correction to the classical power law for decaying turbulence.
  • The results challenge existing theoretical predictions and call for further theoretical development.
  • Experimental validation of universal behavior in turbulence, with deviations from simple power laws, is highlighted.