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Updated: May 18, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Universal dissipation scaling for nonequilibrium turbulence.

P C Valente1, J C Vassilicos

  • 1Department of Aeronautics, Imperial College London, London, United Kingdom. p.valente09@imperial.ac.uk

Physical Review Letters
|September 26, 2012
PubMed
Summary

High Reynolds number turbulence dissipation behavior is consistent across fractal and regular grids. This energy dissipation characteristic, C(ε), scales with global Reynolds number (Re(M)) at high Re(M).

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Area of Science:

  • Fluid Dynamics
  • Turbulence Research
  • Experimental Physics

Background:

  • Turbulence exhibits complex energy dissipation behaviors at high Reynolds numbers.
  • Previous studies observed nonclassical energy dissipation in fractal square grid-generated turbulence.
  • Understanding turbulence behavior across different generating geometries is crucial.

Purpose of the Study:

  • To investigate if the nonclassical high Reynolds number energy dissipation behavior is unique to fractal grids.
  • To compare energy dissipation in decaying turbulence from fractal and regular grids.
  • To analyze the relationship between energy dissipation and Reynolds numbers in various grid-generated turbulence.

Main Methods:

  • Experimental generation of decaying turbulence using fractal square grids and various regular grids.
  • Measurement of turbulence parameters including energy dissipation rate (ε), integral length scale (L), and root-mean-square velocity (u).
  • Calculation of the nonclassical energy dissipation behavior metric C(ε) = εL/u³ and its dependence on global Reynolds number (Re(M)) and local turbulence Reynolds number (Re(L)).

Main Results:

  • The nonclassical high Reynolds number energy dissipation behavior, C(ε) = f(Re(M))/Re(L), was experimentally observed in decaying turbulence from both fractal square grids and various regular grids.
  • This behavior was found to be independent of the grid geometry for sufficiently high global Reynolds numbers.
  • For high global Reynolds numbers (Re(M)), the function f(Re(M)) was shown to scale linearly with Re(M), i.e., f(Re(M)) ~ Re(M).

Conclusions:

  • The nonclassical high Reynolds number energy dissipation behavior is a general characteristic of decaying turbulence, not limited to fractal grids.
  • Grid geometry does not influence this specific dissipation behavior at high global Reynolds numbers.
  • The observed scaling provides insights into the fundamental mechanisms of energy dissipation in turbulent flows.