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Kolmogorov's third hypothesis and turbulent sign statistics
Qiaoning Chen1, Shiyi Chen, Gregory L Eyink
1Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218, USA.
Physical Review Letters
|July 15, 2003
Summary
Turbulent eddy breakdown involves "multipliers" (ratios of velocity increments). These multipliers are not independent, and their correlations rapidly decay with scale separation, leading to new scaling laws for turbulence.
Area of Science:
- Fluid Dynamics
- Turbulence Research
- Statistical Mechanics
Background:
- Kolmogorov's theory describes turbulent eddies using self-similar statistics and scale independence.
- Turbulent energy cascades involve velocity increments at successively smaller scales.
- Multipliers, defined as ratios of these increments, are key to characterizing eddy breakdown.
Purpose of the Study:
- To experimentally and numerically investigate the statistics of turbulent multipliers.
- To determine the independence and correlations of multipliers at adjacent scales.
- To predict and verify new scaling laws for turbulent velocity increments.
Main Methods:
- Experimental measurements of turbulent velocity fields.
- Numerical simulations of turbulent flows.
- Statistical analysis of multiplier magnitudes and signs.
- Verification of predicted scaling laws.
Main Results:
- Multipliers at adjacent scales are shown to be correlated.
- These correlations exhibit rapid decay with increasing scale separation.
- New scaling laws for the roughness and sign of turbulent velocity increments are predicted and verified.
- Sign oscillations per cascade step decrease with increasing velocity roughness or singularity.
Conclusions:
- Kolmogorov's hypothesis of multiplier independence at distant scales is refined.
- The study reveals crucial inter-scale dependencies in turbulent energy cascades.
- The findings provide a more accurate statistical description of turbulence breakdown and scaling laws.