Scalings and structures in turbulent Couette-Taylor flow

Area of Science:

• Fluid Dynamics
• Turbulence Research
• Complex Systems

Background:

• The scaling of velocity structure functions in turbulent flows is crucial for understanding energy dissipation.
• Previous studies in Couette-Taylor flow provided initial insights into scaling exponents.
• The hierarchical symmetry model offers a framework for analyzing intermittency in turbulence.

Purpose of the Study:

• To re-examine velocity structure function scaling in Couette-Taylor flow for improved accuracy.
• To assess the convergence and uncertainty of scaling exponents across a wide Reynolds number range.
• To validate the applicability of the She-Leveque hierarchical symmetry model to this flow regime.

Main Methods:

• Analysis of velocity structure functions in Couette-Taylor flow.
• Systematic examination of statistical convergence with increasing sample size.
• Assessment of scaling exponent uncertainties.
• Comparison of experimental data with the She-Leveque model predictions.

Main Results:

• Accurate scaling exponents were determined for Taylor Reynolds numbers from 34 to 220.
• The She-Leveque hierarchical symmetry model was supported across the investigated range.
• The She-Leveque constant beta was found to be 0.83, indicating higher intermittency than in free jets.
• The singularity constant gamma decreased from 0.14 to 0.10 above R=10^5, correlating with structural changes.

Conclusions:

• The study provides refined scaling exponents for Couette-Taylor turbulence.
• Couette-Taylor turbulence exhibits greater intermittency than free jets.
• A transition in the nature of intermittency occurs with increasing Taylor vortex roll structure breakup.