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Cascades in helical turbulence.

P D Ditlevsen¹, P Giuliani

¹The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 20, 2001

Summary

Researchers propose an inner scale for helicity dissipation in turbulence, larger than the Kolmogorov scale. This suggests turbulent flows become helicity-free at small scales, especially at high Reynolds numbers.

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Area of Science:

Fluid dynamics
Turbulence theory
Statistical mechanics

Background:

Hydrodynamic turbulence is characterized by energy dissipation at the smallest scales (Kolmogorov scale, η).
Helicity, a quantity related to the alignment of vorticity and velocity, plays a role in turbulent flows.
Understanding the behavior of helicity at small scales is crucial for a complete picture of turbulence.

Purpose of the Study:

To propose the existence of a characteristic inner scale (ξ) for helicity dissipation in fully developed hydrodynamic turbulence.
To estimate this scale using dimensional analysis.
To investigate the relationship between the helicity dissipation scale and the Kolmogorov scale.

Main Methods:

Dimensional analysis to estimate the helicity dissipation scale (ξ).
Theoretical arguments regarding the ratio of the Kolmogorov scale (η) to the helicity dissipation scale (ξ).
Illustration using a shell model of turbulence, a simplified system capturing key turbulent dynamics.

Main Results:

A characteristic inner scale (ξ) for helicity dissipation is proposed.
This scale ξ is found to be larger than the Kolmogorov scale η (ξ > η).
The ratio η/ξ approaches zero in the limit of high Reynolds numbers, indicating helicity becomes negligible at small scales.

Conclusions:

Turbulent flows are expected to be helicity-free at small scales, particularly under high Reynolds number conditions.
The proposed helicity dissipation scale provides a new perspective on the small-scale structure of turbulence.
The findings are consistent with simulations using a shell model of turbulence.

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