Exact relationship for third-order structure functions in helical flows

Area of Science:

• Fluid Dynamics
• Turbulence Theory
• Statistical Mechanics

Background:

• Kolmogorov's
• 4/5 law
• describes energy dissipation in isotropic turbulence.
• Helical flows, possessing a specific symmetry, require modified theoretical frameworks.

Purpose of the Study:

• To derive an exact law for third-order structure functions in turbulent flows with helicity invariance.
• To establish a relationship analogous to Kolmogorov's law but applicable to helical turbulence.
• To introduce a new tool for analyzing helical flows and validating vorticity measurements.

Main Methods:

• Formulation of an exact law for third-order structure functions.
• Consideration of flow properties: homogeneity, incompressibility, isotropy, and non-invariance under reflectional symmetry.
• Derivation of a Kolmogorov-type relation using mixed structure functions of velocity and vorticity fields.

Main Results:

• An exact law for third-order structure functions in helical turbulent flows was established.
• The derived law is consistent with previous work on the von Karman-Howarth equation for helical flows.
• A linear scaling relation for the third-order velocity correlation function was obtained.

Conclusions:

• The new law offers an alternative to Kolmogorov's relation for helical turbulence.
• The derived relationship can serve as a stringent test for laboratory vorticity measurements.
• This work provides a supplementary tool for investigating the characteristics of helical flows.