Refined scaling hypothesis for breakdown coefficients in turbulence.

Area of Science:

• Fluid Dynamics
• Statistical Physics

Background:

• Turbulence involves energy dissipation across various scales.
• Novikov's breakdown coefficients quantify these energy dissipation ratios.

Purpose of the Study:

• To model the statistical distribution of Novikov's breakdown coefficients.
• To investigate deviations from Gaussianity and power-law scaling in turbulent energy dissipation.

Main Methods:

• Developed a hierarchical stochastic process model for turbulent cascades.
• Derived an analytic function to describe the distribution of log-breakdown coefficients.
• Analyzed correlations and parameter interpretations within the model.

Main Results:

• The model accurately reproduces the distribution of log-breakdown coefficients.
• Identified two key parameters, one interpretable as a generalized dimension.
• Demonstrated the absence of power-law scaling in breakdown coefficient moments.

Conclusions:

• A hierarchical stochastic model provides a strong analytical description of turbulent energy dissipation statistics.
• The model captures essential features like correlations and non-Gaussianity.
• Proposed an approximation scheme for breakdown coefficient moments, highlighting scaling limitations.