On the Non Specific Nature of Classical Turbulence Statistics

TL;DR

This paper demonstrates that classical turbulence statistics are not unique to turbulence and can be derived from unsteady viscous flow solutions, emphasizing the importance of conditionally averaged statistics for turbulence characterization.

Contribution

It reveals the non-specific nature of classical turbulence statistics and highlights the significance of conditional averages in identifying turbulence-specific features.

Findings

Classical turbulence statistics can be derived from viscous flow solutions.

Conditionally averaged statistics better distinguish turbulence structures.

Classical statistics are not exclusive indicators of turbulence.

Abstract

The classical statistics of turbulence are shown to be not specific to turbulence and can be derived from a solution for recurring unsteady state viscous flow. Care must be exercised in using them to make deductions about turbulence structures and mechanisms. The conditionally averaged statistics, particularly involving the velocities of the ejections in the burst phase, are more distinctive of turbulence. Key words: Turbulence statistics, classical, conditional average, probability density function, energy spectrum