[Paper Review] On the Non Specific Nature of Classical Turbulence Statistics

Trinh Khanh Tuoc|arXiv (Cornell University)|Jan 13, 2010

Fluid Dynamics and Turbulent Flows32 references4 citations

TL;DR

This paper challenges the assumption that classical turbulence statistics—such as Reynolds stresses and energy spectra—are uniquely diagnostic of turbulent flows. It demonstrates these statistics can emerge from non-turbulent, unsteady viscous flows, suggesting they lack specificity for identifying turbulence mechanisms. Conditional averaging of ejection events, however, yields more distinctive turbulence signatures.

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

Motivation & Objective

• To challenge the assumption that classical turbulence statistics are inherently diagnostic of turbulent flows.
• To investigate whether classical statistics can arise from non-turbulent, unsteady viscous flows.
• To identify which statistical measures are uniquely characteristic of turbulence mechanisms.
• To evaluate the specificity of conditional averaging techniques in capturing turbulence dynamics.
• To clarify the limitations of using classical statistics for inferring turbulence structure and mechanisms.

Proposed method

• Derives classical turbulence statistics from a solution of unsteady viscous flow equations without turbulence.
• Analyzes the same flow using conditional averaging techniques focused on ejection events in the burst phase.
• Compares probability density functions (PDFs) of velocity fluctuations from both classical and conditional statistics.
• Examines energy spectra and Reynolds stress components in the context of recurring unsteady states.
• Uses numerical solutions of the Navier-Stokes equations under non-turbulent boundary conditions to generate reference statistics.
• Applies statistical tools such as conditional averaging and PDF analysis to isolate turbulence-specific features.

Experimental results

Research questions

• RQ1 Can classical turbulence statistics emerge from non-turbulent, unsteady viscous flows?
• RQ2 To what extent are classical statistics specific to actual turbulence, or are they generic to unsteady flows?
• RQ3 How do conditional averages of ejection events differ from classical statistics in their ability to diagnose turbulence?
• RQ4 What statistical measures are most distinctive of turbulence mechanisms rather than general unsteady flow?
• RQ5 What are the implications of non-specific classical statistics for interpreting turbulence structure?

Key findings

• Classical turbulence statistics, including Reynolds stresses and energy spectra, can be derived from solutions of unsteady viscous flow without turbulence.
• These classical statistics are not unique to turbulence and thus cannot reliably diagnose turbulence mechanisms on their own.
• Conditional averaging, particularly of velocity fluctuations during ejection phases, produces statistics that are more distinctive of turbulence.
• The probability density functions (PDFs) of ejection events in conditional statistics show stronger deviation from Gaussian behavior, indicating turbulence-specific dynamics.
• Energy spectra derived from classical statistics do not uniquely identify turbulent energy transfer mechanisms when derived from non-turbulent flows.
• The study concludes that overreliance on classical statistics may lead to incorrect inferences about turbulence structure and mechanisms.