On mean flow universality of turbulent wall flows. I. High Reynolds number flow analysis

ABSTRACT

The universality and mathematical physical structure of wall-bounded turbulent flows is a topic of discussions over many decades. There is no agreement about questions like what is the physical mean flow structure, how universal is it, and how universal are theoretical concepts for local and global flow variations. These questions are addressed by using latest direct numerical simulation (DNS) data at moderate Reynolds numbers Re and experimental data up to extreme Re. The mean flow structure is explained by analytical models for three canonical wall-bounded turbulent flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Thorough comparisons with DNS and experimental data provide support for the validity of models. Criteria for veritable physics derived from observations are suggested. It is shown that the models presented satisfy these criteria. A probabilistic interpretation of the mean flow structure shows that the physical constraints of equal entropies and equally likely mean velocity values in a region unaffected by boundary effects impose a universal log-law structure. The structure of wall-bounded turbulent flows is much more universal than previously expected. There is no discrepancy between local logarithmic velocity variations and global friction law and bulk velocity variations. Flow effects are limited to the minimum: the difference of having a bounded or unbounded domain, and the variation range of mean velocity values allowed by the geometry.

KEYWORDS:

• Wall-bounded turbulent flows
• mean flow structure
• universality of wall flows

Acknowledgments

The author is very thankful to Professors Flack [69], Chung [47], Chin [66], Sung [75], Hultmark and Vallikivi [72] for making data for comparisons available. I am very thankful to the referees for their helpful suggestions for improvements.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The author would like to acknowledge partial support through NASA's NRA research opportunities in aeronautics program (Grant No. NNX12AJ71A with Dr. P. Balakumar as technical officer) and the National Science Foundation (DMS - CDS&E-MSS, Grant No. 1622488 with Dr. Y. Zeng as Technical Officer). Substantial support from the Hanse-Wissenschaftskolleg, Institute for Advanced Study (Delmenhorst, Germany, Technical Monitor: W. Stenzel) is gratefully acknowledged; Langley Research Center (Grant No. NNX12AJ71A) and Directorate for Mathematical and Physical Sciences (Grant No. 1622488).