Ultra-High Reynolds Number Is Not Necessary for Comprehensive Log Scaling in a Turbulent Boundary Layer

TL;DR

Experiments in sink flow turbulence demonstrate that comprehensive log scaling of velocity moments occurs at moderate Reynolds numbers, emphasizing streamwise invariance as a key condition, challenging the belief that ultra-high Reynolds numbers are necessary.

Contribution

The study shows that streamwise invariance, rather than ultra-high Reynolds number, is crucial for log scaling in turbulent boundary layers, supported by experimental evidence and a heuristic theory.

Findings

Log scaling observed at moderate Reynolds numbers in sink flow.

Streamwise invariance is essential for log scaling.

Ultra-high Reynolds numbers are not required for comprehensive log scaling.

Abstract

Experiments in an extraordinary turbulent boundary layer called the sink flow, displaying a perfect streamwise invariance, show a wide extent of logarithmic scaling for moments of streamwise velocity up to order 12, even at moderate Reynolds numbers. This is in striking contrast to canonical constant-pressure turbulent boundary layers that show such comprehensive log scaling only at ultra-high Reynolds numbers. This demonstrates that ultra-high Reynolds number is not necessary for comprehensive log scaling to occur; while specific details of the sink flow are special, the relevance to general turbulent boundary layers is that the sink flow underscores the importance of the streamwise invariance condition that needs to be met in a general flow for obtaining log scaling. Indeed, a simple heuristic theory shows that, for log scaling in the inertial sublayer, the invariance of dimensionless mean velocity and higher-order moments along a mean streamline is a necessary and sufficient condition. Ultra-high Reynolds number primarily appears to make these log scalings universal.