  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.
