Kolmogorov's third hypothesis and turbulent sign statistics.

The breakdown of turbulent eddies can be characterized by sets of "multipliers," defined as ratios of velocity increments at successively smaller scales. These quantities were introduced by Kolmogorov, who hypothesized their self-similar statistics and independence at distant scales. Here we report experimental and numerical results on the statistics of these multipliers, for both their magnitude and sign. We show that the multipliers at adjacent scales are not independent but that their correlations decay rapidly in scale separation. New scaling laws are thereby predicted and verified for both roughness and sign of turbulent velocity increments. The sign oscillations per cascade step are found to decrease at points of increasing roughness or singularity of the velocity.