Extended self-similar scaling law of multi-scale eddy structure in wall turbulence

The longitudinal fluctuating velocity of a turbulent boundary layer was mea sured in a water channel at a moderate Reynolds number. The extended self-s imilar scaling law of structure function proposed by Benzi was verified. Th e longitudinal fluctuating velocity, in the turbulent boundary layer was de composed into many multi-scale eddy structures by wavelet transform. The ex tended self-similar scaling law of structure function for each scale eddy v elocity was investigated. The conclusions are I) The statistical properties of turbulence could be self-similar not only at high Reynolds number, but also at moderate and low Reynolds number, and they could be characterized b y the same set of scaling exponents xi (1)(n) = n/3 and xi (2)(n) = n/3 of the fully developed regime. 2) The range of scales where the extended self- similarity valid is much larger than the inertial range and extends far dee p into the dissipation range,vith the same set of scaling exponents. 3) The extended selfsimilarity is applicable not only for homogeneous turbulence, but also for shear turbulence such as turbulent boundary layers.