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

Abstract

The longitudinal fluctuating velocity of a turbulent boundary layer was measured in a water channel at a moderate Reynolds number. The extended self-similar scaling law of structure function proposed by Benzi was verified. The longitudinal fluctuating velocity in the turbulent boundary layer was decomposed into many multi-scale eddy structures by wavalet transform. The extended self-similar scaling law of structure function for each scale eddy velocity was investigated. The conclusions are 1) 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 by the same set of scaling exponents ζ₁(n)=n/3 and ζ₂(n)=n/3 of the fully developed regine. 2) The range of scales where the extended self-similarity valid is much larger than the inertial range and extends far deep into the dissipation range with the same set of scaling exponents. 3) The extended self-similarity is applicable not only for homogeneous turbulence, but also for shear turbulence such as turbulent boundary layers.