Extended Self-Similar Scaling Law of Multi-Scale Eddy Structure in Wall Turbulence

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 wavelet 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 regime.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.