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 ξ 1(n)=n/3 and ξ 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 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.