壁湍流多尺度湍涡结构推广的自相似标度律

在水槽中测量了中等雷诺数下平板湍流边界层中的瞬时流向速度的时间序列,验证了Benzi提出的推广的自相似标度律,用子波变换将壁湍流脉动速度分解为多尺度湍涡结构的速度,研究了每一个尺度的湍涡速度结构函数的推广的自相似标度律。主要结论如下:湍流的统计性质是自相似的,这不仅适用于充分发展湍流,而且适用于中等雷诺数和低雷诺数湍流,而且具有相同的标度指数;推广的自相似标度律的适用的尺度范围远远大于惯性子区的范围,可以一直延伸至耗散区的尺度范围;推广的自相似标度律不仅适用于均匀各向同性湍流,也适用于剪切湍流如边界层湍流。

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.