Abstract
In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations develop power-law scaling as a function of the wall normal distance . Here is the streamwise velocity fluctuation, indicates normalization in wall units (averaged friction velocity), is the distance from the wall, is an independent variable, and is the boundary layer thickness. Previous work has shown that this power-law scaling exists in the log-region where is the friction velocity-based Reynolds number. Here we present empirical evidence that this self-similar scaling can be extended, including bulk and viscosity-affected regions , provided the data are interpreted with the Extended-Self-Similarity (ESS), i.e., self-scaling of the MGFs as a function of one reference value, . ESS also improves the scaling properties, leading to more precise measurements of the scaling exponents. The analysis is based on hot-wire measurements from boundary layers at ranging from 2700 to from the Melbourne High-Reynolds-Number-Turbulent-Boundary-Layer-Wind-Tunnel. Furthermore, we investigate the scalings of the filtered, large-scale velocity fluctuations and of the remaining small-scale component, . The scaling of falls within the conventionally defined log region and depends on a scale that is proportional to ; the scaling of extends over a much wider range from to . Last, we present a theoretical construction of two multiplicative processes for and that reproduce the empirical findings concerning the scalings properties as functions of and in the ESS sense.
1 More- Received 21 May 2016
DOI:https://doi.org/10.1103/PhysRevFluids.1.044405
©2016 American Physical Society