Self-similarity in the logarithmic region of turbulence intensity in high-Reynolds-number pipe flow

Abstract

Establishing a scaling law for the turbulence intensity profile of wall-bounded flows at high Reynolds numbers has been an important theme in fluid dynamics and is increasingly linked to studies on Townsend’s attached eddy hypothesis. In this paper, the self-similarity of turbulence statistics for the three velocity components, derived from the assumption of attached eddy hypothesis, is examined using detailed experimental data for pipe flow from Re_τ = 4200 to 20,750 measured by laser Doppler velocimetry at the High Reynolds Number Actual Flow Facility (Hi-Reff). The region where probability density functions (PDFs) of velocity fluctuations for all three velocity components exhibit similar form was identified around y⁺=220 ∼ 720 through Kullback-Leibuler divergence (KLD) analysis. This region, referred to as the identical PDF region, is approximately located at the outer region of the Reynolds stress peak. Within this region, turbulence statistics for all velocity components exhibit self-similarity. Conversely, in the logarithmic region of the turbulence intensity profile −previously observed to approximately overlap with the logarithmic region of the mean velocity profile- the PDFs are not invariant, and turbulence statistics do not exhibit self-similarity. These findings suggest that the characteristics of the turbulence statistics in the identical PDF region align more closely with the predictions of the attached eddy hypothesis than those in the conventional logarithmic region.