On the existence of self-similar structures in turbulent pipe flow

Townsend's attached eddy hypothesis forms the basis for one of the most far-reaching concepts in the analysis of the logarithmic layer in wall-bounded turbulent flows. The hypothesis proposes that the eddying motions in the inertially dominated region are energetic and geometrically self-similar eddies that scale with the distance from their eddy center to the wall, implying that these three-dimensional eddies can be completely scaled using a single length scale. The attached eddy hypothesis has been used successfully to predict turbulence statistics and the spectral behavior in wall-bounded flows. Here, we experimentally investigate the existence of selfsimilar flow structures in fully-developed turbulent pipe flow at Re_τ ≈ 2390. The data is simultaneously acquired at two pipe crosssections using two stereo PIV systems, where the streamwise separation ranges from 0 to 9.97R. The structures are unconditionally sorted by their spanwise length scale through an azimuthal Fourier decomposition. The sorted structures are thereafter investigated using two-point correlations, and the resulting correlation maps are shown to exhibit self-similar behaviour with respect to its spanwise length scale. This single length scale provides a complete description of the shape of the self-similar eddies.