Self-similarity of wall-attached turbulence in boundary layers

An assessment of the turbulent boundary layer flow structure, which is coherent with the near-wall region, is carried out through a spectral coherence analysis. This spectral method is applied to datasets comprising synchronized two-point streamwise velocity signals at a near-wall reference position and a range of wall-normal positions spanning a Reynolds-number range Re_[STIX]x1D70F~ O(10³)-O(10⁶) . Within each dataset, a self-similar structure is identified from the coherence between the turbulence in the logarithmic region and at the near-wall reference position. This self-similarity is described by a streamwise/wall-normal aspect ratio of [STIX]x1D706ₓ/z≈ 14 , where [STIX]x1D706ₓ and z are the streamwise wavelength and wall-normal distance respectively.