Logarithmic energy profile of the streamwise velocity for wall-attached eddies along the spanwise direction in turbulent boundary layer

Abstract

The present work explores the spanwise logarithmic decay of the turbulence intensity for wall-attached eddies per Townsend's attached eddy hypothesis. Within the dataset spanning a friction Reynolds number range the coherence between the turbulence in the logarithmic region along the spanwise direction and that at a near-wall reference location is used to assess the scale-dependent coherence. Linear coherence spectrum analysis is applied as a filter to separate the coherent and incoherent portions. After this separation procedure, the turbulence intensity decay for wall-attached eddies in the spanwise direction is described in a log-linear manner, which also identifies how the scaling parameter increases with the Reynolds number. This variation is parametrized and consequently can be used to improve existing near-wall models.