Wall-attached structures of velocity fluctuations in a turbulent boundary layer subjected to adverse pressure gradient*

We demonstrate the logarithmic region of turbulent intensity by identifying wall-attached structures of velocity fluctuations through the direct numerical simulation of an adverse pressure gradient turbulent boundary layer (APG TBL) (β = 1.43 and Re_τ = 775). For comparison, the attached structures of zero pressure gradient (ZPG) TBL (Re_τ = 825) are included. The wall-attached structures are self-similar with respect to their heights (l_y), and in particular the population density of the streamwise component (u) scales inversely with l_y, reminiscent of the hierarchy of attached eddies. The turbulence intensities contained within the wall-parallel components (u and w) exhibit the logarithmic behavior. The tall attached structures of u are composed of multiple uniform momentum zones with long streamwise extents. The magnitude of the near-wall peak observed in the streamwise turbulent intensity increases with increasing l_y, reflecting the nested hierarchies of the attached u structures. The spanwise length (l_z) of the wall-attached structures in APG TBL increases more than that of ZPG TBL, while the streamwise length (l_x) decreases.