Wall-attached structures of streamwise velocity fluctuations in an adverse-pressure-gradient turbulent boundary layer

The three-dimensional clusters of streamwise velocity fluctuations (u) in turbulent boundary layers (TBLs) are explored from the perspective of the attached-eddy model, which provides a basis for understanding the asymptotic behaviours of high-Reynolds-number wall turbulence in terms of coherent structures. We extract the u clusters from the direct numerical simulation data of a TBL subjected to an adverse pressure gradient ( fi D 1 :43). For comparison, the direct numerical simulation data of a zero-pressure-gradient TBL are included. The identified structures are decomposed into attached self-similar, attached non-self-similar, detached self-similar and detached non-self-similar motions with respect to the minimum distance from the wall ( ymin) and height (ly). The attached structures ( ymin 0) are the main energy-containing motions and carry approximately half of the streamwise Reynolds stress and the Reynolds shear stress in the logarithmic and outer regions. The sizes of the attached self-similar structures scale with ly, and their population density has an inverse-scale distribution over the range 0:4 < ly < 0:58 ( is the 99% boundary layer thickness). They also contribute to the logarithmic variation of the streamwise Reynolds stress and to the presence of the k 1 z region in the pre-multiplied energy spectra (kz is the spanwise wavenumber), i.e. these structures are universal wall motions in the logarithmic region. The tall attached structures with ly D O./ are non-self-similar and responsible for the enhancement of the outer large scales under the adverse pressure gradient. They extend beyond 6 in the streamwise direction and penetrate deeply into the near-wall region, which is reminiscent of very-large-scale motions or superstructures. The detached self-similar structures ( ymin > 0 and ly > 100=u ) are geometrically isotropic and mainly arise in the outer region, whereas the sizes of the detached non-self-similar structures ( ymin > 0 and ly < 100 =u ) scale with the Kolmogorov length scale. Here, is the kinematic viscosity and u the friction velocity. The present study provides a new perspective on the analysis of turbulence structures in the view of the attached-eddy model.