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Wall-attached structures of streamwise velocity fluctuations in an adverse-pressure-gradient turbulent boundary layer. (English) Zbl 1460.76502

Summary: 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 \((\beta =1.43)\). 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 \((y_{\min})\) and height \((l_y)\). The attached structures \((y_{\min}\approx 0)\) 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 \(l_y\), and their population density has an inverse-scale distribution over the range \(0.4 \delta <l_y<0.58 \delta\) (\(\delta\) is the 99 % boundary layer thickness). They also contribute to the logarithmic variation of the streamwise Reynolds stress and to the presence of the \(k_z^{-1}\) region in the pre-multiplied energy spectra \((k_z\) is the spanwise wavenumber), i.e. these structures are universal wall motions in the logarithmic region. The tall attached structures with \(l_y=O(\delta)\) are non-self-similar and responsible for the enhancement of the outer large scales under the adverse pressure gradient. They extend beyond \(6 \delta\) 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 \((y_{\min}>0\) and \(l_y>100\nu/u_\tau)\) are geometrically isotropic and mainly arise in the outer region, whereas the sizes of the detached non-self-similar structures \((y_{\min}>0\) and \(l_y<100\nu/u_\tau )\) scale with the Kolmogorov length scale. Here, \(\nu\) is the kinematic viscosity and \(u_\tau\) the friction velocity. The present study provides a new perspective on the analysis of turbulence structures in the view of the attached-eddy model.

MSC:

76F40 Turbulent boundary layers
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