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Large-scale structures in a turbulent channel flow with a minimal streamwise flow unit. (English) Zbl 1415.76319
Summary: Direct numerical simulations are used to examine large-scale motions with a streamwise length $$2\sim 4h$$ ($$h$$ denotes the channel half-width) in the logarithmic and outer regions of a turbulent channel flow. We test a minimal ‘streamwise’ flow unit [S. Toh and T. Itano, ibid. 524, 249–262 (2005; Zbl 1065.76553)] (or MSU) for larger Kármán numbers ($$h^+=395$$ and 1020) than in the original work. This flow unit consists of a sufficiently long $$(L_x^+\approx 400)$$ streamwise domain to maintain near-wall turbulence [J. Jiménez and P. Moin, ibid. 225, 213–240 (1991; Zbl 0721.76040)] and a spanwise domain which is large enough to represent the spanwise behaviour of inner and outer structures correctly; as $$h^+$$ increases, the streamwise extent of the MSU domain decreases with respect to $$h$$. Particular attention is given to whether the spanwise organization of the large-scale structures may be represented properly in this simplified system at sufficiently large $$h^+$$ and how these structures are associated with the mean streamwise velocity $$\overline{U}$$. It is shown that, in the MSU, the large-scale structures become approximately two-dimensional at $$h^+=1020$$. In this case, the streamwise velocity fluctuation $$u$$ is energized, whereas the spanwise velocity fluctuation $$w$$ is weakened significantly. Indeed, there is a reduced energy redistribution arising from the impaired global nature of the pressure, which is linked to the reduced linear-nonlinear interaction in the Poisson equation (i.e. the rapid pressure). The logarithmic dependence of $$\overline{ww}$$ is also more evident due to the reduced large-scale spanwise meandering. On the other hand, the spanwise organization of the large-scale $$u$$ structures is essentially identical for the MSU and large streamwise domain (LSD). One discernible difference, relative to the LSD, is that the large-scale structures in the MSU are more energized in the outer region due to a reduced turbulent diffusion. In this region, there is a tight coupling between neighbouring structures, which yields antisymmetric pairs (with respect to centreline) of large-scale structures with a spanwise spacing of approximately $$3h$$; this is intrinsically identical with the outer energetic mode in the optimal transient growth of perturbations [J. C. Del Álamo et al., ibid. 561, 329–358 (2006; Zbl 1157.76346)].

MSC:
 76F40 Turbulent boundary layers 76F65 Direct numerical and large eddy simulation of turbulence
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