Large-scale structures in a turbulent channel flow with a minimal streamwise flow unit

Direct numerical simulations arc used to examine large-scale motions with a streamwise length 2 similar to 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 (Toh & Itano, J. Fluid Mech., vol. 524, 2005, pp. 249-262) (or MSU) for larger Karman numbers (h(+) = 395 and 1020) than in the original work. This flow unit consists of a sufficiently long (L-x+ approximate to 400) streamwise domain to maintain near-wall turbulence (Jimenez & Moin, J. Fluid Mech., vol. 225, 1991, pp. 213-240) and a spanwisc domain which is large enough to represent the spanwisc 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 spanwisc 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 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 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 (del Alamo & Jimenez, J. Fluid Mech., vol. 561, 2006, pp. 329-358).