Abstract
We performed a parametric study of high-aspect-ratio channel flows with spanwise side-walls, i.e., very thin and wide duct flows, in subcritical turbulent transition using direct numerical simulation. We investigated the finiteness in a spanwise domain so-called side-wall effects of a duct flow on the localized turbulence and verified a relevance of the transition process and directed percolation (DP) universality. Many shear flows could sustain turbulence globally with large scale intermittent structures of coexisting laminar and turbulence regions for very low Reynolds number which is enough low from the upper critical values. Also, a transition of some flows can be considered as DP universality class. A duct flow with very wide spanwise domain forms spatial-temporal intermittencies such as the form of stripe or band shown in the channel flow near the lower critical Reynold number just before laminar flow. The present duct flows sustained the intermittencies for Re > 1000, whereas the channel flow formed isolated turbulent bands stably near the global critical Reynolds number as low as Re ≈ 700. In the present widest duct flow, a turbulent band collides on the side-walls and reflects or reverse travels for Re ≈ 1000. Below the global critical Reynold number, a frequency of a turbulence band collapsing goes extremely high. Thus, the spanwise finiteness inhibits the isolated turbulent bands sustaining and prevents deviated from two-dimensional DP transition for 700 < Re < 1000. As a result, the duct flow transition converges to (2+1)-D DP with Reg ≈ 1000 by increasing the distance between the side-walls.
