Sidewall effect on turbulent band in subcritical transition of high-aspect-ratio duct flow

Abstract

We numerically studied high-aspect-ratio channel flows with spanwise sidewalls, that is, wide duct flows, in its subcritical turbulent transitional regime. The infinite channel flow is known to form large-scale intermittency of turbulent-laminar coexistence and undergo two-stage transition (or crossover transition) process: a second-order phase transition with a critical Reynolds number R e c ≈ 1000 and a deviation from it to maintain turbulence down to the global critical value R e g ≈ 700. However, a real channel must have spatial finiteness, and its effect on transition phenomena is nontrivial. With the objective of understanding the turbulence maintenance limitations in the real channel flow, we investigated the effect of spanwise finiteness on the localized turbulence and its criticality, using direct numerical simulation. In our widest duct with an aspect ratio of 1:96 in the flow cross section, turbulent bands colliding with sidewalls above Re = 1069 often stochastically reflected or reversely traveled, keeping two-dimensional intermittencies with oblique bands, similar to the channel flow, whereas, in a narrower duct of 1:24, the critical value was higher as 1151 in the steeper transition profile, forming a quasi-one-dimensional intermittency dominantly. The transition in the high-aspect-ratio duct flow was converged to R e g ≈ 1000 as the sidewall distance was increased. The critical phenomenon differs significantly from the channel flow for all duct flows, even for high aspect ratios. Due to spatial finiteness, the duct flows become fully laminar within a finite time for R e ≲ 1000, unlike the channel flow. Possible causes of the difference in Reg between the two systems with fixed pressure gradient and fixed flow rate are discussed.