Abstract
Channel flow turbulence exhibits interesting spatiotemporal complexities at transitional Reynolds numbers. In this paper, we investigated some aspects of the kinematics and dynamics of fully localized turbulent bands in large flow domains. We discussed the recent advancement in the understanding of the wave-generation at the downstream end of fully localized bands. Based on the discussion, we proposed a possible mechanism for the tilt direction selection. We measured the propagation speed of the downstream end and the advection speed of the low-speed streaks in the bulk of turbulent bands at various Reynolds numbers. Instead of measuring the tilt angle by treating an entire band as a tilted object as in prior studies, we proposed that, from the point of view of the formation and growth of turbulent bands, the tilt angle should be determined by the relative speed between the downstream end and the streaks in the bulk. We obtained a good agreement between our calculation of the tilt angle and the reported results in the literature at relatively low Reynolds numbers.
Highlights
Much below the linear critical Reynolds number of the parabolic channel flow, transition to turbulence can occur under finite-amplitude perturbations, i.e., via a subcritical transition
Here we propose that the moving direction and the tilt direction of a band are probably determined by what type of local flow is formed when a localized perturbation is introduced: One similar to that shown in Figure 4a generates a right-going band and one similar to that shown in Figure 4d generates a left-going band
We propose that the tilt direction should probably be determined by the local inflectional spanwise velocity profile generated/introduced by the initial perturbation
Summary
Much below the linear critical Reynolds number of the parabolic channel flow, transition to turbulence can occur under finite-amplitude perturbations, i.e., via a subcritical transition. A turbulent band becomes sustained because the growth at the head outperforms the decay at the tail and will grow in length. As Reynolds number increases (Re & 800), transverse splitting (or branching) can occur, nucleating daughter bands with the opposite tilt direction such that the flow pattern becomes two-sided (the criss-cross pattern) [8,9]. Using unprecedented large domain and simulating up to very large times (up to O(105 ) time units), Shimizu and Manneville [8] showed that turbulent bands can only form one-sided (parallel) pattern at low Reynolds numbers
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