2018/08/31 by Masaki Shimizu, Paul Manneville · 1 citation
Physics and Astronomy · #physics.flu-dyn #nlin.CD #nlin.PS
paper · pdf · doi:10.1103/physrevfluids.4.113903
published as Phys. Rev. Fluids 4, 113903 (2019) · v2: 36 pages, 12 figures and 9 videos. Resolutions of figures and videos are reduced
arxiv created 2019/12/01 · arxiv updated 2019/12/03
In wall-bounded parallel flows, sustained turbulence can occur even while laminar flow is still stable. Channel flow is one of such flows and displays spatio-temporal fluctuating patterns of localized turbulence along its way from/to featureless turbulence. By direct numerical simulation, we study the observed inconsistency between turbulence decay according to a two-dimensional directed-percolation (2D-DP) scenario and the presence of sustained oblique localized turbulent bands (LTBs) below the DP critical point. Above Reynolds number Reg ∼ 700 sustained LTBs are observed; most LTBs have the same orientation so that the spanwise symmetry of the LTB pattern is broken below Re2 ∼ 1000. The frequency of transversal splitting, by which an LTB generates another one with opposite obliqueness, so that turbulence spreading becomes intrinsically two dimensional, increases in the range Reg < Re < Re2. It reaches a critical rate at Re2 beyond which symmetry is restored. 2D-DP behavior is retrieved only above Re2. A mean-field model is proposed which qualitatively accounts for the above symmetry-restoring bifurcation by considering interactions between space-averaged densities of LTBs propagating in either direction.