Oblique stripe solutions of channel flow

Abstract

With decreasing Reynolds number, turbulence in channel flow becomes spatio-temporally intermittent and self-organises into solitary stripes oblique to the mean flow direction. We report here the existence of localised nonlinear travelling wave solutions of the Navier-Stokes equations possessing this obliqueness property. Such solutions are identified numerically using edge tracking coupled with arclength continuation. All solutions emerge in saddle-node bifurcations at values of lower than the non-localised solutions. Relative periodic orbit solutions bifurcating from branches of travelling waves have also been computed. A complete parametric study is performed, including their stability, the investigation of their large-scale flow, and the robustness to changes of the numerical domain.