DNS of turbulent plane Couette flow with emphasis on turbulent stripe

Abstract

Reverse transition of ‘turbulence → laminar’ in wall-bounded shear flows remains poorly understood and few studies have been reported. A plane Couette flow (CF) is conceptually one of the simplest non-trivial fluid dynamics systems, where the flow is solely driven by the shear. This flow is linearly stable for all Reynolds numbers, but experiences direct transition to turbulence through the development of localized perturbations (cf. [1] for a discussion). Above some threshold, turbulence is sustained with a complex behavior characterized by laminar-turbulent co-existence in the form of eturbulent stripe. The transition, though well-described experimentally [2], is far from being completely elucidated. On the other hand, a direct numerical simulation (DNS) of intermittently turbulent flows is challenging and requires a huge computational domain so that another strategy has been necessary. For instance, existing numerical studies are limited within frameworks of a semi-realistic model [3] or of a tilted geometry with a minimal domain [4]. However, owing to the recent development of computers, DNS of the subcritical CF is now possible to be performed.