Hysteresis behaviour in spanwise rotating plane Couette flow at Re w = 2600

Abstract

Hysteresis behaviour was reported in spanwise rotating plane Couette flow (RPCF) at Reynolds number with varying rotation number in a recent work (Huang et al. Phys. Rev. Fluids 2019;4:052401(R)). Here, is half of the velocity difference between two walls, h is half of the channel width, ν is the kinematic viscosity and is the constant angular velocity in the spanwise direction. In this paper, we perform two groups of direct numerical simulations at where Ro varies in steps along two opposite directions to investigate the hysteresis behaviour in RPCF at a relatively higher Reynolds number. It is found that when Reynolds number increases to 2600, the hysteresis of flow structures still exists in RPCF, but the span of the hysteresis loop shrinks from to . Turbulent statistics, such as the friction Reynolds number, turbulent kinetic energy and mean velocity gradient at the centreline, all exhibit similar hysteresis behaviours.