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 $R{e}_w=U_{w}h/\nu =1300$ with varying rotation number $Ro=2{\mathrm{\Omega }}_{z}h/U_w$ in a recent work (Huang et al. Phys. Rev. Fluids 2019;4:052401(R)). Here, $U_w$ is half of the velocity difference between two walls, h is half of the channel width, ν is the kinematic viscosity and ${\mathrm{\Omega }}_z$ is the constant angular velocity in the spanwise direction. In this paper, we perform two groups of direct numerical simulations at $R{e}_w=2600$ 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 $0.03\le Ro\le 0.3$ to $0.03\le Ro\le 0.2$. Turbulent statistics, such as the friction Reynolds number, turbulent kinetic energy and mean velocity gradient at the centreline, all exhibit similar hysteresis behaviours.

Keywords:

• Spanwise rotating plane Couette flow
• hysteresis
• multiple states

Acknowledgements

We would like to thank the support by the National Science Foundation of China (NSFC grant nos. 11822208, 11772297, 91852205 and 91752202). Xia would also like to thank the support from the Fundamental Research Funds for the central Universities.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Science Foundation of China (NSFC grant numbers 11822208, 11988102, 11772297, 91852205 and 91752202) and Shenzhen Science and Technology Program (grant number KQTD20180411143441009). Xia is also supported from the Fundamental Research Funds for the Central Universities.