Direct numerical simulation of rotating plane Couette flow (RPCF) at $Re_w=1300$ and $Ro=0.02$ was performed with different mesh resolutions and different sizes of computation domain. Our results showed that a grid resolution in wall units with $\Delta~x^+=8.51,~\Delta~z^+=4.26$, $\Delta~y^+|_{\text{min}}=0.0873$ and $\Delta~y^+|_{\text{max}}=3.89$ is fine enough to simulate the problem at the present parameters. The streamwise length $L_x$ and spanwise length $L_z$ of the computational box have different impacts on the flow statistics, where the statistics were converged if $L_x$ is longer than $8\pi~h$, while no converged results were obtained for different $L_z$. More importantly, our results with very long simulation time showed that a state transition would happen if $L_x\geq~8\pi~h$, from a state with four pairs of roll cells to a state with three pairs of roll cells with $L_z=6\pi~h$. Each state could survive for more than $1500h/U_w$, and the flow statistics were different.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11822208, 11772297, 11672123, and 91752201). The simulations were run on the TH-2A super computer in Guangzhou and the supercomputer in Southern University of Science and Technology of China.
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