Numerical investigation of plane Couette flow with weak spanwise rotation

Direct numerical simulation of rotating plane Couette flow (RPCF) at Rew = 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 Δx+ = 8.51, Δz+ = 4.26, Δy+|min = 0.0873 and Δy+|max = 3.89 is fine enough to simulate the problem at the present parameters. The streamwise length Lx and spanwise length Lz of the computational box have different impacts on the flow statistics, where the statistics were converged if Lx is longer than 8πh, while no converged results were obtained for different Lz. More importantly, our results with very long simulation time showed that a state transition would happen if Lx ≥ 8πh, from a state with four pairs of roll cells to a state with three pairs of roll cells with Lz = 6πh. Each state could survive for more than 1500h/Uw, and the flow statistics were different.