In the past, dual states were reported in turbulent plane Couette flow with spanwise rotation at ${\text{Re}}_w=1300$ and $\text{Ro}=0.2$ based on direct numerical simulations at a computational box $10\pi h\times 2h\times 4\pi h$, where the flow would evolve to a state with three or two pairs of roll cells if the simulation started with the initial flow field $u_i^{3p}$ or $u_i^{2p}$. In the present work, the influence of an initial flow field on the dual states is investigated. Nine new simulations with an initial flow field constructed by $u_i=\alpha u_i^{2p}+(1-\alpha )u_i^{3p}$ ($\alpha =0.1,0.2,...,0.9$) are carried out, and it turns out that the flow will evolve to a state with three pairs of roll cells if $\alpha \le 0.6$, while the flow will have only two pairs of roll cells when $\alpha \ge 0.7$, which documents the robustness of two states. The turbulent statistics is also revisited, and it is found that the turbulent kinetic energy and related dissipation are larger in the state with more roll cells. The terms in the transport equations of the Reynolds stresses are generally of the same shape at two different states, but the state with more roll cells has a larger value. The energy transfer between the secondary and the residual fields shows that the secondary flows are more energetic at the state with more roll cells while the residual field is more energetic in the other state. Furthermore, a local inverse energy cascade is observed in the near wall region at the latter state with fewer roll cells where the energy is transferred from the residual field to the secondary flow field. Our results support the conjecture that the large-scale secondary flows play a very important role in the dual states of spanwise rotating plane Couette flows.

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• Rotating geophysical flows
• Shear layer turbulence
• Taylor-Couette system
• Turbulence
• Viscosity