Onset of vortex structures in rotating plane Couette flow

Two new flows, a tilted-vortex flow and a periodic-vortex flow, are found numerically at the onset of instability in rotating plane Couette flow (RPCF). It has hitherto been believed that the first few bifurcation sequences from the laminar state are quite well understood, namely, that a streamwise-independent flow with a two-dimensional roll-cell (2dRC) structure bifurcates first, followed by the bifurcation of a wavy-vortex flow (WVF). The present study shows that the 2dRC is, in fact, unstable from its onset, and that the newly found tilted-vortex flow takes over in place of 2dRC. It is further found that the periodic-vortex flow takes part in the early stages of laminar–turbulent transition. The existence of the new flows can be verified by careful examinations of the experimental observations in Hiwatashi et al. (Phys. Fluids, vol. 19, 2007, 048103) and Kawata & Alfredsson (J. Fluid Mech., vol. 791, 2016, 191–213).