Direct numerical simulation is used to determine the flow that occur as the Reynolds number, Re. is increased in a plane channel undergoing system rotation about a spanwise axis. (Plane Poisuille flow occurs for zero rotation rate and low Re.) A constant system rotation speed of 0.5, non-dimensionalized with respect to the bulk streamwise velocity and channel full width, is used throughout. The spectral numerical method solves the three-dimensional, time-dependent, incompressible Navier-Strokes equation using periodic boundary conditions in the streamwise and spanwise directions. On increasing the Reynolds number above the temporally periodic wavy vortex regime, near Re = 4 Re(c) (Re(c) = 88.6 is the critical Re for development of vortices), a second temporal frequency, omega-2, occurs in the flow that corresponds to slow constant spanwise motion of the vortices. superposed on the much faster, constant, streamwise motion of the wavy vortex waves. Curiously, omega-2 is always frequency locked with the wavy vortex frequency omega-1 for the parameter range explored, although the locking ratio varies. At the slightly higher Re of 4.1 Re(c), omega-2 is replaced by a new frequency omega-2' that corresponds to a modulation of the wavy vortices like that seen in modulated wavy Taylor vortex flow. However, unlike the Taylor-Couette geometry, the modulation frequency here can become frequency locked with the wavy vortex frequency. Increasing Re further to Re = 4.2 Re(c) results in the appearance of a second incommensurate modulation frequency omega-3, yielding a quasi-periodic three-frequency flow, although there are only two frequencies (omega-2' and omega-3) present in the reference frame moving with the travelling wave associated with 2 omega-1. At still higher Re(Re = 4.5 Re(c)), weak temporal chaos occurs. This flow is not turbulent however. Calculations of the instantaneous largest Lyapunov exponent, lambda(t), and the spatial structure of small perturbations of the flow show that the chaos is driven by spanwise shear instability of the streamwise velocity component. At the highest Re of 6.7 Re(c) considered, quasi-coherent turbulent boundary layer structures occur as transient, secondary streamwise-oriented vortices in the viscous sublayer near the inviscidly unstable (high-pressure) wall. Calculations of lambda(t) and the spatial structure of small perturbations to the flow show that the coherent structures are not caused by the local growth of small disturbances to the flow.
