The vortical flow pattern exhibited by the channel flow on a rotating system just past transition under the influence of the Coriolis force

The subject of our paper is the post-transition flow pattern formed in the plane channel flow on a rotating system when transition is induced by the Coriolis force acting when the rotation vector is aligned with the spanwise direction of the channel. It is known from previous work, see eg. [5] [6], that, when transition sets in in this flow, it does so at rather low Reynolds numbers of only around 50 and the flow in the post-transition stage exhibits stationary longitudinal vortices, an observation standing in sharp contrast to the case of no rotation. The object of our present work is to try to extract this salient flow feature in quantitative terms through studying the bifurcation characteristics of this flow on the verge of transition. The focus of our attention is on the spatial periodicity of the longitudinal vortices, for which the relevant properties of the bifurcating solution of the nonlinear equations of motion for disturbances to the basic flow are examined. The velocity profile of the basic flow here is simply the parabola itself. The parameters influencing transition in this flow are, in conventional notation, the Reynolds number \(Re = \frac{U_{ref} H}{v}\) and the rotation number \(Ro = \frac{\Omega H}{U_{ref}}\), where 2H is the channel-height.