A continuation method, accompanied with a linear stability analysis, is employed to investigate the bifurcation
diagram of the flow solutions, as well as the multiple flow states in a cavity with different aspect
ratios for parallel motion of two facing lids. The Reynolds number proportional to the wall velocity is
used as the continuation parameter, and the evolution of the bifurcation diagrams in cases with different
aspect ratios is illustrated. The induced flow patterns are highly dependent upon both the aspect ratios
and the moving velocity of the walls. Three different types of bifurcation diagrams and their corresponding
flow states are classified according to the aspect ratios. One stable symmetric flow state and
one stable asymmetric flow state are identified. The stable asymmetric flow state is obtained at a high
aspect ratio and a low Reynolds number. Meanwhile, the regions of stable and unstable flows are distinguished
according to the different aspect ratios.
