Periodicity and self-similarity of vortex evolution in a double-lid-driven cavity flow

The flow configuration of the two-dimensional low Reynolds number flow in a rectangular cavity with two opposite moving lids and different depth-to-width ratios is investigated. The effects of aspect ratio varying from 0.15 to 6.6 on vortex structure in the cavity were numerated using the differential quadrature method. The critical aspect ratios, streamline patterns and bifurcation diagrams were presented. It is found that the vortex structure distributes in the transverse direction of cavity and the sub-eddy centers gradually merge as aspect ratio increases from 0.15 to 0.7. When the aspect ratio is larger than 0.7, the flow structure unfolds in the longitudinal direction of cavity and the number of vortices gradually increases with the aspect ratio increasing. The evolution of flow pattern exhibits the characteristics of periodicity and self-similarity. The large outer vortices evolve from the growth of new vortices in the middle region of cavity. The flow patterns are always symmetric about the cavity centre at different aspect ratios.