Topology of corner vortices in the lid-driven cavity flow: 2D vis a vis 3D

Abstract

All the previous studies on the cavity flow are confined to either the study of its 2D or its 3D configuration in isolation. In this study, we endeavour to gain some physical insight into the corner vortices from the perspective of the flow topology in the 2D vis a vis 3D driven cavity by employing some recent developments in the field of topological fluid dynamics. The computed flow is post-processed to identify critical points in the flow field leading to the prediction of separation, reattachment and vortical structures in the flow. The limit cycles in the plane of symmetry of the 3D flow representing the vortices are found to be stable ones. The Poincare–Bendixson formula is used to validate the computed flow, i.e., the possible number of critical points in the 2D cavity identified by us from the computation. The topology of the corner vortices in actual 3D flow and its 2D idealization has also been compared in detail.