Flow bifurcation and eddy genesis in an L-shaped cavity

Flow bifurcation and eddy generation in a steady, viscous L-shaped cavity with the lids moving in opposite directions are investigated by a numerical method. The flow is governed by Stokes or Navier–Stokes equations with two control parameters h1 and h2 which are related to the heights of the L-shaped domain. A Galerkin finite element method with a stabilization technique is applied in order to obtain the numerical solution of the specified equations. Attention is focused on the topological behavior near a reentrant corner on the boundary. In general, local reentrant corner analysis provides a key to the understanding of the eddy generation in L-shaped cavities. Finally, the effect of the Reynolds number on flow bifurcations and eddy generation is investigated.

► We examine the local behavior of the degenerate point at the reentrant corner.
► The vortex ring has been observed numerically at the reentrant corner.
► The number of eddies increases from 1 to 3 via several flow transformations.