Moffatt eddies in the driven cavity: A quantification study by an HOC approach

In this paper, we establish Moffatt-likeness of the corner vortices in the lid-driven square cavity for Stokes flow and flow for moderate Reynolds numbers in the pre-asymptotic regime. The flow is computed by using an efficient transient Navier-Stokes (N-S) solver on compact non-uniform space grids. The quantification of the corner vortices in succession as Moffatt vortices follows from them following a fixed geometric ratio in sizes and intensities. In the process, we also provide more detailed benchmarking results for the corner vortices in the cavity flow. The accuracy of the scale resolution of the vortices has been verified by a novel approach to grid independence analysis. This approach utilizes the concept of adverse pressure gradients as a tool to validate that the separation zones in the neighborhood of the corners are consistent with the vortices obtained from our computed solution of the N-S equations.