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In incompressible viscous flows in a confined domain, vortices are known toform at the corners and in the vicinity of separation points. The existence ofa sequence of vortices (known as Moffatt vortices) at the corner withdiminishing size and rapidly decreasing intensity has been indicated byphysical experiments as well as mathematical asymptotics. In this work, weestablish the existence of Moffatt vortices for the flow in the famousLid-driven square cavity at moderate Reynolds numbers by using an efficientNavier-Stokes solver on non-uniform space grids. We establish that Moffattvortices in succession follow fixed geometric ratios in size and intensitiesfor a particular Reynolds number. In order to eliminate the possibility ofspurious solutions, we confirm the physical presence of the small scales bypressure gradient computation along the walls.

Moffatt vortices in the lid-driven cavity flow