Self-similar advective-diffusive transport in the Moffatt vortex flow

Problems involving advective-diffusive transport in corner-bounded geometries arise frequently in science and engineering. Low-Reynolds-number flow patterns near sharp corners often produce the classic, well-studied Moffatt eddies. Here, we consider the effect of Moffatt eddies on diffusive concentration profiles near sharp corners. Using a similarity ansatz, the advection-diffusion problem can be recast as an eigenvalue problem. By investigating the behavior of the resulting eigenfunction, we make conclusions about the evolution of the mixing properties of the system over a range of Peclet number values. This study adds to our understanding of the low-Reynolds-number transport dynamics near sharp corners from a pattern formation perspective that can be extended to other systems.