Bifurcations and inviscid limit of rhombic Navier-Stokes flows in tori

We consider viscous incompressible fluid motions on two‐dimensional tori. Unlike many papers which treat the cases where the basic flow is a parallel flow, we consider here the case where the flow pattern is rhombic. We numerically compute the bifurcating solutions and find that (1) the bifurcating branch is a transcritical one, (2) on one side of the branch, the solution displays a sharp interior layer in the inviscid limit, and (3) on the other side of the branch, the solutions in the inviscid limit do not possess an interior layer.