Stationary flows with highly localized vorticity of the incompressible viscous fluid at large Reynolds numbers

Herein, we present numerical evidence that the two-dimensional Navier–Stokes equations may possess stationary solutions with highly localized vorticity, that is, it is nearly zero in most of the flow region and is of appreciable magnitude only in the rest small region. These solutions appear in the Kolmogorov flows with small aspect ratios and high Reynolds numbers. Moreover, in most of the region where vorticity almost vanishes, the streamlines are nearly straight lines. •Study of 2D Navier–Stokes incompressible flow at large Reynolds numbers.•Mostly irrotational flow with concentrated vorticity in very thin domains.•Flow streamlines show similarity with vortex sheet as a viscous flow.