Unimodal patterns appearing in the two-dimensional Navier-Stokes flows under general forcing at large Reynolds numbers

We consider the Navier-Stokes equations in 2D flat tori. With various external forces and aspect ratios of the tori, we compute steady-states and time-periodic solutions at large Reynolds numbers. Our external forces are more general than those considered previously. We demonstrate, by numerical experiments, that certain solutions having streamline patterns of simple topology appear at large Reynolds numbers.