Late dynamics of large-scale vortices in periodic two-dimensional flows

The inverse cascade in freely decaying two-dimensional flows with periodic boundary conditions will lead to a quasi-steady long-term system of vortices, which has not been well investigated in literature. By performing a series of direct numerical simulations, we focus on the late dynamics of these large-scale vortices. It is found that the theories of point vortices can be also approximately employed for both quadrate and hexagonal periodic conditions, however, in real flows the dynamics can switch among different motions, which differs from the theory of point vortices. It is observed as a special case of the wandering motions that the weakest vortex can migrate among different periods, with the other two vortices co-rotating. This phenomenon can be analogical to the physics of current flow. In addition, the merging procedure of large-scale vortices can be described by using the skewness of vorticity.