Self-similar collapse of point vortices in a scaling limit of filtered-Euler flows

The enstrophy dissipation in the zero viscous limit is a remarkable property to characterize 2D turbulent flows and it could occur for singular solutions of the 2D Euler equations. We study the enstrophy dissipation in terms of vortex dynamics. In particular, we focus on the dynamics of point vortices on inviscid flows. Although the well-posedness of the 2D Euler equations has not been established for point-vortex initial data, we can formally derive the point-vortex system describing motions of point vortices. In addition, the point-vortex system has self-similar collapsing solutions and several preceding results indicate that the triple collapse of point vortices leads to the enstrophy dissipation. In this work, we consider the filtered-Euler equations, which are a regularization of the Euler equations and have a unique global weak solution for the point-vortex initial data. We numerically show that self-similar collapse of four and five point vortices causes the enstrophy dissipation by considering a scaling limit of point-vortex solutions of the 2D filtered-Euler equations. This indicates that the self-similar collapse of point vortices is a generic mechanism for the anomalous enstrophy dissipation in inviscid flows.