Comparison of collapsing processes of point vortices in the filtered point vortex systems

The enstrophy dissipation in inviscid flows is a remarkable property characterizing the 2D turbulent flow. It is challenging attempt to describe the turbulent flow by a dssipative solution to the differential equations governing the inviscid flow and make the vortex dynamics inducing the enstrophy dissipation clear. Our motivation is to investigate non-smooth solutions of inviscid models and understand the physical mechanism of the 2D turbulent flow. The preceding studies have attacked this problem by considering the dynamics of point vortices on the filtered-Euler model and revealed that the collapse of point vortices causes the enstrophy dissipation. This enstrophy dissipation by the vortex collapse is fully solved in the three vortex problem with mathematical rigor, and a recent numerical study has shown that the dissipation occurs for the four and five vortex problems in a specific filtered-model called the Euler-alpha model. In this talk, we show that the enstrophy dissipation by the collapse of point vortices occurs for other filtered-models such as the vortex blob model and the exponential model. This result insists that the enstrophy dissipation by the vortex collapse is a universal phenomenon for the filtering method.