Elliptically Desingularized Vortex Model for the Two-Dimensional Euler Equations

A new self-consistent model of the incompressible Euler equations in two dimensions is presented. The vorticity is assumed to be distributed in well separated disjoint piecewise-constant elliptical finite-area vortex regions (FAVORs) $D_k$ with area $A_k$. The evolution equations for four variables that describe each FAVOR are derived by truncating a physical-space moment description by omitting terms $O\left({\left(\frac{A_k}{R_{k\alpha }^2}\right)}^2\right)$. ($R_{k\alpha }$ is the inter-FAVOR centroid distance.) The model is validated by comparing steady-state configurations and dynamical evolutions with contour dynamical results.