Elliptically Desingularized Vortex Model for the Two-Dimensional Euler Equations

Abstract

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 $O({(\frac{{A}_{k}}{{R}_{k\ensuremath{\alpha}}^{2}})}^{2})$. (${R}_{k\ensuremath{\alpha}}$ is the inter-FAVOR centroid distance.) The model is validated by comparing steady-state configurations and dynamical evolutions with contour dynamical results.