A Role of Filaments in the Axisymmetrization of an Isolated Two-Dimensional Elliptic Vortex with a Non-Uniform Vorticity Distribution

Abstract

We numerically examine the role of filaments in the axisymmetrization of an isolated elliptic vortex with a non-uniform vorticity distribution for a two-dimensional incompressible barotropic fluid. To quantitatively examine the role of filaments in the axisymmetrization, we first divide the vorticity field into a core region and a surrounding region. The former corresponds to the core of the vortex, and the latter corresponds to the filaments and a weak vorticity region just outside the vortex core. Second, we analyze the radial displacement of the maximum and minimum curvature points on a vorticity contour in the core region advected by velocities induced by the vorticity of those regions. This investigation shows that the vorticity of the surrounding region largely contributes to the axisymmetrization at both points, especially when the filaments are forming. Thus, we conclude that the filaments play a significant role in the axisymmetrization of the isolated elliptic vortex.