Chaotic advection by two interacting finite-area vortices

Abstract

This article deals with the advection of fluid particles in the velocity field of two identical vortices with various vorticity distributions. The two-dimensional velocity field is aperiodic in the range of parameters studied here, namely, the neighborhood of the critical distance for merger. Ideas and methods from the theory of transport in dynamical systems are used to describe and quantify particle advection. These methods are applied to the numerical representation of the velocity field, which is obtained by solving the Euler equations with the vortex-in-cell method. It is found that the strongest stirring of vortex fluid occurs slightly above the critical distance for merger. In this regime the fluid located between the vortices is subjected to intense stirring, and some vortex fluid may be entrained into the chaotic region depending on the smoothness of the vorticity distribution. Initial conditions below the critical distance lead to stirring of fluid mainly before merger. In this case the flow geometry is used to quantify the efficiency of merger, which is defined as the ratio of the circulation of the resultant vortex to the total circulation of the original vortices. It is found that the vortices with the smoothest vorticity profile have the lowest efficiency. Experimental visualizations in a two-dimensional rotating fluid confirm the intense stretching and folding of fluid elements that occurs before the vortices merge.