Numerical Studies of Two-Dimensional Vortex Motion by a System of Point Vortices

Abstract

The motions of a vortex tube with an elliptic cross section and of a vortex sheet of finite length in an inviscid, incompressible fluid are simulated by a number of discrete vortex filaments, each vortex moving under the action of the velocity field of all the other vortices. By the use of this simulation, rotation of the vortex tube and rolling-up of the vortex sheet are investigated numerically as initial value problems. Comparison with exact solutions shows the validity of this method of approximation. In order to improve the results, an artificial viscosity is introduced to the equations of motion. This diminishes randomization of vortices inherent to the treatment without viscosity and thus leads to regular rolling-up of a vortex sheet.