Vortices and vortex sources of multiple vortex interaction systems

Abstract

In this paper, a multiple vortex interaction model (MVIM) is proposed to describe the possible stream–vorticity interaction (SVI) and the vorticity–vorticity interaction (VVI) among vortices. The symmetries and conservation laws of the MVIM show that the SVI preserves the momenta, the vortex momenta and the energies of every vortex, and the interaction energies of every two vortices. However, the VVI destroys the energy conservation property for every vortex. Some special types of exact vortices and vortex source solutions including multiple point vortices, vortex dipoles, vortex multi-poles, fractal cyclons, fractal cyclon dipoles and Bessel vortices (BV) are presented. A special theoretical solution, the first BV is just the usual modon solution which can be used to describe the so-called atmospheric blocking. The second BV is supported by an atmospheric observation, saddle field, occurred over the North Pacific on 26 March, 2009. The characteristic features of vortex interactions are discussed under the MVIM without the β-effect via numerical simulations. Several interaction patterns such as merging, separation, mutual orbiting and absorption are reported. Those interaction behaviors are well consistent with some known fluid mechanical experiments and meteorologic observations.