# American Institute of Mathematical Sciences

2005, 2005(Special): 692-699. doi: 10.3934/proc.2005.2005.692

## The dipole dynamical system

 1 Department of Aerospace & Mechanical Engineering and Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1191

Received  September 2004 Revised  March 2005 Published  September 2005

A dynamical system governing the collective interaction of N point-vortexdipoles is derived.Each dipole has an inherent orientation $\psi$ and generates a velocity field that decayslike $O(\mu /2 \pi r^2)$ where $\mu$ is the dipole strength and$r$ is the distance from the dipole.The system of N-complex ordinary differentialequations plus N-real ordinary differentialequations for the dipole positions and orientationsare derived based on theassumption that each dipole moves with and tries to align itselfwith the local fluid velocity field.
Citation: P.K. Newton. The dipole dynamical system. Conference Publications, 2005, 2005 (Special) : 692-699. doi: 10.3934/proc.2005.2005.692
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