The dipole dynamical system
P.K. Newton - Department of Aerospace & Mechanical Engineering and Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1191, United States (email) Abstract: 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.
Keywords: Dipole gas; Two-dimensional turbulence models; Nonequilibrium processes; Two-component BECs.
Received: September 2004; Revised: March 2005; Published: September 2005. |