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The dipole dynamical system

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  • 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.
    Mathematics Subject Classification: 76B47; 76F20; 76M28.


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