Derivation of the Equilibrium Mean Field Equations of Point Vortex System and Vortex Filament System
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We study the point vortex system in a two-dimensional bounded domain and the vortex filament system in a three-dimensional columnar region. We consider the system with the circulation condition that each point vortex (vortex filament) has a unique circulation subject to the distribution function. Then the mean field equation of point vortex system is obtained by three methods based on the different dynamical principles. Moreover, as an extension to the three-dimensional case, the mean field equation of nearly parallel vortex filament system is also obtained by applying one of them.
- Theoretical and Applied Mechanics Japan
Theoretical and Applied Mechanics Japan 56(0), 285-290, 2008
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