2007/06/07 by Makoto Umeki, Umeki, Makoto
Physics and Astronomy · #Data Analysis #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Statistics and Probability (physics.data-an) #physics.data-an #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.0706.0944
7 pages, 14 figures, submitted to Proceedings of NCTAM Japan, Theoretical and Applied Mechanics Japan, Vol. 56 (2007)
arxiv created 2007/06/07 · arxiv updated 2009/12/01
The motion of assemblies of point vortices in a periodic parallelogram can be described by the complex position zj(t) whose time derivative is given by the sum of the complex velocities induced by other vortices and the solid rotation centered at zj. A numerical simulation up to 100 vortices in a square periodic box is performed with various initial conditions, including single and double rows, uniform spacing, checkered pattern, and complete spatial randomness. Point process theory in spatial ecology is applied in order to quantify clustering of the distribution of vortices. In many cases, clustering of the distribution persists after a long time if the initial condition is clustered. In the case of positive and negative vortices with the same absolute value of strength, the L function becomes positive for both types of vortices. Scattering or recoupling of pairs of vortices by a third vortex is remarkable.