Clustering Analysis of Periodic Point Vortices with the $L$ Function

Makoto Umeki

Published 2006-08-28, updated 2007-03-01Version 4

A motion of point vortices with periodic boundary conditions is studied by using Weierstrass zeta functions. Scattering and recoupling of a vortex pair by a third vortex becomes remarkable when the vortex density is large. Clustering of vortices with various initial conditions is quantitated by the $L$ function used in point process theory in spatial ecology. It is shown that clustering persists if it is initially clustered like an infinite row or a checkered pattern.