Abstract
Motions of 1000 point vortices in an infinite fluid region without a solid boundary are computed numerically on the basis of the Biot-Savart law. Three cases for their circulations and initial distributions are treated, one with the same circulations and within a circular domain, one with the same circulations and within a square domain, and one with 500 vortices of positive and 500 vortices of negative circulations within a square domain. The initial distributions are determined by the use of the uniform random numbers. The Runge-Kutta-Gill method is used, because the small scale behavior is the main interest in this work and an accuracy is needed. At each time step of computation the conserved quantities (such as the Hamiltonian), the configuration temperature introduced by Nobikov, the fractal dimension of the point distribution and the enstrophy defined properly are calculated. Computation is made up to 20 time steps. The quantities, which should be conserved, proved to be conserved actually during the computation. The fractal dimension showed a tendency to decrease from 2 to a value near 1. 7. In the third case the configuration temperature continued to increase. The present work shows that the fractal dimension and the configuration temperature, which are geometrical parameters, are affected by the dynamics of the vortex motion.
