On the equilibrium distribution of like-signed vortices in two dimensions
We study the equilibrium statistics for a system of point vortices of different circulations in two-dimensions. We use the methods of Lundgren and Pointin  who have analyzed this problem in the past for vortices of the same strength. This necessitates the development of the probability density functions for each of the vortices. We find a power-law relationship between the probability distributions of vortices with different circulations. These distributions are verified numerically.
KeywordsProbability Density Function Point Vortex Large Vortex Small Vortex Microcanonical Ensemble
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