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Physical Review E - Statistical, Nonlinear, and Soft Matter Physics


We evaluate numerically the velocity field distributions produced by a bounded, two-dimensional fluid model consisting of a collection of parallel ideal line vortices. We sample at many spatial points inside a rigid circular boundary. We focus on “nearest-neighbor” contributions that result from vortices that fall (randomly) very close to the spatial points where the velocity is being sampled. We confirm that these events lead to a non-Gaussian high-velocity “tail” on an otherwise Gaussian distribution function for the Eulerian velocity field. We also investigate the behavior of distributions that do not have equilibrium mean-field probability distributions that are uniform inside the circle, but instead correspond to both higher and lower mean-field energies than those associated with the uniform vorticity distribution. We find substantial differences between these and the uniform case.