NonGaussian probability distributions for a vortex fluid
Abstract
A system of N twodimensional vortices interacting in a bounded region can be described by the statistics of the coordinates of the vortices or by the statistics of the Fourier coefficients of the vorticity field. It is shown that both descriptions give equivalent results. A high energy expression for the probability distribution function of the Fourier coefficients is derived and shown to be nonGaussian; it has at least two, and in some cases a continuum of, equal height maximum points corresponding to distinct, but equally probable, equilibrium states. Other stationary points previously thought to be metastable states are shown to be saddle points of the distribution function and hence unstable.
 Publication:

Physics of Fluids
 Pub Date:
 March 1977
 DOI:
 10.1063/1.861874
 Bibcode:
 1977PhFl...20..356L
 Keywords:

 Probability Distribution Functions;
 Turbulent Flow;
 Two Dimensional Flow;
 Vortices;
 Fourier Series;
 Green'S Functions;
 Harmonic Functions;
 Partial Differential Equations;
 Probability Density Functions;
 Thermodynamics and Statistical Physics