  The motion of one-hundred point vortices in a circular cylinder is simulated
numerically and compared with theoretical predictions based on statistical
mechanics. The novel aspect considered here is that the vortices have greatly
different circulation strengths. As envisaged by Onsager, such an arrangement
leads to a substantial amplification of statistical trends such as the
preferred clustering of the strong vortices in either same-signed or
oppositely-signed pairs, depending on the overall energy level. A
microcanonical ensemble based on the conserved total energy E and angular
momentum M for the whole vortex system is then used, in which the few strong
vortices are treated as a subsystem in contact with a reservoir composed of the
many weak vortices. It is shown that allowing for the finite size of this
reservoir is essential in order to predict the statistics of the strong
vortices accurately. Notably, this goes beyond the standard canonical ensemble
with positive or negative temperature. A certain approximation is then shown to
allow a single random sample of uniformly distributed vortex configurations to
be used to predict the strong vortex statistics for all possible values of E
and M. Detailed predictions for distribution functions are then made for
comparison with three simulated cases of near-zero M and low, neutral, or high
E. It is found that the statistical mechanics predictions compare remarkably
well with the numerical results, including a prediction of vortex accumulation
at the cylinder wall for low values of E.
