A coherent-vortex analysis is made of a computational solution for the free decay of
homogeneous, Charney-isotropic geostrophic turbulence at large Reynolds number.
The method of analysis is a vortex detection and measurement algorithm that we call
a vortex census. The census demonstrates how, through non-conservative interactions
among closely approaching vortices, the vortex population evolves towards fewer,
larger, sparser, and more weakly deformed vortices. After emergence from random
initial conditions and a further period of population adjustment, there is a period of
approximately self-similar temporal evolution in the vortex statistics. This behaviour
is consistent with a mean-vortex scaling theory based on the conservation of energy,
vortex extremum, and vortex aspect ratio. This period terminates as the population
approaches a late-time non-turbulent end-state vortex configuration. The end state
develops out of merger and alignment interactions among like-sign vortices, and even
during the scaling regime, local clusters of nearly aligned vortices are common.