  Using complementary numerical approaches at high resolution, we study the
late-time behaviour of an inviscid, incompressible two-dimensional flow on the
surface of a sphere. Starting from a random initial vorticity field comprised
of a small set of intermediate wavenumber spherical harmonics, we find that --
contrary to the predictions of equilibrium statistical mechanics -- the flow
does not evolve into a large-scale steady state. Instead, significant
unsteadiness persists, characterised by a population of persistent small-scale
vortices interacting with a large-scale oscillating quadrupolar vorticity
field. Moreover, the vorticity develops a stepped, staircase distribution,
consisting of nearly homogeneous regions separated by sharp gradients. The
persistence of unsteadiness is explained by a simple point vortex model
characterising the interactions between the four main vortices which emerge.
