  In a two-dimensional (2D) turbulent fluid containing point-like vortices,
Lars Onsager predicted that adding energy to the fluid can lead to the
formation of persistent clusters of like-signed vortices, i.e., Onsager vortex
(OV) clusters. In the evolution of 2D superfluid turbulence in a uniform
disk-shaped Bose-Einstein condensate (BEC), it was discovered that a pair of OV
clusters with opposite signs can form without any energy input. This striking
spontaneous order was explained as due to a vortex evaporative-heating
mechanism, i.e., annihilations of vortex-antivortex pairs which remove the
lowest-energy vortices and thereby boost the mean energy per vortex. However,
in our search for exotic OV states in a boundaryless 2D spherical BEC, we found
that OV clusters never form despite the annihilations of vortex pairs. Our
analysis reveals that contrary to the general belief, vortex-pair annihilation
emits intense sound waves, which damp the motion of all vortices and hence
suppress the formation of OV clusters. We also present unequivocal evidences
showing that the true mechanism underlying the observed spontaneous OV state is
the escaping of vortices from the BEC boundary. Uncovering this mechanism paves
the way for a comprehensive understanding of emergent vortex orders in 2D
manifolds of superfluids driven far from equilibrium.
