  An inverse cascade - energy transfer to progressively larger scales - is a
salient feature of two-dimensional turbulence. If the cascade reaches the
system scale, it creates a coherent flow expected to have the largest available
scale and conform with the symmetries of the domain. In a doubly periodic
rectangle, the mean flow with zero total momentum was therefore believed to be
unidirectional, with two jets along the short side; while for an aspect ratio
close to unity, a vortex dipole was expected. Using direct numerical
simulations, we show that in fact neither the box symmetry is respected nor the
largest scale is realized: the flow is never purely unidirectional since the
inverse cascade produces coherent vortices, whose number and relative motion
are determined by the aspect ratio. This spontaneous symmetry breaking is
closely related to the hierarchy of averaging times. Long-time averaging
restores translational invariance due to vortex wandering along one direction,
and gives jets whose profile, however, can be deduced neither from the
largest-available-scale argument, nor from the often employed maximum-entropy
principle or quasi-linear approximation.
