This situtation is analogous to that produced by stirring by baroclinic instability in the atmosphere, which produces an eddy-driven near barotropic mid-latitude jet. This jet is to be contrasted with the baroclinic sub-tropical jet, which is in thermal wind balance with the strong meridional temperature gradient at the edge of the Hadley Cell. Click below to get an MPEG movie of a barotropic jet on a beta-plane. (Your browser may play it automatically, or you may have to download it to your computer, and then play it with an MPEG movie player, available on most computers.)
The forcing for the jet is simply random forcing in the middle of the domain:
there is no preferred direction to the forcing. The initial conditions
are of no motion. After a while the motion develops a preferred direction,
eventually producing a fairly sharp jet in the middle of the domain.
Movie of zonal velocity