Experiments on forced circular shear layers performed in both magnetiz
ed plasmas and in rotating fluids reveal qualitatively similar self-or
ganization processes leading to the formation of patterns of coherent
vortical structures with varying complexity. In this paper results are
presented from both weakly nonlinear analysis and full numerical simu
lations that closely reproduce the experimental observations. Varying
the Reynolds number leads to bifurcation sequences accompanied by topo
logical changes in the distribution of the coherent structures as well
as clear transitions in the total energy and enstrophy of the system.
Various oscillating and quasiperiodic states have been found, and reg
imes have been investigated that so far have been experimentally inacc
essible.