  The main aim of this paper is to describe the dynamic transitions in flows
described by the two-dimensional, barotropic vorticity equation in a periodic
zonal channel. In \cite{CGSW03}, the existence of a Hopf bifurcation in this
model as the Reynolds number crosses a critical value was proven. In this
paper, we extend the results in \cite{CGSW03} by addressing the stability
problem of the bifurcated periodic solutions. Our main result is the explicit
expression of a non-dimensional number $\gamma$ which controls the transition
behavior. We prove that depending on $\gamma$, the modeled flow exhibits either
a continuous (Type I) or catastrophic (Type II) transition. Numerical
evaluation of $\gamma$ for a physically realistic region of parameter space
suggest that a catastrophic transition is preferred in this flow.
