  We study the origin and bifurcations of typical classes of unstable periodic
orbits in a jet flow that was introduced before as a kinematic model of chaotic
advection, transport and mixing of passive scalars in meandering oceanic and
atmospheric currents. A method to detect and locate the unstable periodic
orbits and classify them by the origin and bifurcations is developed. We
consider in detail period-1 and period-4 orbits playing an important role in
chaotic advection. We introduce five classes of period-4 orbits: western and
eastern ballistic ones, whose origin is associated with ballistic resonances of
the fourth order, rotational ones, associated with rotational resonances of the
second and fourth orders, and rotational-ballistic ones associated with a
rotational-ballistic resonance. It is a new kind of nonlinear resonances that
may occur in chaotic flow with jets and/or circulation cells. Varying the
perturbation amplitude, we track out the origin and bifurcations of the orbits
for each class.
