  Particle motion is considered in incompressible two-dimensional flows
consisting of a steady background gyre on which an unsteady wave-like
perturbation is superimposed. A dynamical systems point of view that exploits
the action--angle formalism is adopted. It is argued and demonstrated
numerically that for a large class of problems one expects to observe a mixed
phase space, i.e., the occurrence of ``regular islands'' in an otherwise
``chaotic sea.'' This leads to patchiness in the evolution of passive tracer
distributions. Also, it is argued and demonstrated numerically that particle
trajectory stability is largely controlled by the background flow: trajectory
instability, quantified by various measures of the ``degree of chaos,''
increases on average with increasing $|\mathrm{d}\omega/\mathrm{d}I|$, where
$\omega (I)$ is the angular frequency of the trajectory in the background flow
and $I$ is the action.
