  We present a model for the Lagrangian dynamics of inertial particles in a
compressible flow, where fluid velocity gradients are modelled by a telegraph
noise. The model allows for an analytic investigation of the role of time
correlation of the flow in the aggregation-disorder transition of inertial
particle. The dependence on Stokes and Kubo numbers of the Lyapunov exponent of
particle trajectories reveals the presence of a region in parameter space (St,
Ku) where the leading Lyapunov exponent changes sign, thus signaling the
transition. The asymptotics of short and long-correlated flows are discussed,
as well as the fluid-tracer limit.
