  We study the statistics of the relative separation between two fluid
particles in a spatially smooth and temporally random flow. The Lagrangian
strain is modelled by a telegraph noise, which is a stationary random Markov
process that can only take two values with known transition probabilities. The
simplicity of the model enables us to write closed equations for the
inter-particle distance in the presence of a finite-correlated noise. In 1D, we
are able to find analytically the long-time growth rates of the distance
moments and the senior Lyapunov exponent, which consistently turns out to be
negative. We also find the exact expression for the Cram\'er function and show
that it satisfies the fluctuation relation (for the probability of positive and
negative entropy production) despite the time irreversibility of the strain
statistics. For the 2D incompressible isotropic case, we obtain the Lyapunov
exponent (positive) and the asymptotic growth rates of the moments in two
opposite limits of fast and slow strain. The quasi-deterministic limit (of slow
strain) turns out to be singular, while a perfect agreement is found with the
already-known delta-correlated case.
