  Models in which dark energy interacts with dark matter have been proposed in
the literature to help explain why dark energy should only come to dominate in
recent times. In this paper, we present a dynamical framework to calculate
cosmological perturbations for a general quintessence potential and interaction
term. Our formalism is built upon the powerful phase-space approach often used
to analyse the dynamical attractors in the background. We obtain a set of
coupled differential equations purely in terms of dimensionless, bounded
variables and apply these equations to calculate perturbations in a number of
scenarios. Interestingly, in the presence of dark-sector interactions, we find
that dark energy perturbations do not redshift away at late times, but can
cluster even on small scales. We also clarify the initial conditions for the
perturbations in the dark sector, showing that adiabaticity is no longer
conserved in the presence of dark-sector interactions, even on large scales.
Some issues of instability in the perturbations are also discussed.
