  The interaction between Dark Matter and Dark Energy has been proposed as a
mechanism to alleviate the coincidence problem. We analyze the effect of the
interaction on the evolution of the gravitational field and propose two new
observables based on its effect on the matter peculiar velocity field. We find
that for different model parameters the matter peculiar velocity could be
factor 2 times larger or 5 times smaller than the amplitude of velocity
perturbations in the concordance LCDM cosmological model at the same scales. We
compare the effect on the peculiar velocities with those on the Integrated
Sachs-Wolfe effect and we show that velocities can potentially provide
constraints on the strength of the interaction stronger than those currently
available. We show that the current upper limits on the amplitude of the
kinetic Sunyaev-Zel'dovich power spectrum provide constraints on the coupling
within the dark sectors that are consistent with those obtained previously from
the CMB and galaxy clusters. In particular, we show that current upper limits
from the Atacama Cosmology Telescope and the South Pole Telescope favor Dark
Energy decaying into Dark Matter, as required to solve the coincidence problem.
