  The "sloshing" of the cold gas in the cores of relaxed clusters of galaxies
is a widespread phenomenon, evidenced by the presence of spiral-shaped "cold
fronts" in X-ray observations of these systems. In simulations, these flows of
cold gas readily form by interactions of the cluster core with small
subclusters, due to a separation of the cold gas from the dark matter (DM), due
to their markedly different collisionalities. In this work, we use numerical
simulations to investigate the effects of increasing the DM collisionality on
sloshing cold fronts in a cool-core cluster. For clusters in isolation, the
formation of a flat DM core via self-interactions results in modest adiabatic
expansion and cooling of the core gas. In merger simulations, cold fronts form
in the same manner as in previous simulations, but the flattened potential in
the core region enables the gas to expand to larger radii in the initial
stages. Upon infall, the subcluster's DM mass decreases via collisions,
reducing its influence on the core. Thus, the sloshing gas moves slower,
inhibiting the growth of fluid instabilities relative to simulations where the
DM cross section is zero. This also inhibits turbulent mixing and the increase
in entropy that would otherwise result. For values of the cross section
$\sigma/m > 1$, subclusters do not survive as self-gravitating structures for
more than two core passages. Additionally, separations between the peaks in the
X-ray emissivity and thermal Sunyaev-Zeldovich effect signals during sloshing
may place constraints on DM self-interactions.
