  We use direct numerical simulations and scaling arguments to study coarsening
in binary fluid mixtures with a conserved order parameter in the
droplet-spinodal regime -- the volume fraction of the droplets is neither too
small nor symmetric -- for small diffusivity and viscosity. Coagulation of
droplets drives a turbulent flow that eventually decays. We uncover a novel
coarsening mechanism, driven by turbulence where the characteristic length
scale of the flow is different from the characteristic length scale of
droplets, giving rise to a domain growth law of $t^{1/2}$, where $t$ is time.
At intermediate times, both the flow and the droplets form self-similar
structures: the structure factor $S(q) \sim q^{-2}$ and the kinetic energy
spectra $E(q) \sim q^{-5/3}$ for an intermediate range of $q$, the wavenumber.
