Breakdown of Kolmogorov scaling in models of cluster aggregation

We describe a model of cluster aggregation with a source which provides a rare example of an analytically tractable turbulent system. The steady state is characterized by a constant mass flux from small masses to large. Thus it can be studied using a phenomenological theory, inspired by Kolmogorov's 1941 theory, which assumes constant flux and self-similarity. We prove that such self-similarity is violated in dimensions less than or equal to two. We then use dynamical renormalization group techniques to show that the scaling of multipoint correlation functions implies nontrivial multifractality. The analytical results are supported by Monte Carlo simulations.