  Pattern formation in clouds is a well-known feature, which can be observed
almost every day. However, the guiding processes for structure formation are
mostly unknown, and also theoretical investigations of cloud patterns are quite
rare. From many scientific disciplines the occurrence of patterns in
non-equilibrium systems due to Turing instabilities is known, i.e. unstable
modes grow and form spatial structures. In this study we investigate a generic
cloud model for the possibility of Turing instabilities. For this purpose, the
model is extended by diffusion terms. We can show that for some cloud models,
i.e special cases of the generic model, no Turing instabilities are possible.
However, we also present a general class of cloud models, where Turing
instabilities can occur. A key requisite is the occurrence of (weakly)
nonlinear terms for accretion. Using numerical simulations for a special case
of the general class of cloud models, we show spatial patterns of clouds in one
and two spatial dimensions. From the numerical simulations we can see that the
competition between collision terms and sedimentation is an important issue for
the existence of pattern formation.
