  We address the statistical theory of fields that are transported by a
turbulent velocity field, both in forced and in unforced (decaying)
experiments. We propose that with very few provisos on the transporting
velocity field, correlation functions of the transported field in the forced
case are dominated by statistically preserved structures. In decaying
experiments (without forcing the transported fields) we identify infinitely
many statistical constants of the motion, which are obtained by projecting the
decaying correlation functions on the statistically preserved functions. We
exemplify these ideas and provide numerical evidence using a simple model of
turbulent transport. This example is chosen for its lack of Lagrangian
structure, to stress the generality of the ideas.
