  Initial fluctuations in hydrodynamic fields such as energy density or flow
velocity give access to understanding initial state and equilibration physics
as well as thermodynamic and transport properties. We provide evidence that the
fluid dynamic propagation of fluctuations of realistic size can be based on a
background-fluctuation splitting and a systematic perturbative expansion in the
fluctuating fields. Initial conditions are characterized by a Bessel-Fourier
expansion for single events, event-by-event correlations and probability
distributions. The evolution equations can be solved order-by-order in the
expansion which allows to study the fluid dynamical propagation of single
modes, the study of interaction effects between modes, the determination of the
associated particle spectra and the generalization of the whole program to
event-by-event correlations and distributions.
