Mode-by-mode hydrodynamics: Ideas and concepts

The main ideas, technical concepts and perspectives for a mode resolved description of the hydrodynamical regime of relativistic heavy ion collisions are discussed. A background-fluctuation splitting and a Bessel–Fourier expansion for the fluctuating part of the hydrodynamical fields allows for a complete characterization of initial conditions, 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 probability distributions.