  Event-by-event fluctuations in the initial conditions for a hydrodynamical
description of heavy-ion collisions are characterized. We propose a
Bessel-Fourier decomposition with respect to the azimuthal angle, the radius in
the transverse plane and rapidity. This allows for a complete characterization
of fluctuations in all hydrodynamical fields including energy density,
pressure, fluid velocity, shear stress and bulk viscous pressure. It has the
advantage that fluctuations can be ordered with respect to their wave length
and that they can be propagated mode-by-mode within the hydrodynamical
formalism. Event ensembles can then be characterized in terms of a functional
probability distribution. For the event ensemble of a Monte Carlo Glauber
model, we provide evidence that the latter is close to Gaussian form, thus
allowing for a particularly simple characterization of the event distribution.
