  Heavy-ion collisions create deformed quark-gluon plasma (QGP) fireballs which
explode anisotropically. The viscosity of the fireball matter determines its
ability to convert the initial spatial deformation into momentum anisotropies
that can be measured in the final hadron spectra. A quantitatively precise
empirical extraction of the QGP viscosity thus requires a good understanding of
the initial fireball deformation. This deformation fluctuates from event to
event, and so does the finally observed momentum anisotropy. We present a
harmonic decomposition of the initial fluctuations in shape and orientation of
the fireball and perform event-by-event ideal fluid dynamical simulations to
extract the resulting fluctuations in the magnitude and direction of the
corresponding harmonic components of the final anisotropic flow at midrapidity.
The final harmonic flow coefficients are found to depend non-linearly on the
initial harmonic eccentricity coefficients. We show that, on average, initial
density fluctuations suppress the buildup of elliptic flow relative to what one
obtains from a smooth initial profile of the same eccentricity, and discuss
implications for the phenomenological extraction of the QGP shear viscosity
from experimental elliptic flow data.
