  We study the relation between elliptic flow, $v_2$ and the initial
eccentricity, $\varepsilon_2$, in heavy-ion collisions, using hydrodynamic
simulations. Significant deviations from linear eccentricity scaling are seen
in more peripheral collisions. We identify the mechanism responsible for these
deviations as a cubic response, which we argue is a generic property of the
hydrodynamic response to the initial density profile. The cubic response
increases elliptic flow fluctuations, thereby improving agreement of initial
condition models with experimental data.
