  The fourth harmonic of the azimuthal distribution of particles $v_4$ has been
measured for Au-Au collisions at the Relativistic Heavy Ion Collider (RHIC).
The centrality dependence of $v_4$ does not agree with the prediction from
hydrodynamics. In particular, the ratio $v_4/(v_2)^2$, where $v_2$ denotes the
second harmonic of the azimuthal distribution of particles, is significantly
larger than predicted by hydrodynamics. We argue that this discrepancy is
mostly due to elliptic flow ($v_2$) fluctuations. We evaluate these
fluctuations on the basis of a Monte Carlo Glauber calculation. The effect of
deviations from local thermal equilibrium is also studied, but appears to be
only a small correction. Combining these two effects allows us to reproduce
experimental data for peripheral and midcentral collisions. However, we are
unable to explain the large magnitude of $v_4/(v_2)^2$ observed for the most
central collisions.
