  The azimuthal anisotropy coefficients v_2 and v_4 of pi^0 and eta mesons are
measured in Au+Au collisions at sqrt(s_NN)=200 GeV, as a function of transverse
momentum p_T (1-14 GeV/c) and centrality. The extracted v_2 coefficients are
found to be consistent between the two meson species over the measured p_T
range. The ratio of v_4/v_2^2 for pi^0 mesons is found to be independent of p_T
for 1-9 GeV/c, implying a lack of sensitivity of the ratio to the change of
underlying physics with p_T. Furthermore, the ratio of v_4/v_2^2 is
systematically larger in central collisions, which may reflect the combined
effects of fluctuations in the initial collision geometry and finite viscosity
in the evolving medium.
