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Higher harmonics of anisotropic flow ($v_n$ with $n\ge 4$) in heavy-ioncollisions can be measured either with respect to their own plane, or withrespect to a plane constructed using lower-order harmonics. We explain how suchmeasurements are related to event-plane correlations. We show that CMS data on$v_4$ and $v_6$ are compatible with ATLAS data on event-plane correlations. Ifone assumes that higher harmonics are the superposition of non-linear andlinear responses, then the linear and non-linear parts can be isolated underfairly general assumptions. By combining analyses of higher harmonics withanalyses of $v_2$ and $v_3$, one can eliminate the uncertainty from initialconditions and define quantities that only involve nonlinear hydrodynamicresponse coefficients. Experimental data on $v_4$, $v_5$ and $v_6$ are in goodagreement with hydrodynamic calculations. We argue that $v_7$ can be measuredwith respect to elliptic and triangular flow. We present predictions for $v_7$versus centrality in Pb-Pb collisions at the LHC.

$v_4$, $v_5$, $v_6$, $v_7$: nonlinear hydrodynamic response versus LHC data