Correlations between the elliptic or triangular flow coefficients $v_m$ ($m=2$ or 3) and other flow harmonics $v_n$ ($n=2$ to 5) are measured using $\sqrt{s_{{}_{NN}}}=2.76$ TeV $\mathrm{Pb}+\mathrm{Pb}$ collision data collected in 2010 by the ATLAS experiment at the LHC, corresponding to an integrated luminosity of $7 \mu {\mathrm{b}}^{-1}$. The $v_m\text{−}{v}_n$ correlations are measured in midrapidity as a function of centrality, and, for events within the same centrality interval, as a function of event ellipticity or triangularity defined in a forward rapidity region. For events within the same centrality interval, $v_3$ is found to be anticorrelated with $v_2$ and this anticorrelation is consistent with similar anticorrelations between the corresponding eccentricities, ${\epsilon }_2$ and ${\epsilon }_3$. However, it is observed that $v_4$ increases strongly with $v_2$, and $v_5$ increases strongly with both $v_2$ and $v_3$. The trend and strength of the $v_m\text{−}{v}_n$ correlations for $n=4$ and 5 are found to disagree with ${\epsilon }_m\text{−}{\epsilon }_n$ correlations predicted by initial-geometry models. Instead, these correlations are found to be consistent with the combined effects of a linear contribution to $v_n$ and a nonlinear term that is a function of $v_2^2$ or of $v_2{v}_3$, as predicted by hydrodynamic models. A simple two-component fit is used to separate these two contributions. The extracted linear and nonlinear contributions to $v_4$ and $v_5$ are found to be consistent with previously measured event-plane correlations.

• Received 8 April 2015

DOI:https://doi.org/10.1103/PhysRevC.92.034903

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©2015 CERN, for the ATLAS Collaboration