Energy dependence and fluctuations of anisotropic flow in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}}=5.02 \) and 2.76 TeV

Measurements of anisotropic flow coefficients with two- and multi-particle cumulants for inclusive charged particles in Pb-Pb collisions at $ \sqrt{s_{\mathrm{NN}}}=5.02 $ and 2.76 TeV are reported in the pseudorapidity range |η| < 0.8 and transverse momentum 0.2 < p$_{T}$ < 50 GeV/c. The full data sample collected by the ALICE detector in 2015 (2010), corresponding to an integrated luminosity of 12.7 (2.0) μb$^{−1}$ in the centrality range 0-80%, is analysed. Flow coefficients up to the sixth flow harmonic (v$_{6}$) are reported and a detailed comparison among results at the two energies is carried out. The p$_{T}$ dependence of anisotropic flow coefficients and its evolution with respect to centrality and harmonic number n are investigated. An approximate power-law scaling of the form v$_{n}$(p$_{T}$) ∼ p$_{T}^{n}^{/3}$ is observed for all flow harmonics at low p$_{T}$ (0.2 < p$_{T}$ < 3 GeV/c). At the same time, the ratios v$_{n}$/v$_{m}^{n}^{/ }^{m}$ are observed to be essentially independent of p$_{T}$ for most centralities up to about p$_{T}$ = 10 GeV/c. Analysing the differences among higher-order cumulants of elliptic flow (v$_{2}$), which have different sensitivities to flow fluctuations, a measurement of the standardised skewness of the event-by-event v$_{2}$ distribution P(v$_{2}$) is reported and constraints on its higher moments are provided. The Elliptic Power distribution is used to parametrise P(v$_{2}$), extracting its parameters from fits to cumulants. The measurements are compared to different model predictions in order to discriminate among initial-state models and to constrain the temperature dependence of the shear viscosity to entropy-density ratio.