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The second and the third order anisotropic flow, $V_{2}$ and $V_3$, aremostly determined by the corresponding initial spatial anisotropy coefficients,$\varepsilon_{2}$ and $\varepsilon_{3}$, in the initial density distribution.In addition to their dependence on the same order initial anisotropycoefficient, higher order anisotropic flow, $V_n$ ($n > 3$), can also have asignificant contribution from lower order initial anisotropy coefficients,which leads to mode-coupling effects. In this Letter we investigate the linearand non-linear modes in higher order anisotropic flow $V_n$ for $n=4$, $5$, $6$with the ALICE detector at the Large Hadron Collider. The measurements are donefor particles in the pseudorapidity range $|\eta| < 0.8$ and the transversemomentum range $0.2 < p_{\rm T} < 5.0$ GeV/$c$ as a function of collisioncentrality. The results are compared with theoretical calculations and provideimportant constraints on the initial conditions, including initial spatialgeometry and its fluctuations, as well as the ratio of the shear viscosity toentropy density of the produced system.

Linear and non-linear flow mode in Pb-Pb collisions at $\sqrt{s_{\rm NN}} =$ 2.76 TeV