Recent LHC results on the appearance of sub-leading flow modes in PbPb collisions at 2.76~TeV, related to initial-state fluctuations, are analyzed and interpreted within the HYDJET++ model. Using the newly introduced Principal Component Analysis (PCA) method applied to two-particle azimuthal correlations extracted from the model calculations, the leading and the sub-leading flow modes are studied as a function of the transverse momentum ($p_{T}$) over a wide centrality range. The leading modes of the elliptic ($v^{(1)}_{2}$) and triangular ($v^{(1)}_{3}$) flow calculated within the HYDJET++ model reproduce rather well the $v_{2}{2}$ and $v_{3}{2}$ coefficients experimentally measured using the two-particle correlations. Within the $p_{T} le $~3~GeV/c range where hydrodynamics dominates, the sub-leading flow effects are greatest at the highest $p_{T}$ of around 3~GeV/c. The sub-leading elliptic flow mode ($v^{(2)}_{2}$), which corresponds to $n = 2$ harmonic, has a small non-zero value and slowly increases from central to peripheral collisions, while the sub-leading triangular flow mode ($v^{(2)}_{3}$), which corresponds to $n = 3$ harmonic, is even smaller and does not depend on centrality. For $n = $~2, the relative magnitude of the effect measured with respect to the leading flow mode shows a shallow minimum for semi-central collisions and increases for very central and for peripheral collisions. For $n = $~3 case, there is no centrality dependence. The sub-leading flow mode results obtained from the HYDJET++ model are in a rather good agreement with the experimental measurements of the CMS Collaboration.
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