  We perform a systematic study on the decorrelation of anisotropic flows along
the pseudorapidity in relativistic heavy-ion collisions at the LHC and RHIC
energies. The dynamical evolution of the QGP fireball is simulated via the
CLVisc (ideal) (3+1)-dimensional hydrodynamics model, with the fully
fluctuating initial condition from A-Multi-Phase-Transport (AMPT) model.
Detailed analysis is performed on the longitudinal decorrelations of elliptic,
triangular and quadrangular flows in terms of flow vectors, flow magnitudes and
flow orientations (event planes). It is found that pure flow magnitudes have
smaller longitudinal decorrelation than pure flow orientations, and the
decorrelation of flow vectors is a combined effect of both flow magnitudes and
orientations. The longitudinal decorrelation of elliptic flow has a strong and
non-monotonic centrality dependence due to the initial elliptic collision
geometry: smallest decorrelation in mid-central collisions. In contrast, the
decorrelations of triangular and quadrangular flows have weak centrality
dependence, slightly larger decorrelations in more peripheral collisions. Our
numerical results for Pb+Pb collisions at the LHC are in good agreement with
the ATLAS data, while our RHIC results predict much larger longitudinal
decorrelations as compared to the LHC. We further analyze the longitudinal
structures of the AMPT initial conditions and find that the final-state
longitudinal decorrelation effects are strongly correlated with the lengths of
the initial string structures in the AMPT model. The decorrelation effects are
typically larger at lower collision energies and in more peripheral collisions
due to shorter lengths of the string structures in the initial states.
