  We use (3+1)-dimensional hydrodynamics with exact longitudinal
boost-invariance to study the influence of collision centrality and initial
energy density on the transverse flow pattern and the angular distributions of
particles emitted near midrapidity in ultrarelativistic heavy-ion collisions.
We concentrate on radial flow and the elliptic flow coefficient v2 as functions
of the impact parameter and of the collision energy. We demonstrate that the
finally observed elliptic flow is established earlier in the collision than the
observed radial flow and thus probes the equation of state at higher energy
densities. We point out that a phase transition from hadronic matter to a
color-deconfined quark-gluon plasma leads to non-monotonic behaviour in both
beam energy and impact parameter dependences which, if observed, can be used to
identify such a phase transition. Our calculations span collision energies from
the Brookhaven AGS (Alternating Gradient Synchrotron) to beyond the LHC (Large
Hadron Collider); the QGP phase transition signature is predicted between the
lowest available SPS (CERN Super Proton Synchrotron) and the highest RHIC
(Brookhaven Relativistic Heavy Ion Collider) energies. To optimize the chances
for applicability of hydrodynamics we suggest to study the excitation function
of flow anisotropies in central uranium-uranium collisions in the side-on-side
collision geometry.
