  High-resolution, inelastic x-ray scattering measurements of the dynamic
structure factor S(Q,\omega) of liquid water have been performed for wave
vectors Q between 4 and 30 nm^-1 in distinctly different thermodynamic
conditions (T= 263 - 420 K ; at, or close to, ambient pressure and at P = 2
kbar). In agreement with previous inelastic x-ray and neutron studies, the
presence of two inelastic contributions (one dispersing with Q and the other
almost non-dispersive) is confirmed. The study of their temperature- and
Q-dependence provides strong support for a dynamics of liquid water controlled
by the structural relaxation process. A viscoelastic analysis of the
Q-dispersing mode, associated with the longitudinal dynamics, reveals that the
sound velocity undergoes the complete transition from the adiabatic sound
velocity (c_0) (viscous limit) to the infinite frequency sound velocity
(c_\infinity) (elastic limit). On decreasing Q, as the transition regime is
approached from the elastic side, we observe a decrease of the intensity of the
second, weakly dispersing feature, which completely disappears when the viscous
regime is reached. These findings unambiguously identify the second excitation
to be a signature of the transverse dynamics with a longitudinal symmetry
component, which becomes visible in the S(Q,\omega) as soon as the purely
viscous regime is left.
