  Using classical as well as ab-initio molecular dynamics simulations, we
calculate the frequency-dependent shear viscosity of pure water and
water-glycerol mixtures. In agreement with recent experiments, we find
deviations from Newtonian-fluid behavior in the THz regime. Based on an
extension of the Maxwell model, we introduce a viscoelastic model to describe
the observed viscosity spectrum of pure water. We find four relaxation modes in
the spectrum which we attribute to i) hydrogen-bond network topology changes,
ii) hydrogen-bond stretch vibrations of water pairs, iii) collective vibrations
of water molecule triplets, and iv) librational excitations of individual water
molecules. Our model quantitatively describes the viscoelastic response of
liquid water on short timescales, where the hydrodynamic description via a
Newtonian-fluid model breaks down.
