  Glass formers exhibit a viscoelastic behavior: at the laboratory timescale,
they behave like (glassy) solids at low temperatures, and like liquids at high
temperatures. Based on this observation, elastic models relate the long time
supercooled dynamics to short time elastic properties of the supercooled
liquid. In the present work, we assess the validity of elastic models for the
shear viscosity and the $\alpha$-relaxation time of supercooled water, using
molecular dynamics simulations with the TIP4P/2005f force field over a wide
range of temperatures. We show that elastic models provide a good description
of supercooled water dynamics. For the viscosity, two different regimes are
observed and the crossover temperature is found to be close to the one where
the Stokes-Einstein relation starts to be violated. Our simulations show that
only shear properties are important to characterize the effective flow
activation energy. This study calls for experimental determination of the high
frequency elastic properties of water at low temperatures.
