  Inhomogeneities in the velocity field of a moving fluid are dampened by the
inherent viscous behaviour of the system. Both bulk and shear effects, related
to the divergence and the curl of the velocity field, are relevant. On
molecular time scales, beyond the Navier-Stokes description, memory plays an
important role. We demonstrate here on the basis of molecular and overdamped
Brownian dynamics many-body simulations that analogous viscous effects act on
the acceleration field. This acceleration viscous behaviour is associated with
the divergence and the curl of the acceleration field and it can be
quantitatively described using simple exponentially decaying memory kernels.
The simultaneous use of velocity and acceleration fields enables the
description of fast dynamics on molecular scales.
