  In the present study, quantitative feasibility tests of the hydrodynamic
description of a two-dimensional fluid at the molecular level are performed,
both with respect to length and time scales. Using high-resolution fluid
velocity data obtained from extensive molecular dynamics simulations, we
computed the transverse and longitudinal components of the velocity field by
the Helmholtz decomposition and compared them with those obtained from the
linearized Navier-Stokes (LNS) equations with time-dependent transport
coefficients. By investigating the vortex dynamics and the sound wave
propagation in terms of these field components, we confirm the validity of the
LNS description for times comparable to or larger than several mean collision
times. The LNS description still reproduces the transverse velocity field
accurately at smaller times, but it fails to predict characteristic patterns of
molecular origin visible in the longitudinal velocity field. Based on these
observations, we validate the main assumptions of the mode-coupling approach.
The assumption that the velocity autocorrelation function can be expressed in
terms of the fluid velocity field and the tagged particle distribution is found
to be remarkably accurate even for times comparable to or smaller than the mean
collision time. This suggests that the hydrodynamic-mode description remains
valid down to the molecular scale.
