  The dynamic evolution of the baryonic intergalactic medium (IGM) caused by
the underlying dark matter gravity is governed by the Navier-Stokes equations
in which many cooling and heating processes are involved. However, it has long
been recognized that the growth mode dynamics of cosmic matter clustering can
be sketched by a random force driven Burgers' equation if cooling and heating
are ignored. Just how well the dynamics of the IGM can be described as a
Burgers fluid has not been fully investigated probably because cooling and
heating are essential for a detailed understanding of the IGM. Using IGM
samples produced by a cosmological hydrodynamic simulation in which heating and
cooling processes are properly accounted for, we show that the IGM velocity
field in the nonlinear regime shows the features of a Burgers fluid, that is,
when the Reynolds number is high, the velocity field consists of an ensemble of
shocks. Consequently, (1) the IGM velocity $v$ is generally smaller than that
of dark matter; (2) for the smoothed field, the IGM velocity shows tight
correlation with dark matter given by $v \simeq s v_{dm}$, with $s<1$, such
that the lower the redshift, the smaller $s$; (3) the velocity PDFs are
asymmetric between acceleration and deceleration events; (4) the PDF of
velocity difference $\Delta v=v(x+r)-v(x)$ satisfies the scaling relation for a
Burgers fluid, i.e., $P(\Delta v)=(1 r^y)F(\Delta v/r^y)$. We find the scaling
function and parameters for the IGM which are applicable to the entire scale
range of the samples (0.26 - 8 h$^{-1}$ Mpc). These properties show that the
similarity mapping between the IGM and dark matter is violated on scales much
larger than the Jeans length of the IGM.
