  The {\rm HI} 21-cm intensity mapping signal experiences redshift space
distortions due to the motion of the galaxies which contain the {\rm HI} as
well as the motions of the {\rm HI} gas within the galaxies. A detailed
modelling is essential if this signal is to be used for precision cosmology.
Considering dark matter only simulations where the {\rm HI} is assumed to
reside in galaxies which are associated with haloes, in this work we introduce
a technique to incorporate the {\rm HI} motions within the galaxies. This is
achieved through a line profile which accounts for both the rotational and
random (thermal and turbulent) motions of the {\rm HI} within galaxies. The
functional form of the double horned line profiles used here is motivated by
observations of $z=0$ spiral galaxies. Analyzing the simulated 21-cm power
spectrum over the redshift range $1 \le z \le 6$ we find that the {\rm HI}
motions within galaxies makes a significant contribution that is manifested as
an enhancement in the Finger of God (FoG) effect which can be modelled
reasonably well through a Lorentzian damping profile with a single free
parameter $\sigma_p$. The value of $\sigma_p$ is significantly enhanced if
motions within the galaxies are included. This is particularly important at
$z>3$ where $\sigma_p$ is dominated by the internal motions and a measurement
of the FoG effect here could provide a handle on the line profiles of high
redshift galaxies.
