  Prestellar cores are generally spheroidal, some of which appear oblate while
others appear prolate. Very few of them appear circular in projection. Little,
however, is understood about the processes or the physical conditions under
which prolate/oblate cores form. We find that an initially sub-critical
filament experiencing relatively low pressure ($\lesssim 10^{4}$ K cm$^{-3}$)
forms prolate cores (i.e., those with axial ratios in excess of unity) via
gradual accumulation of gas in density crests. Meanwhile, a filament that is
initially transcritical and experiences pressure similar to that in the Solar
neighbourhood (between $\mathrm{few}\ \times 10^{4}$ K cm$^{-3}$ -
$\mathrm{few}\ \times 10^{5}$ K cm$^{-3}$) forms oblate cores (i.e., those with
axial ratios less than unity) via \emph{Jeans like} fragmentation. At higher
pressure, however, fragments within the filament do not tend to survive as they
rebound soon after formation. We also argue that quasi-oscillatory features of
velocity gradient observed along the filament axis, and in the direction
orthogonal to the axis, are integral to the filament evolution process and
arise due to the growth of corrugations on its surface. The axial component of
the velocity gradient, in particular, traces the gas-flow along the filament
length. We therefore posit that it could be used to constrain the
filament-formation mechanism. The magnitude of the respective components of
velocity gradients increases with increasing external pressure.
