  We present a study of the filamentary structure in the emission from the
neutral atomic hydrogen (HI) at 21 cm across velocity channels in the 40'' and
1.5-km/s resolution position-position-velocity cube resulting from the
combination of the single-dish and interferometric observations in The
HI/OH/Recombination (THOR) line survey. Using the Hessian matrix method in
combination with tools from circular statistics, we find that the majority of
the filamentary structures in the HI emission are aligned with the Galactic
plane. Part of this trend can be assigned to long filamentary structures that
are coherent across several velocity channels. However, we also find ranges of
Galactic longitude and radial velocity where the HI filamentary structures are
preferentially oriented perpendicular to the Galactic plane. These are located
(i) around the tangent point of the Scutum spiral arm, $l \approx 28^{\circ}$
and $v_{\rm LSR}\approx 100$ km/s, (ii) toward $l \approx 45^{\circ}$ and
$v_{\rm LSR}\approx 50$ km/s, (iii) around the Riegel-Crutcher cloud, and (iv)
toward the terminal velocities. Comparison with numerical simulations indicates
that the prevalence of horizontal filamentary structures is most likely the
result of the large-scale dynamics and that vertical structures identified in
(i) and (ii) may arise from the combined effect of supernova (SN) feedback and
strong magnetic fields. The vertical filamentary structures in (iv) can be
related to the presence of clouds from extra-planar HI gas falling back into
the Galactic plane after being expelled by SNe. Our results indicate that a
systematic characterization of the emission morphology toward the Galactic
plane provides an unexplored link between the observations and the dynamical
behaviour of the interstellar medium, from the effect of large-scale Galactic
dynamics to the Galactic fountains driven by SNe.
