A Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE).XI.
  Two dimensional H$\alpha$ kinematics of the edge-on ram pressure stripped
  galaxy NGC 4330
  Using the VESTIGE survey, a deep narrow-band H$\alpha$ imaging survey of the
Virgo cluster carried on at the CFHT with MegaCam, we discovered a long diffuse
tail of ionised gas in the edge-on late-type galaxy NGC 4330. This peculiar
feature witnesses an ongoing ram pressure stripping (RPS) event able to remove
the gas in the outer disc region. Tuned hydrodynamic simulations suggest that
the RPS event is occurring almost face-on, making NGC 4330 the ideal candidate
to study the effects of the perturbation in the direction perpendicular to the
disc plane. We present here two new independent sets of Fabry-Perot
observations (R$\simeq$10000) in order to understand the effects of the RPS
process on the ionised gas kinematics. Despite their limited sensitivity to the
diffuse gas emission, the data allowed us to measure the velocity and the
velocity dispersion fields over the galaxy disc and in several features at the
edges or outside the stellar disc formed after the RPS event. We have
constructed the position-velocity diagrams and the rotation curves of the
galaxy using three different techniques. The data show, consistent with the
hydrodynamic simulations, that the galaxy has an inner solid-body rotation up
to $\sim$2.4 kpc, with non-circular streaming motions outwards the disc and in
the several external features formed during the interaction of the galaxy with
the surrounding intracluster medium. The data also indicate a decrease of the
rotational velocity of the gas with increasing distance from the galaxy disc
along the tails, suggesting a gradual but not linear loss of angular momentum
in the stripped gas. Consistent with a RPS scenario, the $i$-band image shows a
boxy shape at the southwest edge of the disc, where the stellar orbits might
have been perturbed by the modification of the gravitational potential well of
the galaxy due to the displacement of the gas in the $z$-direction.
