  The dissipation of tidal inertial waves in planetary and stellar convective
regions is one of the key mechanisms that drive the evolution of
star-planet/planet-moon systems. In this context, the interaction between tidal
inertial waves and turbulent convective flows must be modelled in a realistic
and robust way. In the state-of-the-art simulations, the friction applied by
convection on tidal waves is modelled most of the time by an effective
eddy-viscosity. This approach may be valid when the characteristic length
scales of convective eddies are smaller than those of tidal waves. However, it
becomes highly questionable in the case where tidal waves interact with
potentially stable large-scale vortices, as those observed at the pole of
Jupiter and Saturn. They are potentially triggered by convection in
rapidly-rotating bodies in which the Coriolis acceleration forms the flow in
columnar vortical structures along the direction of the rotation axis. In this
paper, we investigate the complex interactions between a tidal inertial wave
and a columnar convective vortex. We use a quasi-geostrophic semi-analytical
model of a convective columnar vortex. We perform linear stability analysis to
identify the unstable regime and conduct linear numerical simulations for the
interactions between the convective vortex and an incoming tidal inertial wave.
We verify that in the unstable regime, an incoming tidal inertial wave triggers
the most unstable mode of the vortex leading to turbulent dissipation. For
stable vortices, the wave-vortex interaction leads to the momentum mixing while
it creates a low-velocity region around the vortex core and a new wave-like
perturbation in the form of a progressive wave radiating in the far field. The
emission of this secondary wave is the strongest when the wavelength of the
incoming wave is close to the characteristic size of the vortex.
