  Disc stars from the Gaia DR3 RVS catalogue are selected to explore the phase
spiral as a function of position in the Galaxy. The data reveal a two-armed
phase spiral pattern in the local $z-v_z$ plane inside the solar radius, which
appears clearly when colour-coded by $\langle v_R \rangle (z,v_z)$: this is
characteristic of a breathing mode that can in principle be produced by
in-plane non-axisymmetric perturbations. We note the phase spiral pattern
becomes single armed outside the solar radius. When a realistic analytic model
with an axisymmetric background potential plus a steadily rotating bar and
2-armed spiral arms as perturbation is used to perform particle test
integrations, the pseudo stars get a prominent spiral pattern in the $\langle
v_R \rangle$ map in the $x-y$ plane. Additionally, clear breathing mode
evidence at a few $\rm{kms}^{-1}$ level can be seen in the $\langle v_z
\rangle$ map on the $x-z$ plane, confirming that such breathing modes are
non-negligible in the joint presence of a bar and spiral arms. However, no
phase-spiral is perceptible in the $(z, v_z)$ plane. When an initial vertical
perturbation is added to all pseudo stars to carry out the simulation, the
one-armed phase spirals can clearly be seen 500~Myr after the perturbation and
gradually disappear inside-out. Finally, we show as a proof of concept how a
toy model of a time-varying non-axisymmetric in-plane perturbation with varying
amplitude and pattern speed can produce a strong two-armed phase-spiral. We
conclude a time-varying strong internal perturbation together with an external
vertical perturbation could perhaps explain the transition between the
two-armed and one-armed phase-spirals around the Solar radius.
