  Context: The Milky Way's history of recent disturbances is vividly
demonstrated by a structure in the vertical phase-space distribution known as
the Gaia phase spiral. A one-armed phase spiral has been seen widely across the
Milky Way disc, while a two-armed one has only been observed in the solar
neighbourhood. Aims: This study aims to determine the properties of the
two-armed phase spiral and to put it in a Galactic context, with the ultimate
goal of understanding the structure and history of the Milky Way disc. Methods:
The Gaia DR3 data is used to trace and characterise the two-armed phase spiral.
Special focus is put on the phase spiral's spatial distribution, rotational
behaviour, and chemical characteristics. To quantify the properties of the
phase spiral we use a model that fits a spiral pattern to the phase space
distribution of the stars. Results: We find that the two-armed phase spiral is
detectable only within a narrow range of galactocentric distances and angular
momenta in the solar neighbourhood, $R = 8 \pm 0.5 $ kpc, $L_Z = 1450 \pm 50$
kpc km s$^{-1}$. Outside this region, the phase spiral is one-armed. The
two-armed phase spiral rotates with the phase angle, like the one-armed phase
spiral, and changes axis ratio with phase angle. Additionally, stars within the
phase-space overdensity caused by the two-armed phase spiral pattern have
slightly higher mean metallicity than stars in the underdense regions of the
pattern at equivalent galactocentric distances, angular momenta, and vertical
orbit extents. Conclusions: The two-armed phase spiral rotates with phase angle
and its effect can be seen in metallicity, like the one-armed phase spiral.
However, the limited range over which it can be found, and its variation in
shape are quite different from the one-armed version, suggesting it is a much
more localised phenomenon in the Galactic disc.
