  The origin of the Fermi bubbles, which constitute two gamma-ray emitting
lobes above and below the Galactic plane, remains unclear. The possibility that
this Fermi bubbles gamma-ray emission originates from hadronic cosmic rays
advected by a subsonic Galactic outflow, or breeze, is here explored. The
simulation of a breeze solution and subsequent cosmic ray transport is carried
out using the hydrodynamical code, PLUTO, in combination with a cosmic ray
transport code. The Galactic outflow model obtained is found to be compatible
with both inferences of the decelerating outflow velocity profile of the gas in
the Fermi bubbles region, and evidence for the presence of a large amount of
hot ionised gas out in the Galactic halo region. Although simple, this model is
found to be able to reproduce the observed Fermi-LAT energy flux at high
Galactic latitudes. Following these results a prediction concerning the
gamma-ray emission for 1-3~TeV photons is made for future comparison with
CTA/SWGO measurements.
