  Determining the habitability and interpreting future atmospheric observations
of exoplanets requires understanding the atmospheric dynamics and chemistry
from a 3-D perspective. Previous studies have shown significant spatial
variability in the ozone layer of synchronously rotating M-dwarf planets,
assuming an Earth-like initial atmospheric composition. We use a 3-D Coupled
Climate-Chemistry model to understand this distribution of ozone and identify
the mechanism responsible for it. We document a previously unreported
connection between the ozone production regions on the photochemically active
dayside hemisphere and the nightside devoid of stellar radiation and thus
photochemistry. We find that stratospheric dayside-to-nightside overturning
circulation can advect ozone-rich air to the nightside. On the nightside,
ozone-rich air subsides at the locations of two quasi-stationary Rossby gyres,
resulting in an exchange between the stratosphere and troposphere and the
accumulation of ozone at the gyre locations. We identify the hemispheric
contrast in radiative heating and cooling as the main driver of this ozone
circulation. Dynamically-driven chemistry also impacts other tracer species in
the atmosphere (gaseous and non-gaseous phase) as long as chemical lifetimes
exceed dynamical lifetimes. These findings illustrate the 3-D nature of
planetary atmospheres, predicting spatial and temporal variability that will
impact spectroscopic observations of exoplanet atmospheres.
