  Using a three-dimensional general circulation model, we show that the
atmospheric dynamics on a tidally locked Earth-like exoplanet, simulated with
the planetary and orbital parameters of Proxima Centauri b, support a
longitudinally asymmetric stratospheric wind oscillation (LASO), analogous to
Earth's quasi-biennial oscillation (QBO). In our simulations, the LASO has a
vertical extent of 35--55 km, a period of 5--6.5 months, and a peak-to-peak
wind speed amplitude of -70 to +130 m/s with a maximum at an altitude of 41 km.
Unlike the QBO, the LASO displays longitudinal asymmetries related to the
asymmetric thermal forcing of the planet and to interactions with the resulting
stationary Rossby waves. The equatorial gravity wave sources driving the LASO
are localised in the deep convection region at the substellar point and in a
jet exit region near the western terminator, unlike the QBO, for which these
sources are distributed uniformly around the planet. Longitudinally, the
western terminator experiences the highest wind speeds and undergoes reversals
earlier than other longitudes. The antistellar point only experiences a weak
oscillation with a very brief, low-speed westward phase. The QBO on Earth is
associated with fluctuations in the abundances of water vapour and trace gases
such as ozone which are also likely to occur on exoplanets if these gases are
present. Strong fluctuations in temperature and the abundances of atmospheric
species at the terminators will need to be considered when interpreting
atmospheric observations of tidally locked exoplanets.
