  We use a linear shallow-water model to investigate the global circulation of
the atmospheres of tidally locked planets. Simulations, observations, and
simple models show that if these planets are sufficiently rapidly rotating,
their atmospheres have an eastward equatorial jet and a hot-spot east of the
substellar point. We linearize the shallow-water model about this eastward flow
and its associated height perturbation. The forced solutions of this system
show that the shear flow explains the form of the global circulation,
particularly the hot-spot shift and the positions of the cold standing waves on
the night-side.
  We suggest that the eastward hot-spot shift seen in observations and 3D
simulations of these atmospheres is caused by the zonal flow Doppler-shifting
the stationary wave response eastwards, summed with the height perturbation
from the flow itself. This differs from other studies which explained the
hot-spot shift as pure advection of heat from air flowing eastward from the
substellar point, or as equatorial waves travelling eastwards. We compare our
solutions to simulations in our climate model Exo-FMS, and show that the height
fields and wind patterns match.
  We discuss how planetary properties affect the global circulation, and how
they change observables such as the hot-spot shift or day-night contrast. We
conclude that the wave-mean flow interaction between the stationary planetary
waves and the equatorial jet is a vital part of the equilibrium circulation on
tidally locked planets.
