  Numerical simulations of the shallow water equations on rotating spheres
produce mixtures of robust vortices and alternating zonal jets, as seen in the
atmospheres of the gas giant planets. However, simulations that include
Rayleigh friction invariably produce a sub-rotating (retrograde) equatorial jet
for Jovian parameter regimes, whilst observations of Jupiter show a
super-rotating (prograde) equatorial jet that has persisted over several
decades. Super-rotating equatorial jets have recently been obtained in shallow
water simulations that include a Newtonian relaxation of perturbations to the
layer thickness to model radiative cooling to space, and in simulations of the
thermal shallow water equations that include a similar relaxation term in their
temperature equation. Simulations of global quasigeostrophic forms of these
different models produce equatorial jets in the same directions as the parent
models, suggesting that the mechanism responsible for setting the direction
lies within quasigeostrophic theory. We provide such a mechanism by calculating
the effective force acting on the thickness-weighted zonal mean flow due to the
decay of an equatorially trapped Rossby wave. Decay due to Newtonian cooling
creates an eastward zonal mean flow at the equator, consistent with the
formation of a super-rotating equatorial jet, while decay due to Rayleigh
friction leads to a westward zonal mean flow at the equator, consistent with
the formation of a sub-rotating equatorial jet. In both cases the meridionally
integrated zonal mean of the absolute zonal momentum is westward, consistent
with the standard result that Rossby waves carry westward pseudomomentum, but
this does not preclude the zonal mean flow being eastward on and close to the
equator.
