  We present significant differences in the simulated atmospheric flow for
warm, tidally-locked small Neptunes and super Earths (based on a nominal GJ
1214b) when solving the simplified, and commonly used, primitive dynamical
equations or the full Navier-Stokes equations. The dominant prograde,
superrotating zonal jet is markedly different between the simulations which are
performed using practically identical numerical setups, within the same model.
The differences arise due to the breakdown of the so-called `shallow-fluid' and
traditional approximations, which worsens when rotation rates are slowed, and
day-night temperature contrasts are increased. The changes in the zonal
advection between simulations solving the full and simplified equations, give
rise to significant differences in the atmospheric redistribution of heat,
altering the position of the hottest part of the atmosphere and temperature
contrast between the day and night sides. The implications for the atmospheric
chemistry and, therefore, observations need to be studied with a model
including a more detailed treatment of the radiative transfer and chemistry.
Small Neptunes and super Earths are extremely abundant and important,
potentially bridging the structural properties (mass, radius, composition) of
terrestrial and gas giant planets. Our results indicate care is required when
interpreting the output of models solving the primitive equations of motion for
such planets.
