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We present significant differences in the simulated atmospheric flow forwarm, tidally-locked small Neptunes and super Earths (based on a nominal GJ1214b) when solving the simplified, and commonly used, primitive dynamicalequations or the full Navier-Stokes equations. The dominant prograde,superrotating zonal jet is markedly different between the simulations which areperformed using practically identical numerical setups, within the same model.The differences arise due to the breakdown of the so-called `shallow-fluid' andtraditional approximations, which worsens when rotation rates are slowed, andday-night temperature contrasts are increased. The changes in the zonaladvection between simulations solving the full and simplified equations, giverise to significant differences in the atmospheric redistribution of heat,altering the position of the hottest part of the atmosphere and temperaturecontrast between the day and night sides. The implications for the atmosphericchemistry and, therefore, observations need to be studied with a modelincluding 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) ofterrestrial and gas giant planets. Our results indicate care is required wheninterpreting the output of models solving the primitive equations of motion forsuch planets.

The Limits of the Primitive Equations of Dynamics for Warm, Slowly Rotating Small Neptunes and Super Earths