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

## TL;DR

This study reveals that using simplified primitive equations instead of full Navier-Stokes equations significantly affects atmospheric flow simulations of warm, slowly rotating small Neptunes and super Earths, especially under certain conditions.

## Contribution

It demonstrates the limitations of primitive equations for modeling atmospheres of small, slowly rotating exoplanets, highlighting the need for more comprehensive models.

## Key findings

- Differences in atmospheric flow patterns between primitive and full Navier-Stokes simulations.
- Primitive equations become less accurate as rotation slows and temperature contrasts increase.
- Significant impact on heat redistribution and atmospheric temperature distribution.

## Abstract

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.