We analyze the structure and dynamics of the plasma atmospheres and Coulomb-liquid oceans on neutron stars. Salient dynamical parameters are identified and their values estimated for the governing set of magnetohydrodynamics equations. Neutron star atmospheres and oceans are strongly stratified and, depending on the rotation period, contain a multitude of long-lived vortices (spots) and/or narrow zonal jets (free-shear zones) in the large plasma-beta regime - i.e., (hydrodynamic regime). In contrast, when (magnetohydrodynamic regime), the flow is dominated by a global lattice of effectively fixed magnetic islands (plasmoids) - without any jets. Understanding the spatio-temporal variability of dynamic atmospheres and oceans on neutron stars is crucial for interpreting observations of their X-ray emissions.

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