  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., $\beta_p \gg 1$ (hydrodynamic regime). In
contrast, when $\beta_p \lesssim 1$ (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.
