  Two models based on the hydrostatic primitive equa- tions are proposed. The
first model is the primitive equations with partial viscosity only, and is
oriented towards large-scale wave structures in the ocean and atmosphere. The
second model is the viscous primitive equations with spectral eddy viscosity,
and is oriented towards turbulent geophysical flows. For both models, the
existence and uniqueness of global strong solutions is estab- lished. For the
second model, the convergence of the solutions to the solutions of the
classical primitive equations as eddy viscosity parameters tend to zero is also
established.
