Primitive equations

Summary

The primitive equations are the equations of motion used in most models of the global atmosphere and ocean. They come from the Navier–Stokes equations on a rotating planet by replacing the vertical momentum equation with hydrostatic balance. This is accurate because these fluid layers are very thin compared with their horizontal extent. They keep the horizontal momentum equations, conservation of mass, a thermodynamic equation and an equation of state. They are the starting point from which geostrophic balance and the quasi-geostrophic equations are derived.