Primitive Equations Model
The chapter gives the foundations of modelling of large-scale atmospheric and oceanic motions and presents the ‘primitive equations’ (PE) model. After a concise reminder on general fluid mechanics, the main hypotheses leading to the PE model are explained, together with the tangent-plane (so-called f and beta plane) approximations, and ‘traditional’ approximation to the hydrodynamical equations on the rotating sphere. PE are derived in parallel for the ocean and for the atmosphere. It is then shown that, with a judicious choice of the vertical coordinate, the ‘pseudo-height’, in the atmosphere, these two sets of equations are practically equivalent. The main properties of PE are derived and the key concepts of wave–vortex dichotomy, and of slow and fast motions, are explained. The essential notion of potential vorticity is introduced and its conservation by fluid masses is demonstrated. Inertia–gravity waves are explained and their properties presented. Limitations of the hydrostatic hypothesis are demonstrated.