Primitive equations

The primitive equations describe hydrodynamical flow on the sphere under the assumptions that vertical motion is much smaller than horizontal motion (hydrostasis) and that the fluid layer depth is small compared to the radius of the sphere. Thus, they are a good approximation of global atmospheric flow and are used in most meteorological models.

The precise form of the primitive equations depends on the vertical coordinate system chosen, such as pressure coordinates, log pressure coordinates, or sigma coordinates. If pressure is selected as the vertical coordinate, the equations for the five variables on the cartesian tangential plane are

• the horizontal equations of motion

• the hydrostatic equation

• the continuity equation

• and the first law of thermodynamics