We use the quasi-conservative system of equations for the variables and (per unit volume):

Mass conservation:

Momentum conservation:

Energy conservation:

The primitive equations in the *z*-direction (z increases downward)
for the variables, and (per unit volume)
are:

The transformation matrix between these two systems is

These equations are of the wave equation form,

where the -matrix is

Wed Sep 19 18:16:24 MET DST 2001