Moist AQB Equations
The discussion of the AQB equations so far has assumed the working gas to be dry air. As shown in Section 1, the effect of water vapour on the density of air can be accounted for in the perfect gas equation by
introducing the concept of virtual temperature . If one defines the virtual potential temperature according to:
then eq.(7) holds with (note that is no longer dry entropy under this definition). The same steps in the derivation of the vector momentum equation apply except now the buoyancy is given by:
where
and the reference state has been assumed to have no water vapour content. For unsaturated flows, the water vapour mixing ratio (and therefore ) is conserved following the motion and so eq.(12) still holds. For saturated air we shall use the simplified thermodynamic equation eq.(15) which, in the absence of diabatic processes, may be written as:
For non-precipitating, saturated adiabatic motion one might choose to use the conservation of equivalent potential temperature as defined in Section 1. A common approach is to linearize the exponential form of
eq.(18) of the thermodynamics section) giving:
where the small difference between and has been ignored. Betts (1973) proposed another useful quasi-conservative quantity -- the liquid water potential temperature .