Some simplification is afforded by the transformation
where is a constant reference density. Conservation of along the streamlines implies that:
or
and the momentum equation (74) may then be written as:
It is easy to show that the transformed wind is also non-divergent and this suggests the introduction of a modified streamfunction defined by:
Now using eq.(62) to re-express the advective term in eq.(72) gives:
and if is some arbitrary displacement vector with the property that: