implying the existence of a mass streamfunction    defined by:

and

Following Moncrieff and Green (1972), if the variation in    during  moist adiabatic ascent (or descent) is a function of height alone then   and

Substituting this into eq.(67) and rearranging leads to a vorticity conservation law of the form:

or

where    is the upstream vorticity. This unusual and powerful conservation law has been used to good effect in the study of two-dimensional convective overturning (e.g. Moncrieff and Green, 1972; Moncrieff, 1978 and Thorpe et al, 1980). 

For a dry adiabatic process    and the integral in eq.(68) becomes trivial leading to:

If the flow sufficiently far upstream is undisturbed then:

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