Eq.(78) is the direct analogue of the Moncrieff and Green result (eq.(69)) though the height-dependence of in the latter is an additional complication. Although this remarkable result has been obtained at the expense of assuming flow incompressibility, it has not been necessary to make an assumption about the relative size of density perturbations as in the AQB equation set. On the other hand, flows whose trajectories ascend or
descend by an appreciable fraction of the density scale height ( ) cannot justifiably considered to be governed by incompressible flow dynamics. For this reason, the Moncrieff and Green conservation principle is preferable to that of Long (1953) and Yih(1965) when considering meteorological flows.
References
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