On moist atmosphere Ertel potential vorticity and its flux

The Ertel potential vorticity (EPV) is formulated for a general moist atmosphere containing dry air and all sedimenting and non‐sedimenting water constituents. As a scalar in the EPV, an effective entropy potential temperature is defined. Unlike other versions, this effective entropy potential temperature is a combination of the entropy potential temperature and another adiabatic invariant, the total water content. This combination avoids introducing reference‐state entropies into the formulation. The actual EPV flux consists of an active dynamical EPV flux, a friction term, a term related to the forcing in the entropy equation, and a mixing term due to the presence of various constituents. The mixing term has not yet been documented in the meteorological literature in an easily accessible form. The entropy budget equation is discussed, including the entropy‐flux divergence term and the entropy production term. In the statistically steady state, the dynamical forcing represented by the active EPV flux is equilibrated by the remaining terms. Among them, radiation is known to establish such an equilibrium. Future research questions therefore concern the role of the moisture‐related terms in the EPV flux.