Conservation principles for potential vorticity in a moist atmopshere

Conservation of Ertel potential vorticity (PV) is one of the central conservation laws in geophysical fluid dynamics. Due to its conserved nature, PV is used to study a wide range of weather phenomena. However, these laws only apply under idealized assumptions and it has proven challenging to extend the laws to realistic fluids. Here, the conservation laws are generalized to include fundamental features of geophysical flows such as moisture and clouds in the atmosphere. This process also enables identification of suitable analogs of Ertel PV for a moist atmopshere. We show that unlike in idealized flows, moist PV is not conserved following fluid parcels but for certain volumes that move with the flow. These PV conservation and non-conservation principles are illustrated for the first time using numerical simulations of a rising thermal by tracking the changes in PV both before and after the formation of a cloud.