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Abstract Potential vorticity (PV) is one of the most important quantities in atmospheric science. In the absence of dissipative processes, the PV of each fluid parcel is known to be conserved, for a dry atmosphere. However, a parcel's PV is not conserved if clouds or phase changes of water occur. Recently, PV conservation laws were derived for a cloudy atmosphere, where each parcel's PV is not conserved but parcel‐integrated PV is conserved, for integrals over certain volumes that move with the flow. Hence a variety of different statements are now possible for moist PV conservation and non‐conservation, and in comparison to the case of a dry atmosphere, the situation for moist PV is more complex. Here, in light of this complexity, several different definitions of moist PV are compared for a cloudy atmosphere. Numerical simulations are shown for a rising thermal, both before and after the formation of a cloud. These simulations include the first computational illustration of the parcel‐integrated, moist PV conservation laws. The comparisons, both theoretical and numerical, serve to clarify and highlight the different statements of conservation and non‐conservation that arise for different definitions of moist PV.
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Conservation Laws for Potential Vorticity in a Salty Ocean or Cloudy Atmosphere
Abstract One of the most important conservation laws in atmospheric and oceanic science is conservation of potential vorticity. The original derivation is approximately a century old, in the work of Rossby and Ertel, and it is related to the celebrated circulation theorems of Kelvin and Bjerknes. However, the laws apply to idealized fluids, and extensions to more realistic scenarios have been problematic. Here, these laws are extended to hold with additional fundamental complexities, including salinity in the ocean, or moisture and clouds in the atmosphere. In the absence of these additional complexities, it is known that potential vorticity is conserved following each fluid parcel; here, for a salty ocean or cloudy atmosphere, the general conserved quantity is potential vorticity integrated over certain pancake‐shaped volumes. Furthermore, the conservation laws are also related to a symmetry in the Lagrangian, which brings a connection to the symmetry‐conservation relationships seen in other areas of physics.
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- Award ID(s):
- 1907667
- PAR ID:
- 10372740
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Geophysical Research Letters
- Volume:
- 49
- Issue:
- 17
- ISSN:
- 0094-8276
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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