A generalization of Ertel's potential vorticity to a cloudy, precipitating atmosphere
This paper discusses the generalization of Ertel's PV to a cloudy, precipitating atmosphere. The recommended generalization is P = ρ-1ζ ˙ ∇θρ, where ρ is the total density of moist air, ζ is the absolute vorticity, and θρ is the virtual potential temperature. Associated with this form are three...
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| Format: | Article |
| Language: | English |
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Borntraeger
2004-12-01
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| Series: | Meteorologische Zeitschrift |
| Online Access: | http://dx.doi.org/10.1127/0941-2948/2004/0013-0465 |
| _version_ | 1797320710930038784 |
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| author | Wayne Schubert |
| author_facet | Wayne Schubert |
| author_sort | Wayne Schubert |
| collection | DOAJ |
| description | This paper discusses the generalization of Ertel's PV to a cloudy, precipitating atmosphere. The recommended generalization is P = ρ-1ζ ˙ ∇θρ, where ρ is the total density of moist air, ζ is the absolute vorticity, and θρ is the virtual potential temperature. Associated with this form are three important properties: (1) the solenoidal term is annihilated (i.e., ∇θρ˙ (∇ρ × ∇p) = 0, where p is the total pressure, the sum of the partial pressures of dry air and water vapor); (2) the limiting form for a dry atmosphere is the classical Ertel PV; (3) P is invertible, i.e., it carries all the necessary dynamical information about the balanced wind and mass fields. Two other possible generalizations are discussed,ρ-1ζ ˙∇θe and ρ-1ζ ˙∇θ*e, where θe is the equivalent potential temperature and θ*e is the saturation equivalent potential temperature. The former is rejected because properties (1) and (3) are lost, while the latter is rejected because property (2) is lost. |
| first_indexed | 2024-03-08T04:46:55Z |
| format | Article |
| id | doaj.art-8ba61548536247f5ba384142e80086fc |
| institution | Directory Open Access Journal |
| issn | 0941-2948 |
| language | English |
| last_indexed | 2024-03-08T04:46:55Z |
| publishDate | 2004-12-01 |
| publisher | Borntraeger |
| record_format | Article |
| series | Meteorologische Zeitschrift |
| spelling | doaj.art-8ba61548536247f5ba384142e80086fc2024-02-08T08:44:37ZengBorntraegerMeteorologische Zeitschrift0941-29482004-12-0113646547110.1127/0941-2948/2004/0013-046553382A generalization of Ertel's potential vorticity to a cloudy, precipitating atmosphereWayne SchubertThis paper discusses the generalization of Ertel's PV to a cloudy, precipitating atmosphere. The recommended generalization is P = ρ-1ζ ˙ ∇θρ, where ρ is the total density of moist air, ζ is the absolute vorticity, and θρ is the virtual potential temperature. Associated with this form are three important properties: (1) the solenoidal term is annihilated (i.e., ∇θρ˙ (∇ρ × ∇p) = 0, where p is the total pressure, the sum of the partial pressures of dry air and water vapor); (2) the limiting form for a dry atmosphere is the classical Ertel PV; (3) P is invertible, i.e., it carries all the necessary dynamical information about the balanced wind and mass fields. Two other possible generalizations are discussed,ρ-1ζ ˙∇θe and ρ-1ζ ˙∇θ*e, where θe is the equivalent potential temperature and θ*e is the saturation equivalent potential temperature. The former is rejected because properties (1) and (3) are lost, while the latter is rejected because property (2) is lost.http://dx.doi.org/10.1127/0941-2948/2004/0013-0465 |
| spellingShingle | Wayne Schubert A generalization of Ertel's potential vorticity to a cloudy, precipitating atmosphere Meteorologische Zeitschrift |
| title | A generalization of Ertel's potential vorticity to a cloudy, precipitating atmosphere |
| title_full | A generalization of Ertel's potential vorticity to a cloudy, precipitating atmosphere |
| title_fullStr | A generalization of Ertel's potential vorticity to a cloudy, precipitating atmosphere |
| title_full_unstemmed | A generalization of Ertel's potential vorticity to a cloudy, precipitating atmosphere |
| title_short | A generalization of Ertel's potential vorticity to a cloudy, precipitating atmosphere |
| title_sort | generalization of ertel s potential vorticity to a cloudy precipitating atmosphere |
| url | http://dx.doi.org/10.1127/0941-2948/2004/0013-0465 |
| work_keys_str_mv | AT wayneschubert ageneralizationofertelspotentialvorticitytoacloudyprecipitatingatmosphere AT wayneschubert generalizationofertelspotentialvorticitytoacloudyprecipitatingatmosphere |