Non-conservation and conservation for different formulations of moist potential vorticity

Kooloth, Parvathi; Smith, Leslie M.; Stechmann, Samuel N.

doi:10.1002/asl.1237

Title: Non-conservation and conservation for different formulations of moist potential vorticity

Journal Article · 11 April 2024 · Atmospheric Science Letters

DOI: https://doi.org/10.1002/asl.1237 · OSTI ID:2440200

Kooloth, Parvathi ^[1]; Smith, Leslie M. ^[2]; Stechmann, Samuel N. ^[2]

Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Univ. of Wisconsin, Madison, WI (United States)

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 2440200

Report Number(s):: PNNL-SA--192366

Journal Information:: Atmospheric Science Letters, Journal Name: Atmospheric Science Letters Journal Issue: 8 Vol. 25; ISSN 1530-261X

Publisher:: Royal Meteorological SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (47)

Between land and sea: Relational environments in Makili, Atauro Island, East Timor Abbott, Helen The Australian National University https://doi.org/10.25911/83pm-mv16	other	January 2024
Euler solutions using flux-based wave decomposition Ahmad, Nash'at; Lindeman, John International Journal for Numerical Methods in Fluids, Vol. 54, Issue 1 https://doi.org/10.1002/fld.1392	journal	January 2007
On the definition of a moist‐air potential vorticity Marquet, Pascal Quarterly Journal of the Royal Meteorological Society, Vol. 140, Issue 680 https://doi.org/10.1002/qj.2182	journal	July 2013
Non-precipitating cumulus convection and its parameterization Betts, A. K. Quarterly Journal of the Royal Meteorological Society, Vol. 99, Issue 419 https://doi.org/10.1002/qj.49709941915	journal	January 1973
Conditional symmetric instability - a possible explanation for frontal rainbands Bennetts, D. A.; Hoskins, B. J. Quarterly Journal of the Royal Meteorological Society, Vol. 105, Issue 446 https://doi.org/10.1002/qj.49710544615	journal	October 1979
On the use and significance of isentropic potential vorticity maps Hoskins, B. J.; McIntyre, M. E.; Robertson, A. W. Quarterly Journal of the Royal Meteorological Society, Vol. 111, Issue 470 https://doi.org/10.1002/qj.49711147002	journal	October 1985
Definition of a moist entropy potential temperature: application to FIRE-I data flights: Moist Entropy Potential Temperature Marquet, Pascal Quarterly Journal of the Royal Meteorological Society, Vol. 137, Issue 656 https://doi.org/10.1002/qj.787	journal	March 2011
Fast-Wave Averaging with Phase Changes: Asymptotics and Application to Moist Atmospheric Dynamics Zhang, Yeyu; Smith, Leslie M.; Stechmann, Samuel N. Journal of Nonlinear Science, Vol. 31, Issue 2 https://doi.org/10.1007/s00332-021-09697-2	journal	March 2021
Balanced and Unbalanced Components of Moist Atmospheric Flows with Phase Changes Wetzel, Alfredo N.; Smith, Leslie M.; Stechmann, Samuel N. Chinese Annals of Mathematics, Series B, Vol. 40, Issue 6 https://doi.org/10.1007/s11401-019-0170-4	journal	November 2019
Multiscale eddy simulation for moist atmospheric convection: Preliminary investigation Stechmann, Samuel N. Journal of Computational Physics, Vol. 271 https://doi.org/10.1016/j.jcp.2014.02.009	journal	August 2014
4. On Vortex Atoms Thomson, William Proceedings of the Royal Society of Edinburgh, Vol. 6 https://doi.org/10.1017/S0370164600045430	journal	January 1869
Minimal models for precipitating turbulent convection Hernandez-Duenas, Gerardo; Majda, Andrew J.; Smith, Leslie M. Journal of Fluid Mechanics, Vol. 717 https://doi.org/10.1017/jfm.2012.597	journal	February 2013
Effects of clouds and phase changes on fast-wave averaging: a numerical assessment Zhang, Yeyu; Smith, Leslie M.; Stechmann, Samuel N. Journal of Fluid Mechanics, Vol. 920 https://doi.org/10.1017/jfm.2021.427	journal	June 2021
Generation of generalized moist potential vorticity in a frictionless and moist adiabatic flow Gao, Shouting; Wang, Xingrong; Zhou, Yushu Geophysical Research Letters, Vol. 31, Issue 12 https://doi.org/10.1029/2003GL019152	journal	June 2004
Ertel's potential vorticity theorem in physical oceanography Müller, Peter Reviews of Geophysics, Vol. 33, Issue 1 https://doi.org/10.1029/94RG03215	journal	February 1995
Dynamics of the oceanic general circulation: the potential vorticity field Holland, W. R.; Keffer, T.; Rhines, P. B. Nature, Vol. 308, Issue 5961 https://doi.org/10.1038/308698a0	journal	April 1984
Large variations in potential vorticity at small spatial scales in the upper ocean Pollard, R. T.; Regier, L. Nature, Vol. 348, Issue 6298 https://doi.org/10.1038/348227a0	journal	November 1990
Lectures on Geophysical Fluid Dynamics Salmon, Rick Oxford University Press https://doi.org/10.1093/oso/9780195108088.001.0001	book	May 1998
Convergence to precipitating quasi-geostrophic equations with phase changes: asymptotics and numerical assessment Zhang, Yeyu; Smith, Leslie M.; Stechmann, Samuel N. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 380, Issue 2226 https://doi.org/10.1098/rsta.2021.0030	journal	May 2022
Convection in Conditionally Unstable Atmosphere Kuo, H. L. Tellus, Vol. 13, Issue 4 https://doi.org/10.1111/j.2153-3490.1961.tb00107.x	journal	November 1961
On the numerical simulation of buoyant convection Lilly, D. K. Tellus, Vol. 14, Issue 2 https://doi.org/10.1111/j.2153-3490.1962.tb00128.x	journal	May 1962
Atmospheric Moist Convection Stevens, Bjorn Annual Review of Earth and Planetary Sciences, Vol. 33, Issue 1 https://doi.org/10.1146/annurev.earth.33.092203.122658	journal	May 2005
Vorticity Dynamics of the Oceanic General Circulation Rhines, P. B. Annual Review of Fluid Mechanics, Vol. 18, Issue 1 https://doi.org/10.1146/annurev.fl.18.010186.002245	journal	January 1986
Inertial Instability and Mesoscale Convective Systems. Part I: Linear Theory of Inertial Instability in Rotating Viscous Fluids Emanuel, Kerry A. Journal of the Atmospheric Sciences, Vol. 36, Issue 12 https://doi.org/10.1175/1520-0469(1979)036<2425:IIAMCS>2.0.CO;2	journal	December 1979
Diagnosis of Balanced Vortex Structure Using Potential Vorticity Thorpe, A. J. Journal of the Atmospheric Sciences, Vol. 42, Issue 4 https://doi.org/10.1175/1520-0469(1985)042<0397:DOBVSU>2.0.CO;2	journal	February 1985
A Theory for Nonprecipitating Moist Convection between Two Parallel Plates. Part I: Thermodynamics and “Linear” Solutions Bretherton, Christopher S. Journal of the Atmospheric Sciences, Vol. 44, Issue 14 https://doi.org/10.1175/1520-0469(1987)044<1809:ATFNMC>2.0.CO;2	journal	July 1987
Cloud–Environment Interface Instability: Rising Thermal Calculations in Two Spatial Dimensions Grabowski, Wojciech W.; Clark, Terry L. Journal of the Atmospheric Sciences, Vol. 48, Issue 4 https://doi.org/10.1175/1520-0469(1991)048<0527:CIIRTC>2.0.CO;2	journal	February 1991
Cloud-Environment Interface Instability: Part II: Extension to Three Spatial Dimensions Grabowski, Wojciech W.; Clark, Terry L. Journal of the Atmospheric Sciences, Vol. 50, Issue 4 https://doi.org/10.1175/1520-0469(1993)050<0555:CEIIPI>2.0.CO;2	journal	February 1993
Generation of Moist Potential Vorticity in Extratropical Cyclones Cao, Zuohao; Cho, Han-Ru Journal of the Atmospheric Sciences, Vol. 52, Issue 18 https://doi.org/10.1175/1520-0469(1995)052<3263:GOMPVI>2.0.CO;2	journal	September 1995
A Dynamic and Thermodynamic Foundation for Modeling the Moist Atmosphere with Parameterized Microphysics Ooyama, Katsuyuki V. Journal of the Atmospheric Sciences, Vol. 58, Issue 15 https://doi.org/10.1175/1520-0469(2001)058<2073:ADATFF>2.0.CO;2	journal	August 2001
Potential Vorticity in a Moist Atmosphere Schubert, Wayne H.; Hausman, Scott A.; Garcia, Matthew Journal of the Atmospheric Sciences, Vol. 58, Issue 21 https://doi.org/10.1175/1520-0469(2001)058<3148:PVIAMA>2.0.CO;2	journal	November 2001
Fluid Dynamics of Oceanic Thermocline Ventilation Marshall, John C.; Nurser, A. J. George Journal of Physical Oceanography, Vol. 22, Issue 6 https://doi.org/10.1175/1520-0485(1992)022<0583:FDOOTV>2.0.CO;2	journal	June 1992
Application of the Piecewise Parabolic Method (PPM) to Meteorological Modeling Carpenter, Richard L.; Droegemeier, Kelvin K.; Woodward, Paul R. Monthly Weather Review, Vol. 118, Issue 3 https://doi.org/10.1175/1520-0493(1990)118<0586:AOTPPM>2.0.CO;2	journal	March 1990
Potential Vorticity Diagnostics of Cyclogenesis Davis, Christopher A.; Emanuel, Kerry A. Monthly Weather Review, Vol. 119, Issue 8 https://doi.org/10.1175/1520-0493(1991)119<1929:PVDOC>2.0.CO;2	journal	August 1991
Cold-Frontal Potential Vorticity Maxima, the Low-Level Jet, and Moisture Transport in Extratropical Cyclones Lackmann, Gary M. Monthly Weather Review, Vol. 130, Issue 1 https://doi.org/10.1175/1520-0493(2002)130<0059:CFPVMT>2.0.CO;2	journal	January 2002
Thermodynamic Consistency of the Anelastic Approximation for a Moist Atmosphere Pauluis, Olivier Journal of the Atmospheric Sciences, Vol. 65, Issue 8 https://doi.org/10.1175/2007JAS2475.1	journal	August 2008
A Climatology of the Tropospheric Thermal Stratification Using Saturation Potential Vorticity Korty, Robert L.; Schneider, Tapio Journal of Climate, Vol. 20, Issue 24 https://doi.org/10.1175/2007JCLI1788.1	journal	December 2007
Multiscale Models for Cumulus Cloud Dynamics Stechmann, Samuel N.; Stevens, Bjorn Journal of the Atmospheric Sciences, Vol. 67, Issue 10 https://doi.org/10.1175/2010JAS3380.1	journal	October 2010
Buoyancy and Wind-Driven Convection at Mixed Layer Density Fronts Taylor, John R.; Ferrari, Raffaele Journal of Physical Oceanography, Vol. 40, Issue 6 https://doi.org/10.1175/2010JPO4365.1	journal	June 2010
The Bjerknes' Circulation Theorem: A Historical Perspective Thorpe, Alan J.; Volkert, Hans; Ziemiański, Michał J. Bulletin of the American Meteorological Society, Vol. 84, Issue 4 https://doi.org/10.1175/BAMS-84-4-471	journal	April 2003
Potential Vorticity and Balanced and Unbalanced Moisture Wetzel, Alfredo N.; Smith, Leslie M.; Stechmann, Samuel N. Journal of the Atmospheric Sciences, Vol. 77, Issue 6 https://doi.org/10.1175/JAS-D-19-0311.1	journal	June 2020
Comparing Growth Rates of Simulated Moist and Dry Convective Thermals Morrison, Hugh; Peters, John M.; Sherwood, Steven C. Journal of the Atmospheric Sciences, Vol. 78, Issue 3 https://doi.org/10.1175/JAS-D-20-0166.1	journal	March 2021
Warm Conveyor Belts in the ERA-Interim Dataset (1979–2010). Part I: Climatology and Potential Vorticity Evolution Madonna, Erica; Wernli, Heini; Joos, Hanna Journal of Climate, Vol. 27, Issue 1 https://doi.org/10.1175/JCLI-D-12-00720.1	journal	January 2014
The Evolution and Arrest of a Turbulent Stratified Oceanic Bottom Boundary Layer over a Slope: Upslope Regime and PV Dynamics Ruan, Xiaozhou; Thompson, Andrew F.; Taylor, John R. Journal of Physical Oceanography, Vol. 51, Issue 4 https://doi.org/10.1175/JPO-D-20-0168.1	journal	April 2021
The Influence of Incipient Latent Heat Release on the Precipitation Distribution of the 24–25 January 2000 U.S. East Coast Cyclone Brennan, Michael J.; Lackmann, Gary M. Monthly Weather Review, Vol. 133, Issue 7 https://doi.org/10.1175/MWR2959.1	journal	July 2005
Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action Rossby, C. -G. Journal of Marine Research, Vol. 2, Issue 1 https://doi.org/10.1357/002224039806649023	journal	June 1939
Idealized moist Rayleigh-Benard convection with piecewise linear equation of state Pauluis, Olivier; Schumacher, Jörg Communications in Mathematical Sciences, Vol. 8, Issue 1 https://doi.org/10.4310/CMS.2010.v8.n1.a15	journal	January 2010

Similar Records

Hurricane‐Like Vortices in Conditionally Unstable Moist Convection

Journal Article · 2022 · Journal of Advances in Modeling Earth Systems · OSTI ID:1874595

Chien, Mu‐Hua; Pauluis, Olivier M.; Almgren, Ann S.

Entrainment, Detrainment, and Dilution of Dry and Moist Atmospheric Thermals

Journal Article · 2025 · Journal of the Atmospheric Sciences · OSTI ID:2515629

Morrison, Hugh

MSE Minus CAPE is the True Conserved Variable for an Adiabatically Lifted Parcel

Journal Article · 2015 · Journal of the Atmospheric Sciences · OSTI ID:1511419

Romps, David M

Related Subjects

54 ENVIRONMENTAL SCIENCES
clouds
conservation law
latent heating
moist potential vorticity
phase changes
water vapor

Title: Non-conservation and conservation for different formulations of moist potential vorticity

Citation Formats

References (47)

Similar Records

Related Subjects