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Journal articles on the topic 'Potential vorticity'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 September 2023

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1

Herbert, Fritz. "The physics of potential vorticity." Meteorologische Zeitschrift 16, no. 3 (June 21, 2007): 243–54. http://dx.doi.org/10.1127/0941-2948/2007/0198.

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2

Millán, Luis F., Gloria L. Manney, and Zachary D. Lawrence. "Reanalysis intercomparison of potential vorticity and potential-vorticity-based diagnostics." Atmospheric Chemistry and Physics 21, no. 7 (April 7, 2021): 5355–76. http://dx.doi.org/10.5194/acp-21-5355-2021.

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Abstract. Global reanalyses from data assimilation systems are among the most widely used datasets in weather and climate studies, and potential vorticity (PV) from reanalyses is invaluable for many studies of dynamical and transport processes. We assess how consistently modern reanalyses represent potential vorticity (PV) among each other, focusing not only on PV but also on process-oriented dynamical diagnostics including equivalent latitude calculated from PV and PV-based tropopause and stratospheric polar vortex characterization. In particular we assess the National Centers for Environmental Prediction Climate Forecast System Reanalysis/Climate Forecast System, version 2 (CFSR/CFSv2) reanalysis, the European Centre for Medium-Range Weather Forecasts Interim (ERA-Interim) reanalysis, the Japanese Meteorological Agency's 55-year (JRA-55) reanalysis, and the NASA Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2). Overall, PV from all reanalyses agrees well with the reanalysis ensemble mean, providing some confidence that all of these recent reanalyses are suitable for most studies using PV-based diagnostics. Specific diagnostics where some larger differences are seen include PV-based tropopause locations in regions that have strong tropopause gradients (such as around the subtropical jets) or are sparse in high-resolution data (such as over Antarctica), and the stratospheric polar vortices during fall vortex formation and (especially) spring vortex breakup; studies of sensitive situations or regions such as these should examine PV from multiple reanalyses.
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3

Rotunno, R., V. Grubišić, and P. K. Smolarkiewicz. "Vorticity and Potential Vorticity in Mountain Wakes." Journal of the Atmospheric Sciences 56, no. 16 (August 1999): 2796–810. http://dx.doi.org/10.1175/1520-0469(1999)056<2796:vapvim>2.0.co;2.

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4

Davis, Christopher A. "Piecewise Potential Vorticity Inversion." Journal of the Atmospheric Sciences 49, no. 16 (August 1992): 1397–411. http://dx.doi.org/10.1175/1520-0469(1992)049<1397:ppvi>2.0.co;2.

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5

Keffer, Thomas. "The potential of vorticity." Nature 334, no. 6178 (July 1988): 105–6. http://dx.doi.org/10.1038/334105a0.

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6

McTaggart-Cowan, R., J. R. Gyakum, and M. K. Yau. "Moist Component Potential Vorticity." Journal of the Atmospheric Sciences 60, no. 1 (January 2003): 166–77. http://dx.doi.org/10.1175/1520-0469(2003)060<0166:mcpv>2.0.co;2.

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7

McDougall, Trevor J. "Neutral-surface potential vorticity." Progress in Oceanography 20, no. 3 (January 1988): 185–221. http://dx.doi.org/10.1016/0079-6611(88)90002-x.

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8

Kirwan, A. D., Bruce Lipphardt, and Juping Liu. "Negative potential vorticity lenses." International Journal of Engineering Science 30, no. 10 (October 1992): 1361–78. http://dx.doi.org/10.1016/0020-7225(92)90147-9.

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9

Arbogast, P. "Sensitivity to potential vorticity." Quarterly Journal of the Royal Meteorological Society 124, no. 549 (July 1998): 1605–15. http://dx.doi.org/10.1002/qj.49712454912.

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10

Viúdez, Álvaro. "On Ertel’s Potential Vorticity Theorem. On the Impermeability Theorem for Potential Vorticity." Journal of the Atmospheric Sciences 56, no. 4 (February 1999): 507–16. http://dx.doi.org/10.1175/1520-0469(1999)056<0507:oespvt>2.0.co;2.

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11

Xiao-Peng, Cui, Gao Shou-Ting, and Wu Guo-Xiong. "Moist Potential Vorticity and Up-Sliding Slantwise Vorticity Development." Chinese Physics Letters 20, no. 1 (December 9, 2002): 167–69. http://dx.doi.org/10.1088/0256-307x/20/1/350.

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12

Egger, Joseph, Klaus-Peter Hoinka, and Thomas Spengler. "Inversion of Potential Vorticity Density." Journal of the Atmospheric Sciences 74, no. 3 (March 1, 2017): 801–7. http://dx.doi.org/10.1175/jas-d-16-0133.1.

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Abstract Inversion of potential vorticity density with absolute vorticity and function η is explored in η coordinates. This density is shown to be the component of absolute vorticity associated with the vertical vector of the covariant basis of η coordinates. This implies that inversion of in η coordinates is a two-dimensional problem in hydrostatic flow. Examples of inversions are presented for (θ is potential temperature) and (p is pressure) with satisfactory results for domains covering the North Pole. The role of the boundary conditions is investigated and piecewise inversions are performed as well. The results shed new light on the interpretation of potential vorticity inversions.
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13

Stan, Cristiana, and David A. Randall. "Potential Vorticity as Meridional Coordinate." Journal of the Atmospheric Sciences 64, no. 2 (February 1, 2007): 621–33. http://dx.doi.org/10.1175/jas3839.1.

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Abstract The dynamical equations of atmospheric flow are written using potential vorticity as the meridional coordinate and potential temperature as the vertical coordinate. Within this system, the atmosphere is divided into undulating tubes bounded by isentropic and constant potential vorticity surfaces, and, under adiabatic and frictionless conditions, the air moves through the tubes without penetrating through the walls.
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14

Davis, Christopher A., and Kerry A. Emanuel. "Potential Vorticity Diagnostics of Cyclogenesis." Monthly Weather Review 119, no. 8 (August 1991): 1929–53. http://dx.doi.org/10.1175/1520-0493(1991)119<1929:pvdoc>2.0.co;2.

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15

Shapiro, Lloyd J., and James L. Franklin. "Potential Vorticity in Hurricane Gloria." Monthly Weather Review 123, no. 5 (May 1995): 1465–75. http://dx.doi.org/10.1175/1520-0493(1995)123<1465:pvihg>2.0.co;2.

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16

Spengler, Thomas, and Joseph Egger. "Potential Vorticity Attribution and Causality." Journal of the Atmospheric Sciences 69, no. 8 (August 1, 2012): 2600–2607. http://dx.doi.org/10.1175/jas-d-11-0313.1.

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Abstract The electrostatic analogy provides a well-known paradigm for the concept of potential vorticity (PV) attribution. Just as electric fields can be attributed to electric charges, so are localized PV anomalies thought to induce far fields of flow and temperature, at least after geostrophic adjustment. Piecewise PV inversion (PPVI) exploits this concept. Idealized examples of PPVI are discussed by selecting isolated anomalies that are inverted to yield the far field “caused” by the PV anomaly. The causality of attribution is tested in this study by seeking an unbalanced initial state containing the same PV anomaly but without a far field from which the balanced state can be attained by geostrophic adjustment. It is shown that the far field of a balanced axisymmetric PV anomaly in shallow water, without mean PV gradients, may evolve from a localized anomaly without a far field. For the more general example of the electrostatics analogy, namely a three-dimensional spherical PV anomaly, the initial state has to be nonhydrostatic and needs to exhibit a mass deficit. As this mass deficit cannot be removed during hydrostatic and geostrophic adjustment, it follows that PV attribution does not imply a causal relationship between the far field of a PV anomaly and the anomaly itself.
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17

Bannon, Peter R., Jürg Schmidli, and Christoph Schär. "On Potential Vorticity Flux Vectors." Journal of the Atmospheric Sciences 60, no. 23 (December 2003): 2917–21. http://dx.doi.org/10.1175/1520-0469(2003)060<2917:opvfv>2.0.co;2.

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18

Hide, Raymond. "Superhelicity, helicity and potential vorticity." Geophysical & Astrophysical Fluid Dynamics 48, no. 1-3 (October 1989): 69–79. http://dx.doi.org/10.1080/03091928908219526.

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19

Viúdez, Álvaro. "The Relation between Beltrami's Material Vorticity and Rossby–Ertel's Potential Vorticity." Journal of the Atmospheric Sciences 58, no. 17 (September 2001): 2509–17. http://dx.doi.org/10.1175/1520-0469(2001)058<2509:trbbmv>2.0.co;2.

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20

Chan, Douglas S. T., and Han-Ru Cho. "Meso-βScale Potential Vorticity Anomalies and Rainbands. Part I: Adiabatic Dynamics of Potential Vorticity Anomalies." Journal of the Atmospheric Sciences 46, no. 12 (June 1989): 1713–23. http://dx.doi.org/10.1175/1520-0469(1989)046<1713:mpvaar>2.0.co;2.

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21

Wagner, G. L., and W. R. Young. "Available potential vorticity and wave-averaged quasi-geostrophic flow." Journal of Fluid Mechanics 785 (November 23, 2015): 401–24. http://dx.doi.org/10.1017/jfm.2015.626.

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We derive a wave-averaged potential vorticity equation describing the evolution of strongly stratified, rapidly rotating quasi-geostrophic (QG) flow in a field of inertia-gravity internal waves. The derivation relies on a multiple-time-scale asymptotic expansion of the Eulerian Boussinesq equations. Our result confirms and extends the theory of Bühler & McIntyre (J. Fluid Mech., vol. 354, 1998, pp. 609–646) to non-uniform stratification with buoyancy frequency $N(z)$ and therefore non-uniform background potential vorticity $f_{0}N^{2}(z)$, and does not require spatial-scale separation between waves and balanced flow. Our interest in non-uniform background potential vorticity motivates the introduction of a new quantity: ‘available potential vorticity’ (APV). Like Ertel potential vorticity, APV is exactly conserved on fluid particles. But unlike Ertel potential vorticity, linear internal waves have no signature in the Eulerian APV field, and the standard QG potential vorticity is a simple truncation of APV for low Rossby number. The definition of APV exactly eliminates the Ertel potential vorticity signal associated with advection of a non-uniform background state, thereby isolating the part of Ertel potential vorticity available for balanced-flow evolution. The effect of internal waves on QG flow is expressed concisely in a wave-averaged contribution to the materially conserved QG potential vorticity. We apply the theory by computing the wave-induced QG flow for a vertically propagating wave packet and a mode-one wave field, both in vertically bounded domains.
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22

Hide, Raymond. "Potential magnetic field and potential vorticity in magnetohydrodynamics." Geophysical Journal International 125, no. 1 (April 1996): F1—F3. http://dx.doi.org/10.1111/j.1365-246x.1996.tb06529.x.

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23

Gao, ShouTing, PengCheng Xu, Na Li, and YuShu Zhou. "Second order potential vorticity and its potential applications." Science China Earth Sciences 57, no. 10 (September 3, 2014): 2428–34. http://dx.doi.org/10.1007/s11430-014-4897-1.

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24

Egger, Joseph, and Klaus-Peter Hoinka. "Potential Temperature and Potential Vorticity Inversion: Complementary Approaches." Journal of the Atmospheric Sciences 67, no. 12 (December 1, 2010): 4001–16. http://dx.doi.org/10.1175/2010jas3532.1.

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Abstract Given the distribution of one atmospheric variable, that of nearly all others can be derived in balanced flow. In particular, potential vorticity inversion (PVI) selects potential vorticity (PV) to derive pressure, winds, and potential temperature θ. Potential temperature inversion (PTI) starts from available θ fields to derive pressure, winds, and PV. While PVI has been applied extensively, PTI has hardly been used as a research tool although the related technical steps are well known and simpler than those needed in PVI. Two idealized examples of PTI and PVI are compared. The 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) datasets are used to determine typical anomalies of PV and θ in the North Atlantic storm-track region. Statistical forms of PVI and PTI are applied to these anomalies. The inversions are equivalent but the results of PTI are generally easier to understand than those of PVI. The issues of attribution and piecewise inversion are discussed.
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25

VIÚDEZ, ÁLVARO, and DAVID G. DRITSCHEL. "An explicit potential-vorticity-conserving approach to modelling nonlinear internal gravity waves." Journal of Fluid Mechanics 458 (May 10, 2002): 75–101. http://dx.doi.org/10.1017/s0022112002007747.

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This paper discusses a potential-vorticity-conserving approach to modelling nonlinear internal gravity waves in a rotating Boussinesq fluid. The focus of the work is on the pseudo-plane motion (motion in the x, z-plane), for which we present a broad range of numerical results. In this case there are two material coordinates, the density and the y-component of the velocity in the inertial frame of reference, which are related to the x and z displacements of fluid particles relative to a reference configuration. The amount of potential vorticity within a fluid region bounded by isosurfaces of these material coordinates is proportional to the area within this region, and is therefore conserved as well. Two new potentials, defined in terms of the displacements and combining the vorticity and density fields, are introduced as new dependent variables. These potentials entirely govern the dynamics of internal gravity waves for the linearized system when the basic state has uniform potential vorticity. The final system of equations consists of three prognostic equations (for the potential vorticity and the Laplacians of the two potentials) and one diagnostic equation, of Monge–Ampère type, for a third potential. This diagnostic equation arises from the nonlinear definition of potential vorticity. The ellipticity of the Monge–Ampère equation implies both inertial and static stability. In three dimensions, the three potentials form a vector, whose (three-dimensional) Laplacian is equal to the vorticity plus the gradient of the perturbation density.Numerical simulations are carried out using a novel algorithm which directly evolves the potential vorticity, in a Lagrangian manner (following fluid particles), without diffusion. We present results which emphasize the way in which potential vorticity anomalies modify the characteristics of internal gravity waves, e.g. the propagation of internal wave packets, including reflection, refraction, and amplification. We also show how potential vorticity anomalies may generate internal gravity waves, along with the subsequent ‘geostrophic adjustment’ of the flow to a ‘balanced’ wave-less state. These examples, and the straightforward extension of the theoretical and numerical approach to three dimensions, point to a direct and accurate means to elucidate the role of potential vorticity in internal gravity wave interactions. As such, this approach may help a better understanding of the observed characteristics of internal gravity waves in the oceans.
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26

Claussen, Martin, and Michael Hantel. "Hans Ertel and potential vorticity a century of geophysical fluid dynamics." Meteorologische Zeitschrift 13, no. 6 (December 23, 2004): 451. http://dx.doi.org/10.1127/0941-2948/2004/0013-0451.

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27

Schubert, Wayne. "A generalization of Ertel's potential vorticity to a cloudy, precipitating atmosphere." Meteorologische Zeitschrift 13, no. 6 (December 23, 2004): 465–71. http://dx.doi.org/10.1127/0941-2948/2004/0013-0465.

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28

Röbcke, Matthias, Sarah C. Jones, and Detlev Majewski. "The extratropical transition of Hurricane Erin (2001): a potential vorticity perspective." Meteorologische Zeitschrift 13, no. 6 (December 23, 2004): 511–25. http://dx.doi.org/10.1127/0941-2948/2004/0013-0511.

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29

Waite, Michael L., and Nicholas Richardson. "Potential Vorticity Generation in Breaking Gravity Waves." Atmosphere 14, no. 5 (May 18, 2023): 881. http://dx.doi.org/10.3390/atmos14050881.

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Potential vorticity (PV) is an important quantity in stratified flows because it is conserved following the flow in the absence of forcing and viscous and diffusive effects. However, as shown by previous work for unstratified turbulence, viscosity and diffusion, when present, are not purely dissipative and can create potential vorticity even when none is present initially. In this work, we use direct numerical simulations to investigate the viscous and diffusive generation of potential vorticity and potential enstrophy (integrated square PV) in stratified turbulence. Simulations are initialized with a two-dimensional standing internal gravity wave, which has no potential vorticity apart from some low-level random noise; as a result, all potential vorticity and enstrophy comes from viscous and diffusive effects. Significant potential enstrophy is found when the standing wave breaks, and the maximum potential enstrophy increases with increasing Reynolds number. The mechanism for the initial PV generation is spanwise diffusion of buoyancy perturbations, which grow as the standing wave three-dimensionalizes, into the direction of spanwise vorticity. The viscous and diffusive terms responsible are small-scale and are sensitive to under-resolution, so high resolution is required to obtain robust results.
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30

Balasuriya, S. "Gradient evolution for potential vorticity flows." Nonlinear Processes in Geophysics 8, no. 4/5 (October 31, 2001): 253–63. http://dx.doi.org/10.5194/npg-8-253-2001.

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Abstract. Two-dimensional unsteady incompressible flows in which the potential vorticity (PV) plays a key role are examined in this study, through the development of the evolution equation for the PV gradient. For the case where the PV is conserved, precise statements concerning topology-conservation are presented. While establishing some intuitively well-known results (the numbers of eddies and saddles is conserved), other less obvious consequences (PV patches cannot be generated, some types of Lagrangian and Eulerian entities are equivalent) are obtained. This approach enables an improvement on an integrability result for PV conserving flows (if there were no PV patches at time zero, the flow would be integrable). The evolution of the PV gradient is also determined for the nonconservative case, and a plausible experiment for estimating eddy diffusivity is suggested. The theory is applied to an analytical diffusive Rossby wave example.
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31

Hausman, Scott A., Katsuyuki V. Ooyama, and Wayne H. Schubert. "Potential Vorticity Structure of Simulated Hurricanes." Journal of the Atmospheric Sciences 63, no. 1 (January 1, 2006): 87–108. http://dx.doi.org/10.1175/jas3601.1.

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Abstract To better understand the processes involved in tropical cyclone development, the authors simulate an axisymmetric tropical-cyclone-like vortex using a two-dimensional model based on nonhydrostatic dynamics, equilibrium thermodynamics, and bulk microphysics. The potential vorticity principle for this nonhydrostatic, moist, precipitating atmosphere is derived. The appropriate generalization of the dry potential vorticity is found to be P = ρ−1 {(−∂υ/∂z) (∂θρ/∂r) + [ f + ∂(rυ)/r∂r] (∂θρ/∂z)}, where ρ is the total density, υ is the azimuthal component of velocity, and θρ is the virtual potential temperature. It is shown that P carries all the essential dynamical information about the balanced wind and mass fields. In the fully developed, quasi-steady-state cyclone, the P field and the θ̇ρ field become locked together, with each field having an outward sloping region of peak values on the inside edge of the eyewall cloud. In this remarkable structure, the P field consists of a narrow, leaning tower in which the value of P can reach several hundred potential vorticity (PV) units. Sensitivity experiments reveal that the simulated cyclones are sensitive to the effects of ice, primarily through the reduced fall velocity of precipitation above the freezing level rather than through the latent heat of fusion, and to the effects of vertical entropy transport by precipitation.
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32

Schröder, Wilfried, and Hans-Jürgen Treder. "Ertel's Potential Vorticity and Irreversible Processes." Zeitschrift für Naturforschung A 54, no. 3-4 (April 1, 1999): 270–71. http://dx.doi.org/10.1515/zna-1999-3-418.

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33

Egger, Joseph. "Piecewise Potential Vorticity Inversion: Elementary Tests." Journal of the Atmospheric Sciences 65, no. 6 (June 1, 2008): 2015–24. http://dx.doi.org/10.1175/2007jas2564.1.

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Abstract Piecewise potential vorticity inversion (PPVI) is widely accepted as a useful tool in atmospheric diagnostics. This method is thought to quantify the instantaneous interaction at a distance of anomalies of potential vorticity (PV) separated horizontally and/or vertically. Doubts with respect to the dynamical justification of PPVI are formulated. In particular, it is argued that the tendency of the inverted streamfunction must be determined in order to quantify far-field effects. Elementary tests of PPVI are conducted to clarify these points. First, PPVI is performed for the textbook case of linear Rossby waves in a one-dimensional barotropic fluid. Analytic solutions are presented for PPVI and the related tendency problem. It is found that PPVI does not contribute to an understanding of Rossby wave dynamics. On the other hand, PPVI turns out to be more useful when applied to confined PV extrema. Neither the application of PPVI to linear baroclinic waves in zonal shear flow nor the inversions of the related temperature anomalies at the boundaries help to better understand the wave development. It is concluded that PPVI with additional tendency calculations poses and solves a specific problem by retaining observed PV anomalies in one subdomain and removing them in others. The usefulness of the results with regard to the diagnosis of the observed state depends strongly on the flows considered and on the partitions chosen, which must comply with a simple rule.
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34

Jamaloodeen, Mohamed I., and Paul K. Newton. "Two-layer quasigeostrophic potential vorticity model." Journal of Mathematical Physics 48, no. 6 (June 2007): 065601. http://dx.doi.org/10.1063/1.2469221.

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35

Egger, Joseph. "Some Aspects of Potential Vorticity Inversion." Journal of the Atmospheric Sciences 47, no. 10 (May 1990): 1269–75. http://dx.doi.org/10.1175/1520-0469(1990)047<1269:saopvi>2.0.co;2.

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36

Berrisford, P., J. C. Marshall, and A. A. White. "Quasigeostrophic Potential Vorticity in Isentropic Coordinates." Journal of the Atmospheric Sciences 50, no. 5 (March 1993): 778–82. http://dx.doi.org/10.1175/1520-0469(1993)050<0778:qpviic>2.0.co;2.

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37

Herring, J. R., R. M. Kerr, and R. Rotunno. "Ertel's Potential Vorticity in Unstratified Turbulence." Journal of the Atmospheric Sciences 51, no. 1 (January 1994): 35–47. http://dx.doi.org/10.1175/1520-0469(1994)051<0035:epviut>2.0.co;2.

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38

Lait, Leslie R. "An Alternative Form for Potential Vorticity." Journal of the Atmospheric Sciences 51, no. 12 (June 1994): 1754–59. http://dx.doi.org/10.1175/1520-0469(1994)051<1754:aaffpv>2.0.co;2.

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39

Swanson, K. L., and R. T. Pierrehumbert. "Potential Vorticity Homogenization and Stationary Waves." Journal of the Atmospheric Sciences 52, no. 7 (April 1995): 990–94. http://dx.doi.org/10.1175/1520-0469(1995)052<0990:pvhasw>2.0.co;2.

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40

McIntyre, Michael E., and Warwick A. Norton. "Potential Vorticity Inversion on a Hemisphere." Journal of the Atmospheric Sciences 57, no. 9 (May 2000): 1214–35. http://dx.doi.org/10.1175/1520-0469(2000)057<1214:pvioah>2.0.co;2.

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41

Egger, Joseph, and Klaus-Peter Hoinka. "Stochastic Forcing of Potential Vorticity: Observations." Journal of the Atmospheric Sciences 68, no. 6 (June 1, 2011): 1340–46. http://dx.doi.org/10.1175/2011jas3654.1.

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Abstract The linear theory of point correlation maps for synoptic systems relies so far mainly on specifications of stochastic forcing due to nonlinear processes that are not based on observations. Forty-year ECMWF Re-Analysis (ERA-40) data are used to derive time series of the forcing terms in a potential vorticity equation for a correlation point in the North Atlantic storm-track region. It is found that the forcing correlations are restricted to distances less than 1500 km to the correlation point in zonal direction and just a few hundred kilometers in meridional direction. The forcing is not even approximately white in time. Covariances of forcing and potential vorticity are presented as well. An advection equation with simple damping and realistic stochastic forcing is solved to approximate the observed covariances of forcing and potential vorticity.
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42

Treder, H. J., and W. Schröder. "Ertel’s potential vorticity and irreversible processes." Meteorologische Zeitschrift 4, no. 1 (February 20, 1995): 22–23. http://dx.doi.org/10.1127/metz/4/1995/22.

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43

Hsu, Pei-Chun, and P. H. Diamond. "On calculating the potential vorticity flux." Physics of Plasmas 22, no. 3 (March 2015): 032314. http://dx.doi.org/10.1063/1.4916401.

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44

Newman, Paul A., Mark R. Schoeberl, R. Alan Plumb, and Joan E. Rosenfield. "Mixing rates calculated from potential vorticity." Journal of Geophysical Research 93, no. D5 (1988): 5221. http://dx.doi.org/10.1029/jd093id05p05221.

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45

Schubert, Wayne H., and Matthew T. Masarik. "Potential vorticity aspects of the MJO." Dynamics of Atmospheres and Oceans 42, no. 1-4 (December 2006): 127–51. http://dx.doi.org/10.1016/j.dynatmoce.2006.02.003.

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46

Hoskins, Brian. "Potential vorticity and the PV perspective." Advances in Atmospheric Sciences 32, no. 1 (November 28, 2014): 2–9. http://dx.doi.org/10.1007/s00376-014-0007-8.

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47

Ringler, Todd, and Peter Gent. "An eddy closure for potential vorticity." Ocean Modelling 39, no. 1-2 (January 2011): 125–34. http://dx.doi.org/10.1016/j.ocemod.2011.02.003.

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48

Schubert, Wayne H., Scott A. Hausman, Matthew Garcia, Katsuyuki V. Ooyama, and Hung-Chi Kuo. "Potential Vorticity in a Moist Atmosphere." Journal of the Atmospheric Sciences 58, no. 21 (November 2001): 3148–57. http://dx.doi.org/10.1175/1520-0469(2001)058<3148:pviama>2.0.co;2.

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49

Schneider, Tapio, Isaac M. Held, and Stephen T. Garner. "Boundary Effects in Potential Vorticity Dynamics." Journal of the Atmospheric Sciences 60, no. 8 (April 2003): 1024–40. http://dx.doi.org/10.1175/1520-0469(2003)60<1024:beipvd>2.0.co;2.

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50

Thomas, Leif N. "Destruction of Potential Vorticity by Winds." Journal of Physical Oceanography 35, no. 12 (December 1, 2005): 2457–66. http://dx.doi.org/10.1175/jpo2830.1.

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Abstract:
Abstract The destruction of potential vorticity (PV) at ocean fronts by wind stress–driven frictional forces is examined using PV flux formalism and numerical simulations. When a front is forced by “downfront” winds, that is, winds blowing in the direction of the frontal jet, a nonadvective frictional PV flux that is upward at the sea surface is induced. The flux extracts PV out of the ocean, leading to the formation of a boundary layer thicker than the Ekman layer, with nearly zero PV and nonzero stratification. The PV reduction is not only active in the Ekman layer but is transmitted through the boundary layer via secondary circulations that exchange low PV from the Ekman layer with high PV from the pycnocline. Extraction of PV from the pycnocline by the secondary circulations results in an upward advective PV flux at the base of the boundary layer that scales with the surface, nonadvective, frictional PV flux and that leads to the deepening of the layer. At fronts forced by both downfront winds and a destabilizing atmospheric buoyancy flux FBatm, the critical parameter that determines whether the wind or the buoyancy flux is the dominant cause for PV destruction is (H/δe)(FBwind/FBatm), where H and δe are the mixed layer and Ekman layer depths, FBwind = S2τo/(ρof ), S2 is the magnitude of the lateral buoyancy gradient of the front, τo is the downfront component of the wind stress, ρo is a reference density, and f is the Coriolis parameter. When this parameter is greater than 1, PV destruction by winds dominates and may play an important role in the formation of mode water.
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