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1

Hans, Ertel, Wilfried Schröder, and Hans Jürgen Treder. Ertel's potential vorticity. Bremen-Roennebeck: Interdivisional Commission on History of IAGA, 1997.

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2

Williams, Robin. Potential vorticity estimates at small scales in the ocean. Honolulu, Hawaii: Hawaii Institute of Geophysics, University of Hawaii, 1986.

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3

Ertel, Hans. Geophysical hydrodynamics and Ertel's potential vorticity: Selected papers of Hans Ertel. Bremen-Rönnebeck: I.A.G.A., 1991.

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4

Wardle, Richard M. Representation of eddies in climate models by a potential vorticity flux. Woods Hole, Mass: Massachusetts Institute of Technology, Woods Hole Oceanographic Institution, Joint Program in Oceanography/Applied Ocean Science and Engineering, 1999.

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5

Boerlage, Andrew P. A description of tropical cyclone recurvature in terms of isentropic potential vorticity. Monterey, Calif: Naval Postgraduate School, 1989.

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6

G, Georgiev Christo, ed. Weather analysis and forecasting: Applying satellite water vapor imagery and potential vorticity analysis. Amsterdam: Elsevier, 2005.

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7

Hall, Melinda M. Horizontal and vertical structure of velocity, potential vorticity and energy in the Gulf Stream. Woods Hole, Mass: Woods Hole Oceanographic Institution, 1985.

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8

Unbalanced Frontogenesis with Constant Potential Vorticity. Storming Media, 1996.

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9

Cao, Zuohao. Moist potential vorticity generation in extratropical cyclones. 1995.

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10

Du, Jun. On the Mei-Yu front and the associated potential vorticity anomaly. 1998.

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11

Santurette, Patrick, and Christo Georgiev. Weather Analysis and Forecasting: Applying Satellite Water Vapor Imagery and Potential Vorticity Analysis. Academic Press, 2005.

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12

Kirchoffer, Peter J. Analyzed potential vorticity fields for explosive and non-explosive cyclogenesis events during FGGE. 1986.

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13

Santurette, Patrick, Christo Georgiev, and Karine Maynard. Weather Analysis and Forecasting: Applying Satellite Water Vapor Imagery and Potential Vorticity Analysis. Elsevier Science & Technology Books, 2016.

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14

Santurette, Patrick, and Christo Georgiev. Weather Analysis and Forecasting: Applying Satellite Water Vapor Imagery and Potential Vorticity Analysis. Academic Press, 2005.

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15

Santurette, Patrick, Christo Georgiev, and Karine Maynard. Weather Analysis and Forecasting: Applying Satellite Water Vapor Imagery and Potential Vorticity Analysis. Elsevier Science & Technology Books, 2016.

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16

Santurette, Patrick, and Christo Georgiev. Weather Analysis and Forecasting: Applying Satellite Water Vapor Imagery and Potential Vorticity Analysis. Elsevier Science & Technology Books, 2005.

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17

A nonlinear multigrid solver for an atmospheric general circulation model based on semi-implicit semi-Lagrangian advection of potential vorticity: Final report. [Washington, DC: National Aeronautics and Space Administration, 1998.

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18

Development and Implementation of an Isentropic Potential Vorticity Algorithm for use at Air Force Global Weather Center. Storming Media, 1997.

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19

Zeitlin, Vladimir. Simplifying Primitive Equations: Rotating Shallow-Water Models and their Properties. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0003.

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In this chapter, one- and two-layer versions of the rotating shallow-water model on the tangent plane to the rotating, and on the whole rotating sphere, are derived from primitive equations by vertical averaging and columnar motion (mean-field) hypothesis. Main properties of the models including conservation laws and wave-vortex dichotomy are established. Potential vorticity conservation is derived, and the properties of inertia–gravity waves are exhibited. The model is then reformulated in Lagrangian coordinates, variational principles for its one- and two-layer version are established, and conservation laws are reinterpreted in these terms.
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20

Zeitlin, Vladimir. Primitive Equations Model. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0002.

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The chapter gives the foundations of modelling of large-scale atmospheric and oceanic motions and presents the ‘primitive equations’ (PE) model. After a concise reminder on general fluid mechanics, the main hypotheses leading to the PE model are explained, together with the tangent-plane (so-called f and beta plane) approximations, and ‘traditional’ approximation to the hydrodynamical equations on the rotating sphere. PE are derived in parallel for the ocean and for the atmosphere. It is then shown that, with a judicious choice of the vertical coordinate, the ‘pseudo-height’, in the atmosphere, these two sets of equations are practically equivalent. The main properties of PE are derived and the key concepts of wave–vortex dichotomy, and of slow and fast motions, are explained. The essential notion of potential vorticity is introduced and its conservation by fluid masses is demonstrated. Inertia–gravity waves are explained and their properties presented. Limitations of the hydrostatic hypothesis are demonstrated.
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