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Ertel, H.; Laves, F.; Bubnoff, S. v.

doi:10.1007/bf01475604

Cited by 9 publications

(7 citation statements)

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“…Finally, a word about the pseudoscalar W , the weighted relative potential vorticity. In accordance with the potential vorticity theorem of Ertel (1942), the full (unweighted) potential vorticity based on the absolute (rather than relative) vorticity, namely 2 + ω, and potential density can in realistic limits be used as a Lagrangian tracer, and so can the familiar approximation to potential vorticity used by meteorologists and oceanographers in diagnostics work going back to the late 1940s (see, for example, Truesdell (1954), Gill (1982), Hoskins et al (1985), Pedlosky (1987), Schroeder (1988), Haynes and McIntyre (1990), Monin (1990), Kurgansky (1991), Mueller (1995, and Read et al (2002)). Such tracer-like behaviour is clearly not in general a property of W , but this does not detract from the likely importance of diagnostic studies of W , H and S. What might be expected to emerge from such studies is a better understanding of how in fully developed sloping convection the fields of relative vorticity and density equilibrate in the main body of the fluid, and in particular how they are influenced by frictional effects in boundary layers (see above and H89, pp.…”

Section: Discussionmentioning

confidence: 76%

Helicity, superhelicity and weighted relative potential vorticity: Useful diagnostic pseudoscalars?

Hide¹

2002

Quart J Royal Meteoro Soc

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Advances in techniques of data assimilation in meteorology and oceanography and continuing improvements in the scope and reliability of numerical simulations of motions in atmospheres and oceans and other rotating fluid systems offer opportunities for experimenting with novel diagnostic schemes for elucidating basic dynamical processes. Here attention is drawn to the likely diagnostic value of determinations of the fields of certain pseudoscalar quantities, namely helicity, superhelicity and weighted relative potential vorticity. Copyright © 2002 Royal Meteorological Society.

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Section: Discussionmentioning

confidence: 76%

Helicity, superhelicity and weighted relative potential vorticity: Useful diagnostic pseudoscalars?

Hide¹

2002

Quart J Royal Meteoro Soc

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“…The former goes back to the early studies of Rossby (1940), Ertel (1942) and Kleinschmidt (1957). It was given a boost by the production by Charney and Stern (1962) of the quasigeostrophic (QG) form of the PV conservation equation.…”

Section: Introductionmentioning

confidence: 99%

The omega equation and potential vorticity

Hoskins

Pedder

Jones

2003

Quart J Royal Meteoro Soc

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SUMMARYTwo fundamental perspectives on the dynamics of midlatitude weather systems are provided by potential vorticity (PV) and the omega equation. The aim of this paper is to investigate the link between the two perspectives, which has so far received very little attention in the meteorological literature. It also aims to give a quantitative basis for discussion of quasi-geostrophic vertical motion in terms of components associated with system movement, maintaining a constant thermal structure, and with the development of that structure. The former links with the isentropic relative-ow analysis technique. Viewed in a moving frame of reference, the measured development of a system depends on the velocity of that frame of reference. The requirement that the development should be a minimum provides a quantitative method for determining the optimum system velocity. The component of vertical velocity associated with development is shown to satisfy an omega equation with forcing determined from the relative advection of interior PV and boundary temperature. The analysis carries through in the presence of diabatic heating provided the omega equation forcing is based on the interior PV and boundary thermal tendencies, including the heating effect. The analysis is shown to be possible also at the level of the semi-geostrophic approximation.The analysis technique is applied to a number of idealized problems that can be considered to be building blocks for midlatitude synoptic-scale dynamics. They focus on the in uences of interior PV, boundary temperature, an interior boundary, baroclinic instability associated with two boundaries, and also diabatic heating. In each case, insights yielded by the new perspective are sought into the dynamical behaviour, especially that related to vertical motion.

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“…In its most fundamental form, a suitably defined potential vorticity is the pivotal variable in the formulation of Ertel's 'new hydrodynamic vorticity theorem' (Ertel 1942), which is closely linked to other famous vorticity and circulation theorems such as those of Helmholtz, Kelvin and Bjerknes. The fact that, under certain conditions, PV may be materially and/or globally conserved is also of major importance in various geophysical contexts, since Ertel's theorem then provides an important constraint on fluid motion and can help simplify its analysis under some circumstances.…”

Section: Introductionmentioning

confidence: 99%

Mapping potential-vorticity dynamics on Jupiter. I: Zonal-mean circulation from Cassini and Voyager 1 data

Read

Gierasch

Conrath

et al. 2006

Q. J. R. Meteorol. Soc.

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SUMMARYMaps of Ertel potential vorticity on isentropic surfaces (IPV) and/or quasi-geostrophic potential vorticity (QGPV) are well established in dynamical meteorology as powerful sources of insight into dynamical processes involving 'balanced' flow. In the present study, we derive maps of zonal-mean IPV and QGPV in Jupiter's upper troposphere and lower stratosphere by making use of a combination of velocity measurements, derived from the tracking of cloud features in images from the Voyager 1 and 2 and Cassini missions, and thermal measurements from the Voyager 1 IRIS and Cassini CIRS instruments. IPV and QGPV are mapped and compared for the entire globe between latitudes ±55 • . Profiles of zonally averaged PV show some evidence for a step-like pattern suggestive of local PV homogenization, separated by strong PV gradients in association with eastward jets, though on differing scales in the northern and southern hemispheres. The northward gradient of PV (IPV or QGPV) is found to change sign in several places in each hemisphere, even when baroclinic contributions are taken into account. The relationship of lateral gradients of IPV and QGPV with the corresponding mean zonal flows indicate that the northern hemisphere may be closer to marginal stability with respect to Arnol'd's second stability theorem than the southern hemisphere.

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Cited by 9 publications

References 0 publications

Helicity, superhelicity and weighted relative potential vorticity: Useful diagnostic pseudoscalars?

Helicity, superhelicity and weighted relative potential vorticity: Useful diagnostic pseudoscalars?

The omega equation and potential vorticity

Mapping potential-vorticity dynamics on Jupiter. I: Zonal-mean circulation from Cassini and Voyager 1 data

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