On Ertel's potential vorticity theorem. On the impermeability theorem for potential vorticity

Journal of the Atmospheric Sciences

Volumn 56, Issue 4, 1999, Pages 507-516

  Viúdez, Álvaro ^a,b  

^a NAVAL POSTGRADUATE SCHOOL   (United States)

^b UNIVERSITAT DE LES ILLES BALEARS   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; KINEMATICS; MATHEMATICAL TRANSFORMATIONS; THEOREM PROVING; VARIATIONAL TECHNIQUES; VORTEX FLOW;

ERTEL'S POTENTIAL VORTICITY THEOREM; IMPERMEABILITY THEOREM;

ATMOSPHERIC MOVEMENTS;

EID: 0033076062     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0469(1999)056<0507:OESPVT>2.0.CO;2     Document Type: Article

References (36)

1. Bretherton, C. S., and C. Schär, 1993: Flux of potential vorticity substance: A simple derivation and a uniqueness property. J. Atmos. Sci., 50, 1834-1836.
2. Casey, J., and P. M. Naghdi, 1991: On the Lagrangian description of vorticity. Arch. Ration. Mech. Anal., 115, 1-14.
3. Csanady, G. T., and G. Vittal, 1996: Vorticity balance of outcropping isopycnals. J. Phys. Oceanogr., 26, 1952-1956.
4. Danielsen, E. F., 1990: In defense of Ertel's potential vorticity and its general applicability as a meteorological tracer. J. Atmos. Sci., 47, 2013-2020.
5. Dutton, J. A., 1976: The Ceaseless Wind. An Introduction to the Theory of Atmospheric Motion. McGraw-Hill, 579 pp.
6. Ericksen, J. L., 1960: Tensor fields. Handbuch der Physik III/I, S. Flügge, Ed., Springer-Verlag, 902 pp.
7. Ertel, H., 1942a: Ein neuer hydrodynamischer Erhaltungssatz. Naturwiss., 30, 543-544.
8. _, 1942b: Ein neuer hydrodynamischer Wirbelsatz. Meteor. Z., 59, 277-281.
9. _, 1942c: Über das Verhältnis des neuen hydrodynamischen Wirbelsatzes zum Zirkulationssatz von V. Bjerknes. Meteor. Z., 59, 385-387.
10. _, 1942d: Über hydrodynamische Wirbelsätze. Phys. Z., 43, 526-529.
11. _, 1960a: Teorema sobre invariantes sustanciales de la Hidrodinámica. Gerl. Beitr. Geophys., 69, 290-293.
12. _, 1960b: Relación entre la derivada individual y una cierta divergencia espacial en Hidrodinámica. Gerl. Beitr. Geophys., 69, 357-361.
13. Haynes, P. H., and M. E. McIntyre, 1987: On the evolution of vorticity and potential vorticity in the presence of diabatic heating and frictional and other forces. J. Atmos. Sci., 44, 828-841.
14. _, and _, 1990: On the conservation and impermeability theorems for potential vorticity. J. Atmos. Sci., 47, 2021-2031.
15. Hestenes, D., 1993: New Foundations for Classical Mechanics. Kluwer Academic, 644 pp.
16. Hollmann, G., 1964: Ein vollständiges System hydrodynamischer Erhaltungssätze. Arch. Meteor. Geophys. Bioklim., A14, 1-13.
17. Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877-946.
18. Howard, L. N., 1958: Divergence formulas involving vorticity. Arch. Ration. Mech. Anal., 1, 113-123.
19. Koshyk, J. N., and N. A. McFarlane, 1996: The potential vorticity budget of an atmospheric general circulation model. J. Atmos. Sci., 53, 550-563.
20. Marshall, J. C., and A. J. G. Nurser, 1992: Fluid dynamics of oceanic thermocline ventilation. J. Phys. Oceanogr., 22, 583-595.
21. McIntyre, M. E., and W. A. Norton, 1990: Dissipative wave-mean interactions and the transport of vorticity or potential vorticity. J. Fluid Mech., 212, 403-435.
22. Palmer, T. N., 1988: Analogues of potential vorticity in electrically conducting fluids. Geophys. Astrophys. Fluid Dyn., 40, 133-145.
23. Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2d ed. Springer-Verlag, 710 pp.
24. Ripa, P., 1981: Symmetries and conservation laws for internal gravity waves. Amer. Inst. Phys. Conf. Proc., 76, 281-306.
25. Salmon, R., 1982: Hamilton's principle and Ertel's theorem. Amer. Inst. Phys. Conf. Proc., 88, 127-135.
26. _, 1983: Practical use of Hamilton's principle. J. Fluid Mech., 132, 431-444.
27. _, 1988: Hamiltonian fluid mechanics. Annu. Rev. Fluid Mech., 20, 225-256.
28. Santilli, R. M., 1978: Foundations of Theoretical Mechanics I. Springer-Verlag, 266 pp.
29. Schär, C., 1993: A generalization of Bernoulli's theorem. J. Atmos. Sci., 50, 1437-1443.
30. Serrin, J., 1959: Mathematical principles of classical fluid mechanics. Handbuch der Physik VIII/1. S. Flügge, Ed., Springer-Verlag, 471 pp.
31. Truesdell, C. A. T., 1951: On Ertel's vorticity theorem. Z. Angew. Math. Phys., 2, 109-114.
32. _, 1954: The Kinematics of Vorticity. Indiana University Press, 232 pp.
33. _, 1991: A First Course in Rational Continuum Mechanics. Vol. 1. 2d ed. Academic Press, 391 pp.
34. _, and R. Toupin, 1960: The classical field theories. Handbuch der Physik III/1. S. Flügge, Ed., Springer-Verlag, 902 pp.
35. Vujanovic, B. D., and S. E. Jones, 1989: Variational Methods in Nonconservative Phenomena. Academic Press, 370 pp.
36. Xu, Q., 1992: Formation and evolution of frontal rainbands and geostrophic potential vorticity anomalies. J. Atmos. Sci., 49, 629-648.