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On generalized vorticity-conservation laws

Published online by Cambridge University Press:  20 April 2006

B. Gaffet
B. Gaffet
Affiliation:
Centre d'Etudes Nucléaires de Saclay, Service d'Astrophysique, 91191 Gif-sur-Yvette Cedex, France
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Abstract

We present here a new type of generalization of the conservation law of circulation, in two dimensions, and of the helicity-conservation law in three dimensions assuming zero potential vorticity. The conserved quantities keep their usual expressions ∫∫k· rot vd2r, ∫∫∫v· rot vd3r, respectively, as in the barotropic case.

These generalizations are based upon the general formulation of conservation laws in terms of potentials (here the Clebsch potentials). The conserved currents that we derive are expressible in terms of the ordinary physical variables (r, t, v, P, ρ) only, as they should.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 156 , July 1985 , pp. 141 - 149
Copyright
© 1985 Cambridge University Press

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References

Betchov, R. 1961 Phys. Fluids 4, 925.
Bretherton, F. P. 1970 J. Fluid Mech. 44, 19.
Clebsch, A. 1859 J. reine angew. Math. 56, 1.
Eckart, C. 1960 Phys. Fluids 3, 421.
Ertel, H. 1942 Met. Z. 59, 277.
Ertel, H. 1960 Gerl. Beitr. Geophys 69, 351.
Herivel, J. W. 1955 Proc. Camb. Phil. Soc. 51, 344.
Hollmann, G. 1964 Arch. Met. Geophys. Bioklim. A 14, 1.
Katz, J. & Lynden-Bell, D. 1982 Proc. R. Soc. Lond. A 381, 263.
Kelvin, Lord 1868 Vortex Motion.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Landau, L. & Lifshitz, E. 1951 The Classical Theory of Fields, chap. X. equation (83; 2) p. 307 and equation (86;9) p. 330. Ed. de la Paix, Moscow.
Lin, C. C. 1963 Liquid helium. In Proc. Intl School of Physics, Course XXI. Academic.
Mobbs, S. D. 1981 J. Fluid Mech. 108, 475.
Mobbs, S. D. 1982 Proc. R. Soc. Lond. A 381, 457.
Moffatt, H. K. 1969 J. Fluid Mech. 35, 117.
Moreau, J. J. 1961 C. R. Acad. Sci. Paris 252, 2810.
Seliger, R. L. & Whitham, G. B. 1968 Proc. R. Soc. Lond. A 305, 1.
Serrin, J. 1959 in Handbuch der Physik, vol. 8, pp. 125–263. Springer.