Hamilton's principle for quasigeostrophic motion

Physics of Fluids

Volumn 10, Issue 4, 1998, Pages 800-806

  Holm, Darryl D ^a   Zeitlin, Vladimir ^b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b LABORATOIRE DE MÉTÉOROLOGIE DYNAMIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347093085     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869623     Document Type: Article

References (30)

1. J. Pedlosky, Geophysical Fluid Dynamics, 2nd ed. (Springer, New York, 1987).
2. J. S. Allen and D. D. Holm, "Extended-geostrophic Hamiltonian models for rotating shallow water motion," Physica D 98, 229 (1996).
3. A. Stegner and V. Zeitlin, "Asymptotic expansions and monopolar solitary Rossby vortices in barotropic and two-layer models," Geophys. Astrophys. Fluid Dyn. 83, 159 (1996).
4. A. Weinstein, "Hamiltonian structure for drift waves and geostrophic flow," Phys. Fluids 26, 388 (1983).
5. V. Zeitlin and R. A. Pasmanter, "On the differential geometry approach to the geophysical flows," Phys. Lett. A 189, 59 (1994).
6. D. D. Holm, J. E. Marsden, T. Ratiu, and A. Weinstein, "Nonlinear stability of fluid and plasma equilibria," Phys. Rep. 123, 1 (1985).
7. D. D. Holm, "Hamiltonian formulation of the baroclinic quasigeostrophic fluid equations," Phys. Fluids 29, 7 (1986).
8. D. D. Holm, J. E. Marsden, and T. Ratiu, "The Euler-Poincaré equations and semidirect products with applications to continuum theories," Adv. in Math. to appear.
9. M. A. Virasoro, "Variational principle for two-dimensional incompressible hydrodynamics and quasi-geostrophic flows," Phys. Rev. Lett. 47, 1181 (1981).
10. R. L. Seliger and G. B. Whitham, "Variational principles in continuum mechanics," Proc. R. Soc. London, Ser. A 305, 1 (1968).
11. D. D. Holm and B. A. Kupershmidt, "Poisson brackets and Clebsch representations for magnetohydrodynamics, multifluid plasmas, and elasticity," Physica D 6, 347 (1983).
12. J. E. Marsden and A. Weinstein, "Coadjoint orbits, vortices and Clebsch variables for incompressible fluids," Physica D 7, 305 (1983).
13. R. Salmon, "Hamiltonian fluid mechanics," Annu. Rev. Fluid Mech. 20, 225 (1988).
14. V. Zeitlin, "Finite-mode analogs of 2D ideal hydrodynamics: Coadjoint orbits and local canonical structure," Physica D 49, 353 (1991).
15. V. Zeitlin, "On the structure of phase-space, Hamiltonian variables and statistical approach to the description of 2D hydrodynamics and magnetohydrodynamics," J. Phys. A 25, L171 (1992).
16. V. Zeitlin, "Vorticity and waves: Geometry of the phase-space and the problem of normal variables," Phys. Lett. A 164, 177 (1992).
17. V. I. Arnold, Mathematical Methods of Classical Mechanics, (Springer, New York, 1989), Appendix 2.
18. R. I. McLachlan, I. Szunyogh, and V. Zeitlin, "Hamiltonian finite-dimensional models of baroclinic instability," Phys. Lett. A 229, 299 (1997).
19. H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1993).
20. B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry - Methods and Applications (Springer, New York, 1992), Part I, Chap. 5.
21. D. D. Holm, J. E. Marsden, and T. Ratiu, Hamiltonian Structure and Lyapunov Stability for Ideal Continuum Dynamics, ISBN 2-7606-0771-2, Séminaire de Mathématiques supérieures, Les Presses de L'Univ. de Montréal, Vol. 100, pp. 11-208.
22. D. D. Holm, "Hamiltonian balance equations," Physica D 98, 379 (1996).
23. J. L. Lagrange, Miscellania Taurinensia, II (Evres, Paris, 1867), Vol. 2.
24. B. J. Hoskins, "The geostrophic momentum approximation and the semigeostrophic equations," J. Atmos. Sci. 32, 233 (1975).
25. A. A. White, "Modified quasi-geostrophic equations using height as a vertical coordinate," Q. J. R. Meteorol. Soc. 103, 383 (1977).
26. D. D. Holm, "Nonlinear stability of ideal fluid equilibria," in Proceedings of the Enrico Fermi School of Physics, Nonlinear Topics in Ocean Physics, edited by A. Osborne (North-Holland, Amsterdam, 1991), p. 133.
27. D. D. Holm, B. A. Kupershmidt and C. D. Levermore, "Hamiltonian differencing of fluid dynamics," Adv. Appl. Math. 6, 52 (1985).
28. J. E. Marsden and J. M. Wendlandt, "Mechanical systems with symmetry, variational principles, and integration algorithms," in Current and Future Directions in Applied Mathematics, edited by M. Alber, B. Hu, and J. Rosenthal (Birkhäuser, Bose, 1997), p. 219.
29. J. M. Wendlandt and J. E. Marsden, "Mechanical integrators derived from a discrete variational principle," UC Berkeley preprint, 1997.
30. A. F. Bennett, Inverse Methods in Physical Oceanography, Cambridge Monographs on Mechanics and Applied Mathematics (Cambridge University Press, Cambridge, 1992).