Dynamically consistent shallow-atmosphere equations with a complete Coriolis force

Quarterly Journal of the Royal Meteorological Society

Volumn 140, Issue 684, 2014, Pages 2388-2392

  Tort, M ^a   Dubos, T ^a  

^a ECOLE POLYTECHNIQUE   (France)

Author keywords

Complete Coriolis force; Conservation laws; Hamilton's Principle; Shallow atmosphere approximation

Indexed keywords

EARTH ATMOSPHERE; METEOROLOGY;

CONSERVATION LAW; CONSERVATION OF ENERGY; HAMILTON'S PRINCIPLE; NON-HYDROSTATIC; PLANETARY ROTATION; POTENTIAL VORTICITY; SHALLOW-ATMOSPHERE APPROXIMATION; TRADITIONAL APPROXIMATION;

CORIOLIS FORCE;

EID: 84922953736     PISSN: 00359009     EISSN: 1477870X     Source Type: Journal    
DOI: 10.1002/qj.2274     Document Type: Article

References (22)

1. Dellar PJ. 2011. Variations on a β-plane: Derivation of non-traditional β-plane equations from Hamilton's principle on a sphere. J. Fluid Mech. 674: 174-195.
2. Dellar PJ, Salmon R. 2005. Shallow-water equations with a complete Coriolis force and topography. Phys. Fluids 17: 106601-106619, doi: 10.1063/1.2116747.
3. Dubois E. 1885. Résumé analytique de la théorie des marées telle qu'elle est établie dans la mécanique céleste de Laplace. Revue Maritime et Coloniale 85: 116-154.
4. Eckart C. 1960. Hydrodynamics of Oceans and Atmospheres. Pergamon: New York, NY.
5. Gerkema T, Zimmerman JTF, Maas LRM, van Haren H. 2008. Geophysical and astrophysical fluid dynamics beyond the traditional approximation. Rev. Geophys. 46: RG2004, doi: 10.1029/2006RG000220.
6. Hayashi M, Itoh H. 2012. The importance of the non-traditional Coriolis terms in large-scale motions in the tropics forced by prescribed cumulus heating. J. Atmos. Sci. 69: 2699-2716.
7. Holm DD, Marsden JE, Ratiu TS. 2002. The Euler-Poincaré Equations in Geophysical Fluid Dynamics, 2. Cambridge University Press: Cambridge, UK.
8. Hua BL, Moore DW, LeGentil S. 1997. Inertial nonlinear equilibration of equatorial flows. J. Fluid Mech. 331: 345-371.
9. Morrison P. 1998. Hamiltonian description of the ideal fluid. Rev. Mod. Phys. 70: 467-521.
10. Phillips NA. 1966. The equations of motion for a shallow rotating atmosphere and the 'traditional approximation'. J. Atmos. Sci. 23: 626-628.
11. Phillips NA. 1968. Reply. J. Atmos. Sci. 25: 1155-1157.
12. Raymond WH. 2000. Equatorial meridional flows: Rotationally induced circulations. Pure Appl. Geophys. 157: 1767-1779.
13. Roulstone I, Brice SJ. 1995. On the Hamiltonian formulation of the quasi-hydrostatic equations. Q. J. R. Meteorol. Soc. 121: 927-936.
14. Salmon R. 1988. Hamiltonian fluid mechanics. Annu. Rev. Fluid Mech. 20: 225-256.
15. Staniforth A. 2012. Exact stationary axisymmetric solutions of the Euler equations on β-γ planes. Atmos. Sci. Lett. 13: 79-87.
16. Stewart AL, Dellar PJ. 2011a. Cross-equatorial flow through an abyssal channel under the complete Coriolis force: Two-dimensional solutions. Ocean Modell. 40: 87-104.
17. Stewart AL, Dellar PJ. 2011b. The rôle of the complete Coriolis force in cross-equatorial flow of abyssal ocean currents. Ocean Modell. 38 187-202.
18. Vallis GK. 2006. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press: Cambridge, UK.
19. Veronis G. 1968. Comments on Phillips' proposed simplification of the equations of motion for a shallow rotating atmosphere. J. Atmos. Sci. 25: 1154-1155.
20. Wangsness RK. 1970. Comments on the equations of motion for a shallow rotating atmosphere and the 'traditional approximation'. J. Atmos. Sci. 27: 504-506.
21. White AA, Bromley RA. 1995. Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force. Q. J. R. Meteorol. Soc. 121: 399-418.
22. White AA, Hoskins BJ, Roulstone I, Staniforth A. 2005. Consistent approximate models of the global atmosphere: Shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic. Q. J. R. Meteorol. Soc. 131: 2081-2107.