Variational formulations of sound-proof models

Quarterly Journal of the Royal Meteorological Society

Volumn 140, Issue 683, 2014, Pages 1966-1973

  Cotter, C J ^a   Holm, D D ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Anelastic; Kelvin circulation laws; Slice models; Sound proof; Variational principles

Indexed keywords

VARIATIONAL TECHNIQUES;

ANELASTIC; ANELASTIC APPROXIMATIONS; EQUILIBRIUM SOLUTIONS; HAMILTONIAN FORMULATIONS; KELVIN CIRCULATION LAWS; THREE-DIMENSIONAL (3D) SOUND; VARIATIONAL FORMULATION; VARIATIONAL PRINCIPLES;

HAMILTONIANS;

EID: 84908888400     PISSN: 00359009     EISSN: 1477870X     Source Type: Journal    
DOI: 10.1002/qj.2260     Document Type: Article

References (20)

1. Abarbanel H, Holm DD, Marsden JE, Ratiu T. 1986. Nonlinear stability analysis of stratified ideal fluid equilibria. Philos. Trans. R. Soc. 318: 349-409.
2. Bannon PR. 1995. Hydrostatic adjustment: Lamb's problem. J. Atmos. Sci. 52: 1743-1752.
3. Bannon PR. 1996. On the anelastic approximation for a compressible atmosphere. J. Atmos. Sci. 53: 3618-3628.
4. Bernardet P. 1995. The pressure term in the anelastic model: a symmetric elliptic solver for an Arakawa C grid in generalized coordinates. Mon. Weather Rev. 123: 2474-2490.
5. Cotter C, Holm D. 2013. On Noether's theorem for the Euler-Poincaré equation on the diffeomorphism group with advected quantities. Found. Comput. Math. 13: 457-477.
6. Cotter CJ, Holm DD. 2013. A variational formulation of vertical slice models. In Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 469.2155. http://arxiv.org/abs/1211.2067.
7. Cullen M. 2007. Modelling atmospheric flows. Acta Numer. 16: 67-154.
8. Durran DR. 1989. Improving the anelastic approximation. J. Atmos. Sci. 46: 1453-1461.
9. Durran DR. 2008. A physically motivated approach for filtering acoustic waves from the equations governing compressible stratified flow. J. Fluid. Mech. 601: 365-379.
10. Dutton DR, John A, Fichtl GH. 1969. Approximate equations of motion for gases and liquids. J. Atmos. Sci. 26: 241-254.
11. Holm DD, Marsden JE, Ratiu TS, Weinstein A. 1985. Nonlinear stability of fluid and plasma equilibria. Phys. Rep. 123: 1-116.
12. Holm DD, Marsden JE, Ratiu TS. 1998. The Euler-Poincaré equations and semidirect products with applications to continuum theories. Adv. Math. 137: 1-81.
13. Holm DD, Marsden JE, Ratiu TS. 2002. 'The Euler-Poincaré equations in geophysical fluid dynamics'. Large-Scale Atmosphere-Ocean Dynamics II: Geometric Methods and Models. In Proceedings of the Isaac Newton Institute Programme on the Mathematics of Atmospheric and Ocean Dynamics. Cambridge University Press: Cambridge, UK; 251-300.
14. Klein R. 2009. Asymptotics, structure, and integration of soundproof atmospheric flow equations. Theor. Comput. Fluid Dyn. 23 161-195.
15. Lipps FB, Hemler RS. 1982. A scale analysis of deep moist convection and some related numerical calculations. J. Atmos. Sci. 39: 2192-2210.
16. Marsden JE, Ratiu TS. 1995. Introduction to Mechanics and Symmetry, Texts in Applied Mathematics, 17. Springer-Verlag: Berlin.
17. Ogura Y, Phillips NA. 1962. Scale analysis for deep and shallow convection in the atmosphere. J. Atmos. Sci. 19: 173-179.
18. Scinocca JF, Shepherd TG. 1992. Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations. J. Atmos. Sci. 49: 5-27.
19. Thuburn J. 2008. Some conservation issues for the dynamical cores of NWP and climate models. J. Comput. Phys. 227: 3715-3730.
20. Visram AR, Cotter CJ, Cullen MJP. 2013. A framework for evaluating model error using asymptotic convergence in the Eady model. Q.J.R. Meteorol. Soc., doi: 10.1002/qj.2244.