A semihydrostatic theory of gravity-dominated compressible flow

Journal of the Atmospheric Sciences

Volumn 71, Issue 12, 2014, Pages 4621-4638

  Dubos, Thomas ^a   Voitus, Fabrice ^b  

^a ECOLE POLYTECHNIQUE   (France)

^b CENTRE NATIONAL DE RECHERCHES MÉTÉOROLOGIQUES   (France)

Author keywords

Anelastic models; Conservation equations; General circulation models; Nonhydrostatic models

Indexed keywords

ACOUSTIC WAVE PROPAGATION; ACOUSTICS; BUDGET CONTROL; DEGREES OF FREEDOM (MECHANICS); DISPERSIONS; HYDRAULICS; LAGRANGE MULTIPLIERS; MECHANICAL WAVES; MECHANICS; SURFACE WAVES;

ANELASTIC MODELS; COMPRESSIBLE EULER EQUATIONS; CONSERVATION EQUATIONS; GENERAL CIRCULATION MODEL; HYDROSTATIC PRIMITIVE EQUATIONS; NON-HYDROSTATIC PRESSURE; NONHYDROSTATIC MODEL; SYMMETRIC POSITIVE DEFINITE;

EULER EQUATIONS;

ACCURACY ASSESSMENT; ACOUSTIC WAVE; COMPRESSIBLE FLOW; EULERIAN ANALYSIS; GENERAL CIRCULATION MODEL; GRAVITY WAVE; INTERNAL WAVE; POTENTIAL TEMPERATURE; RICHARDSON NUMBER; ROSSBY WAVE;

EID: 84916201191     PISSN: 00224928     EISSN: 15200469     Source Type: Journal    
DOI: 10.1175/JAS-D-14-0080.1     Document Type: Article

References (32)

1. Almgren, A. S., 2000: A new look at the pseudo-incompressible solution to Lamb's problem of hydrostatic adjustment. J. Atmos. Sci., 57, 995-998, doi:10.1175/1520-0469(2000)057,0995: ANLATP.2.0.CO;2.
2. Arakawa, A., and C. S. Konor, 2009: Unification of the anelastic and quasi-hydrostatic systems of equations. Mon. Wea. Rev., 137, 710-726, doi:10.1175/2008MWR2520.1.
3. Bernardet, P., 1995: The pressure term in the anelastic model: A symmetric elliptic solver for an Arakawa C grid in generalized coordinates. Mon. Wea. Rev., 123, 2474-2490, doi:10.1175/ 1520-0493(1995)123,2474:TPTITA.2.0.CO;2.
4. Cotter, C. J., and D. D. Holm, 2013: Variational formulations of sound-proof models. Quart. J. Roy. Meteor. Soc., 140, 1966- 1973, doi:10.1002/qj.2260.
5. Cressman, G. P., 1958: Barotropic divergence and very long atmospheric waves. Mon. Wea. Rev., 86, 293-297, doi:10.1175/ 1520-0493(1958)086,0293:BDAVLA.2.0.CO;2.
6. Davies, T., A. Staniforth, N. Wood, and J. Thuburn, 2003: Validity of anelastic and other equation sets as inferred from normalmode analysis. Quart. J. Roy. Meteor. Soc., 129, 2761-2775, doi:10.1256/qj.02.1951.
7. Dubos, T., and M. Tort, 2014: Equations of atmospheric motion in non-Eulerian vertical coordinates: Vector-invariant form and Hamiltonian formulation. Mon. Wea. Rev., 142, 3860-3880, doi:10.1175/MWR-D-14-00069.1.
8. Dukowicz, J. K., 2013: Evaluation of various approximations in atmosphere and ocean modeling based on an exact treatment of gravity wave dispersion. Mon. Wea. Rev., 141, 4487-4506, doi:10.1175/MWR-D-13-00148.1.
9. Durran, D. R., 1989: Improving the anelastic approximation. J. Atmos. Sci., 46, 1453-1461, doi:10.1175/1520-0469(1989)046,1453: ITAA.2.0.CO;2.
10. Durran, D. R., 2008: A physically motivated approach for filtering acoustic waves from the equations governing compressible stratified flow. J. Fluid Mech., 601, 365-379, doi:10.1017/S0022112008000608.
11. Holm, D. D., J. E. Marsden, and T. S. Ratiu, 1998: The Euler- Poincaré equations and semidirect products with applications to continuum theories. Adv. Math., 137, 1-81, doi:10.1006/ aima.1998.1721.
12. Holm, D. D., J. E. Marsden, and T. S. Ratiu, 2002: The Euler-Poincaré equations in geophysical fluid dynamics. Large-Scale Atmosphere-Ocean Dynamics, Vol. 2, Geometric Methods and Models, J. Norbury and I. Roulstone, Eds., Cambridge University Press, 251-299.
13. Jung, J.-H., and A. Arakawa, 2008: A three-dimensional anelastic model based on the vorticity equation. Mon. Wea. Rev., 136, 276-294, doi:10.1175/2007MWR2095.1.
14. Kasahara, A., 1974: Various vertical coordinate systems used for numerical weather prediction. Mon. Wea. Rev., 102, 509-522, doi:10.1175/1520-0493(1974)102,0509:VVCSUF.2.0.CO;2.
15. Klein, R., and O. Pauluis, 2012: Thermodynamic consistency of a pseudoincompressible approximation for general equations of state. J. Atmos. Sci., 69, 961-968, doi:10.1175/JAS-D-11-0110.1.
16. Konor, C. S., 2014: Design of a dynamical core based on the nonhydrostatic ''unified system'' of equations. Mon. Wea. Rev., 142, 364-385, doi:10.1175/MWR-D-13-00187.1.
17. Laprise, R., 1992: The Euler equations of motion with hydrostatic pressure as an independent variable. Mon.Wea. Rev., 120, 197-207, doi:10.1175/1520-0493(1992)120,0197: TEEOMW.2.0.CO;2.
18. Lipps, F. B., and R. S. Hemler, 1982: A scale analysis of deep moist convection and some related numerical calculations. J. Atmos. Sci., 39, 2192-2210, doi:10.1175/1520-0469(1982)039,2192: ASAODM.2.0.CO;2.
19. Madden, R. A., 2007: Large-scale, free Rossby waves in the atmosphere-An update. Tellus, 59A, 571-590, doi:10.1111/ j.1600-0870.2007.00257.x.
20. Morrison, P. J., 1998:Hamiltonian description of the ideal fluid. Rev. Mod. Phys., 70, 467-521, doi:10.1103/RevModPhys.70.467.
21. Newcomb, W. A., 1962: Lagrangian and Hamiltonian methods in magnetohydrodynamics. Nucl. Fusion, (Suppl.), 451-463.
22. Ogura, Y., and N. A. Phillips, 1962: Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci., 19, 173-179, doi:10.1175/1520-0469(1962)019,0173:SAODAS.2.0.CO;2.
23. O'Neill, W. P., and R. Klein, 2014: A moist pseudoincompressible model. Atmos. Res., 142, 133-141, doi:10.1016/j.atmosres.2013.08.004.
24. Ooyama, K. V., 1990:Athermodynamic foundation for modeling the moist atmosphere. J. Atmos. Sci., 47, 2580-2593, doi:10.1175/ 1520-0469(1990)047,2580:ATFFMT.2.0.CO;2.
25. Richardson, L. F., 1922: Weather Prediction by Numerical Process. Cambridge University Press, 236 pp.
26. Salmon, R., 1983: Practical use of Hamilton's principle. J. Fluid Mech., 132, 431-444, doi:10.1017/S0022112083001706.
27. Skamarock, W. C., and J. B. Klemp, 2008: A time-split nonhydrostatic atmospheric model for weather research and forecasting applications. J. Comput. Phys., 227, 3465-3485, doi:10.1016/j.jcp.2007.01.037.
28. Smolarkiewicz, P. K., C. Kühnlein, and N. P. Wedi, 2014: A consistent framework for discrete integrations of soundproof and compressible PDEs of atmospheric dynamics. J. Comput. Phys., 263, 185-205, doi:10.1016/j.jcp.2014.01.031.
29. Tort, M., and T. Dubos, 2014a: Dynamically consistent shallowatmosphere equations with a complete Coriolis force. Quart. J. Roy. Meteor. Soc., 140, 2388-2392, doi:10.1002/qj.2274.
30. Tort, M., and T. Dubos, 2014b: Usual approximations to the equations of atmospheric motion: A variational perspective. J. Atmos. Sci., 71, 2452-2466, doi:10.1175/JAS-D-13-0339.1.
31. Weller, H., S.-J. Lock, and N. Wood, 2013: Runge-Kutta IMEX schemes for the horizontally explicit/vertically implicit (HEVI) solution of wave equations. J. Comput. Phys., 252, 365-381, doi:10.1016/j.jcp.2013.06.025.
32. White, A. A., and R. A. Bromley, 1995: Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force. Quart. J. Roy. Meteor. Soc., 121, 399-418, doi:10.1002/qj.49712152208.