Exact axisymmetric solutions of the deep- and shallow-atmosphere Euler equations in curvilinear and plane geometries

Quarterly Journal of the Royal Meteorological Society

Volumn 139, Issue 673, 2013, Pages 1113-1120

  Staniforth, Andrew ^a   Wood, Nigel ^a  

^a MET OFFICE   (United Kingdom)

Author keywords

Baroclinic wave test; Beta gamma plane; Dynamical core; Model validation; Spherical geometry; Spheroidal geometry

Indexed keywords

EID: 84879232310     PISSN: 00359009     EISSN: 1477870X     Source Type: Journal    
DOI: 10.1002/qj.2018     Document Type: Note

References (15)

1. Davies T, Cullen MJP, Malcolm A, Mawson M, Staniforth A, White AA, Wood N. 2005. A new dynamical core for the Met Office's global and regional modelling of the atmosphere. Q. J. R. Meteorol. Soc. 131: 1759-1782.
2. Dellar PJ. 2011. Variations on a beta-plane: derivation of non-traditional beta-plane equations from Hamilton's principle on a sphere. J. Fluid Mech. 674: 174-195.
3. Gill AE. 1982. Atmosphere-ocean dynamics. Academic Press: London.
4. Jablonowski C, Williamson DL. 2006. A baroclinic instability test case for atmospheric model dynamical cores. Q. J. R. Meteorol. Soc. 132: 2943-2975.
5. Lauritzen PH, Jablonowski C, Taylor MA, Nair RD. 2010. Rotated versions of the Jablonowski steady-state and baroclinic wave test cases: A dynamical core intercomparison. J. Adv. Model. Earth Syst. 2: Art. 15.
6. Staniforth A. 2012. Exact stationary axisymmetric solutions of the Euler equations on beta-gamma planes. Atmos. Sci. Lett. 13: 79-87.
7. Staniforth A, White AA. 2011. Further non-separable exact solutions of the deep- and shallow-atmosphere equations. Atmos. Sci. Lett. 12: 356-361.
8. Staniforth A, White AA, Wood N. 2010. Treatment of vector equations in deep-atmosphere, semi-Lagrangian models. I: Momentum equation. Q. J. R. Meteorol. Soc. 136: 497-506.
9. Thuburn J, Wood N, Staniforth A. 2002. Normal modes of deep atmospheres. II: f-F-plane geometry. Q. J. R. Meteorol. Soc. 128: 1793-1806.
10. Ullrich PA, Jablonowski C. 2012. Operator-split Runge-Kutta-Rosenbrock methods for non-hydrostatic atmospheric models. Mon. Weather Rev. 140: 1257-1284.
11. 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.
12. White AA, Staniforth A. 2008. A generalized thermal wind equation and some non-separable exact solutions of the flow equations for three-dimensional spherical atmospheres. Q. J. R. Meteorol. Soc.: 134: 1931-1939.
13. White AA, Staniforth A, Wood N. 2008. Spheroidal coordinate systems for modelling global atmospheres. Q. J. R. Meteorol. Soc. 134: 261-270.
14. White AA, Wood N. 2012. Consistent approximate models of the global atmosphere in non-spherical geopotential coordinates. Q. J. R. Meteorol. Soc. 138: 980-988.
15. Williamson DL, Olson JG, Jablonowski C. 2009. Two dynamical core formulation flaws exposed by a baroclinic instability test case. Mon. Weather Rev. 137: 790-796.