The mathematical structure of theories of semigeostrophic type

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 355, Issue 1734, 1997, Pages 2489-2517

  Roulstone, I ^a   Sewell, M J ^a,b  

^a MET OFFICE   (United Kingdom)

^b UNIVERSITY OF READING   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 5344252362     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1997.0144     Document Type: Article

References (36)

1. Blumen, W. 1981 The geostrophic coordinate transformation. J. Atmos. Sci. 38, 1100-1105.
2. Broad, A. S., Porter, D. & Sewell, M. J. 1992 A new approach to shallow flow over an obstacle. I. General theory. U.K. Meteorological Office Short Range Forecasting Division Scientific paper no. 11, pp. 54.
3. Broad, A. S., Porter, D. & Sewell, M. J. 1994 Shallow flow over general topography with applications to monotonic mountains. Proc. 4th IMA Conf. on Stably Stratified Flows (ed. I. Castro & N. Rockliff), pp. 133-138. Oxford University Press.
4. Broad, A. S., Porter, D. & Sewell, M. J. 1997 New shallow flows over an obstacle. Q. Jl Appl. Math. 50, 625-653.
5. Carathéodory, C. 1982 Calculus of variations and partial differential equations of the first order, 2nd edn (revised). New York: Chelsea.
6. Chynoweth, S., Porter, D. & Sewell, M. J. 1988 The parabolic umbilic and atmospheric fronts. Proc. R. Soc. Lond. A 419, 337-362.
7. Chynoweth, S. & Sewell, M. J. 1989 Dual variables in semigeostrophic theory. Proc. R. Soc. Lond. A 424, 155-186.
8. Chynoweth, S. & Sewell, M. J. 1991 A concise derivation of the semigeostrophic equations. Q. Jl R. Met. Soc. 117, 1109-1128.
9. Cullen, M. J. P., Norbury, J. & Purser, R. J. 1991 Generalised Lagrangian solutions for atmospheric and oceanic flows. SIAM J. Appl. Math. 51, 20-31.
10. Cullen, M. J. P. & Purser, R. J. 1984 An extended Lagrangian theory of semigeostrophic frontogenesis. J. Atmos. Sci. 41, 1477-1497.
11. Eliassen, A. 1948 The quasi-static equations of motion with pressure as independent variable. Geofys. Publ. 17, 1-44.
12. Eliassen, A. 1962 On the vertical circulation in frontal zones. Geofys. Publ. 24, 147-160.
13. Fjørtoft, R. 1962 On the integration of a system of geostrophically balanced prognostic equations. Proc. Intern. Symp. Numerical Weather Prediction, pp. 153-159. Tokyo: Meteorological Society of Japan.
14. Forsyth, A. R. 1890 Theory of differential equations. Part I. Exact equations and Pfaff's problem. Cambridge University Press.
15. Forsyth, A. R. 1906 Theory of differential equations. Part IV. Partial differential equations. Cambridge University Press.
16. Hoskins, B. J. 1971 Atmospheric frontogenesis models: some solutions. Q. Jl R. Met. Soc. 97, 139-153.
17. Hoskins, B. J. 1975 The geostrophic momentum approximation and the semigeostrophic equations. J. Atmos. Sci. 32, 233-242.
18. Hoskins, B. J. & Bretherton, F. P. 1972 Atmospheric frontogenesis models: mathematical formulation and solution. J. Atmos. Sci. 29, 11-37.
19. Magnusdottir, G. & Schubert, W. H. 1990 The generalization of semigeostrophic theory to the β-plane. J. Atmos. Sci. 47, 1714-1720.
20. Magnusdottir, G. & Schubert, W. H. 1991 Semigeostrophic theory on the hemisphere. J. Atmos. Sci. 48, 1449-1456.
21. McIntyre, M. E. & Roulstone, I. 1997 Hamiltonian balanced models: constraints, slow manifolds and velocity splitting. Forecasting Research Scientific Paper 41, Meteorological Office, UK. J. Fluid Mech. (Submitted.)
22. Purser, R. J. 1988 Variational aspects of semigeostrophic theory. Meteorological Office Forecasting Research Scientific Note no. 5, pp. 20.
23. Purser, R. J. 1993 Contact transformations and Hamiltonian dynamics in generalized semi-geostrophic theories. J. Atmos. Sci. 50, 1449-1468.
24. Purser, R. J. & Cullen, M. J. P. 1987 A duality principle in semigeostrophic theory. J. Atmos. Sci. 44, 3449-3468.
25. Roulstone, I. & Sewell, M. J. 1996 Potential vorticities in semigeostrophic theory. Q. Jl R. Met. Soc. 122, 983-992.
26. Rubtsov, V. N. & Roulstone, I. 1997 Examples of quaternionic and Kahler structures in Hamiltonian models of nearly geostrophic flow. J. Phys. A 30, L63-L68.
27. Salmon, R. 1983 Practical use of Hamilton's principle. J. Fluid Mech. 132, 431-444.
28. Salmon, R. 1985 New equations for nearly geostrophic flow. J. Fluid Mech. 153, 461-477.
29. Sewell, M. J. 1987 Maximum and minimum principles. A unified approach, with applications. Cambridge University Press.
30. Sewell, M. J. 1997 Some applications of transformation theory in mechanics. UK Meteorological Office Forecasting Research Division Scientific Paper. In Proc. Isaac Newton Institute Programme on the Mathematics of Atmosphere and Ocean Dynamics, Cambridge, July-December 1996. Cambridge University Press.
31. Sewell, M. J. & Porter, D. 1980 Constitutive surfaces in fluid mechanics. Math. Proc. Camb. Phil. Soc. 88, 517-546.
32. Sewell, M. J. & Roulstone, I. 1993 Anatomy of the canonical transformation. Phil. Trans. R. Soc. Lond. A 345, 577-598.
33. Sewell, M. J. & Roulstone, I. 1994 Families of lift and contact transformations. Proc. R. Soc. Lond. A 447, 493-512.
34. Shutts, G. J. 1989 Planetary semigeostrophic equations derived from Hamilton's principle. J. Fluid Mech. 208, 545-573.
35. Shutts, G. J. & Cullen, M. J. P. 1987 Parcel stability and its relation to semigeostrophic theory. J. Atmos. Sci. 44, 1318-1330.
36. Stoker, J. J. 1957 Water waves. New York: Interscience.