A mathematical theory of large-scale atmosphere/ocean flow

A Mathematical Theory of Large-Scale Atmosphere/Ocean Flow

Volumn , Issue , 2006, Pages 1-260

  Cullen, Michael J P ^a  

^a MET OFFICE   (United Kingdom)

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EID: 84967647240     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/P375     Document Type: Book

References (156)

1. Adams, R. A. (1975) Sobolev spaces. Academic Press, New York.
2. Allen, J. S., Barth, J. A. and Newberger, P. (1990) On intermediate models for barotropic continental shelf and slope flow fields. Paxt III: Comparison of numerical model solutions in periodic channels. J. Phys. Oceanog. 20, pp. 1949-1973.
3. Ambrosio, L. (2003) Transport equation and Cauchy problem for BV vector fields. Invent. Math. 158, pp. 227-260.
4. Angenent, S., Haker, S. and Tannenbaum, A. (2003) Minimising flows for the Monge-Kantorovich problem. S. I. A. M. J. Math. Anal. 359, pp. 61-97.
5. Babin, A., Mahalov, A. and Nicolaenko, B. (1999), Global regularity of 3D rotating Navier-Stokes equations for resonant domains. Indiana University Mathematics Journal 48, pp. 1133-1176.
6. Babin, A., Mahalov, A. and Nicolaenko, B. (1999) Fast singular oscillating limits of stably stratified 3-D Euler and Navier-Stokes equations and ageostrophic wave fronts. In Large-Scale Atmosphere-Ocean Dynamics, J. Norbury and I. Roulstone eds., Cambridge University Press, vol. I, pp. 126-201.
7. Benamou, J.-D. and Brenier, Y. (1997) A numerical method for the optimal time-continuous mass transport problem and related problems. In Monge-Ampere equations: applications to geometry and optimisation. (Deerfield Beach, FL. 1997). Contemporary Math., Amer. Math. Soc. 226, pp. 1-11.
8. Benamou, J.-D. and Brenier, Y. (1998) Weak existence for the semi-geostrophic equations formulated as a coupled Monge-Ampere/transport problem. SIAM J. Appl. Math. 58, pp. 1450-1461.
9. Bennetts, D. A. and Hoskins, B. J. (1979) Conditional symmetric instability-a possible explanation for frontal rainbands. Quart. J. Roy. Meteor. Soc. 105, pp. 945-962.
10. Bogue, N. M., Huang, R. X. and Bryan, K. (1986) Verification experiments with an isopycnal coordinate ocean model. J. Phys. Oceanogr. 16, pp. 985-990.
11. Bourgeois, A. J. and Beale, J. T. (1994) Validity of the quasigeostrophic model for large-scale flow in the atmosphere and ocean. SIAM J. Math. Anal. 25, pp. 1023-1068.
12. Brenier, Y. (1991) Polar factorisation and monotone rearrangement of vector-valued functions. Commun. Pure Appl. Math. 44, pp. 375-417.
13. Burton, G. R. and Douglas, R. J. (1998) Rearrangements and polar factorisation of countably degenerate functions. Proc. Roy. Soc. Edin. 128A, pp. 671-681.
14. Burton, G. R. and McLeod, J. B. (1991) Maximisation and minimisation on classes of rearrangements. Proc. Roy. Soc. Edin. 119A, pp. 287-300.
15. Burton, G. R. and Nycander, J. (1999) Stationary vortices in three-dimensional quasi-geostrophic flow. J. Fluid Mech. 389, pp. 255-274.
16. Caffarelli, L. A. (1992) The regularity of mappings with a convex potential. J. A. M. S. 5, pp. 99-104.
17. Caffarelli, L. A. (1992) Boundary regularity of maps with convex potentials. Comm. Pure Appl. Math. 45, pp. 1141-1151.
18. Caffarelli, L. A. (1996) Boundary regularity of maps with convex potentials-II. Ann. Math. 144, pp. 453-496.
19. Charney, J. G. (1949) On the scale of atmospheric motions. Geofys. Publ. 17, (2) 17pp.
20. Charney, J. G. (1971) Geostrophic turbulence. J. Atmos. Sci., 28, pp. 1087-1095.
21. Charney, J. G. and Devore, J. (1979) Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci., 36, pp. 1205-1216.
22. Charney, J. G., Fjortoft, R. and von Neumann, J. (1950) Numerical integration of the barotropic vorticity equations. Tellus 2, pp. 237-254.
23. Chemin, J-Y. Perfect incompressible fluids. Oxford University Press, 185pp.
24. Chynoweth, S. (1987) The semi-geostrophic equations and the Legendre transform. Ph. D thesis. University of Reading, Whiteknights, PO Box 220, Reading, RG6 2AX, U. K., 248pp.
25. Chynoweth, S. and Sewell, M. J. (1989) Dual variables in semi-geostrophic theory. Proc. Roy. Soc. Lond. A424, pp. 155-186.
26. Cloke, P. and Cullen, M. J. P. (1994) A semi-geostrophic ocean model with outcropping. Dyn. Atmos. Ocean. 21, pp. 23-48.
27. Cordero-Erausquin, D. (1999) Sur le transport de mesures périodiques. C. R. Acad. Sci. Paris Ser. I Math. 329, pp. 199-202.
28. Craig, G. C. (1991) A three-dimensional generalisation of Eliassen's balanced vortex equations derived from Hamilton's principle. Quart. J. Roy. Meteor. Soc. 117, pp. 435-448.
29. Cullen, M. J. P. and Purser, R. J. (1984) An extended Lagrangian theory of semi-geostrophic frontogenesis. J. Atmos. Sci. 41, pp. 1477-1497.
30. Cullen, M. J. P., Chynoweth, S. and Purser, R. J. (1987) On semi-geostrophic flow over synoptic-scale topography. Quart. J. Roy. Meteor. Soc. 113, pp. 163-180.
31. Cullen, M. J. P. (1989) On the incorporation of atmospheric boundary layer effects into a balanced model. Quart. J. Roy. Meteor. Soc. 115, pp. 1109-1131.
32. Cullen, M. J. P. (1989) Implicit finite difference methods for modelling discontinuous atmospheric flows. J. Comp. Phys. 81, pp. 319-348.
33. Cullen, M. J. P. and Purser, R. J. (1989) Properties of the Lagrangian semi-geostrophic equations. J. Atmos. Sci. 46, pp. 2684-2697.
34. Cullen, M. J. P. and Mawson, M. H. (1992) An idealised simulation of the Indian monsoon using primitive-equation and quasi-equilibrium models. Quart. J. Roy. Meteor. Soc. 118, pp. 153-164.
35. Cullen, M. J. P. and Roulstone, I. (1993) A geometric model of the nonlinear equilibration of two-dimensional Eady waves. J. Atmos. Sci. 50, pp. 328-332.
36. Cullen, M. J. P. (2000) On the accuracy of the semi-geostrophic approximation. Quart. J. Roy. Meteor. Soc. 126, pp. 1099-1115.
37. Cullen, M. J. P. and Gangbo, W. (2001) A variational approach for the 2-D semi-geostrophic shallow water equations. Arch. Rat. Mech. Anal. 156, pp. 241-273.
38. Cullen, M. J. P. and Maroofi, H. (2003) The fully compressible semi-geostrophic system from meteorology. Arch. Rat. Mech. Anal. 167, pp. 309-336.
39. Cullen, M. J. P. (2002) Large scale non-turbulent dynamics in the atmosphere. Quart. J. Roy. Meteorol. Soc. 128, pp. 2623-2640.
40. Cullen, M. J. P. and Douglas, R. J. (2003) Large amplitude nonlinear stability results for atmospheric circulations. Quart. J. Roy. Meteorol. Soc. 129, pp. 1969-1988.
41. Cullen, M. J. P. and Salmond, D. J. (2003) On the use of a predictor-corrector scheme to couple the dynamics with the physical parametrizations in the ECMWF model. Quart. J. Roy. Meteorol. Soc. 129, pp. 1217-1236.
42. Cullen, M. J. P., Douglas, R. J., Roulstone, I. and Sewell, M. J. (2005) Generalised semi-geostrophic theory on a sphere. J. Fluid Mech. 531, pp. 123-157.
43. Cullen, M. J. P. and Feldman, M. (2004) Lagrangian solutions of semi-geostrophic equations in physical space. SIAM J. Math. Anal., to appear.
44. Davies, T., Cullen, M. J. P., Malcolm, A. J., Mawson, M. H., Staniforth, A., White, A. A. and Wood, N. (2005) A new dynamical core for the Met Office's global and regional modelling of the atmosphere. Quart. J. Roy. Meteorol. Soc. 131, pp. 1759-1782.
45. DiPerna, R. J. and Lions, P. L. (1989) Ordinary differential equations, transport theory, and Sobolev spaces. Invent. Math. 98, pp. 511-547.
46. Douglas, R. J. (1994) Rearrangements of functions on unbounded domains. Proc. Roy. Soc. Edin. 124A, pp. 621-644.
47. Douglas, R. J. (2002) Rearrangements of functions with application to meteorology and ideal fluid flow. In Large-Scale Atmosphere-Ocean Dynamics, J. Norbury and I. Roulstone eds., Cambridge University Press, vol. I, pp. 288-341.
48. Elhmaidi, D., Provencale, A. and Babiano, A. (1993) Elementary topology of twodimensional turbulence from a Lagrangian viewpoint and single-particle dispersion. J. Fluid Mech. 257, pp. 533-558.
49. Eliassen, A. (1949) The quasi-static equations of motion with pressure as an independent variable. Geofys. Publ. 17, 44pp.
50. Eliassen, A. and Kleinschmidt, E. (1957) Dynamic meteorology. Handbuch der Physik, Geophysik II. Springer Verlag, p. 154.
51. Emanuel, K. A. (1983) The Lagrangian parcel dynamics of moist symmetric instability. J. Atmos. Sci. 40, pp. 2368-2376.
52. Fincham, A. M., Maxworthy, T. and Spedding, G. R. (1996) The horizontal and vertical structure of the vorticity field in freely-decaying stratified grid turbulence. Dyn. Atmos. Ocean. 23, pp. 153-160.
53. Ford, R., McIntyre, M. E. and Norton, W. A. (2000) Balance and the slow quasimanifold: some explicit results. J. Atmos. Sci. 57, pp. 1236-1254.
54. Fjortoft, R. (1946) On the frontogenesis and cyclogenesis in the atmosphere. Part I. On the stability of the stationary circular vortex. Geofys. Publik. 16(5), pp. 1-28.
55. Fjortoft, R. (1950) Applications of integral theorems in deriving criteria of stability for laminar flows and for the baroclinic circular vortex. Geofys. Publ. 17(6).
56. Handbook of weather forecasting. Meteorological Office Met. O, No. 875 London, Meteorological Office, 1975.
57. Gangbo, W. and McCann, R. J. (1996) The geometry of optimal transportation. Acta Math. 177, pp. 113-161.
58. Gérard, P. 1992 Résultats récents sur les fluides parfaits incompressibles bidimen-sionnels. Seminaire Bourbaki 757, pp. 411-444.
59. Gill, A. E. (1982) Atmosphere-Ocean Dynamics. Academic Press. 662pp.
60. Godson, W. L. (1950) Generalised criteria for dynamic instability. J. Meteor. 7, pp. 268-278.
61. Gordon, A., Grace, W., Schwerdtfeger, P. and Byron-Scott, R. (1998) Dynamic Meteorology: a Basic Course. Arnold, 325pp.
62. Halmos, P. R. (1950) Measure Theory, van Nostrand.
63. Haltiner, G. J. and Williams, R. T. (1980) Numerical Prediction and Dynamic Meteorology. John Wiley. 477pp.
64. Haynes, P. H. and McIntyre, M. E. (1990) On the conservation and impermeability theorems for potential vorticity. J. Atmos. Sci. 47, pp. 2021-2031.
65. Holm, D. D. (1996) Hamiltonian balance equations. Physica D, 98, pp. 379-414.
66. Holt, M. W. (1990) Semi-geostrophic moist frontogenesis in a Lagrangian model. Dyn. Atmos. Ocean. 14, pp. 463-481.
67. Holt, M. W. and Thorpe, A. J. (1991) Localised forcing of slantwise motion at fronts. Quart. J. Roy. Meteorol. Soc. 117, pp. 943-963.
68. Holton, J. R. (1992) An Introduction to Dynamic Meteorology. Academic Press. 511 pp.
69. Hoskins, B. J. and Bretherton, F. P. (1972) Atmospheric frontogenesis models: formulation and solutions. J. Atmos. Sci. 29, pp. 233-242.
70. Hoskins, B. J. (1975) The geostrophic momentum approximation and the semi-geostrophic equations. J. Atmos. Sci. 32, pp. 233-242.
71. Hoskins, B. J. and Draghici, I. (1977) The forcing of ageostrophic motion according to the semi-geostrophic equations and in an isentropic coordinate model. J. Atmos. Sci. 34, pp. 1859-1867.
72. Hoskins, B. J. and West, N. V. (1979) Baroclinic waves and frontogenesis. Part II: uniform potential vorticity jet flows-cold and warm fronts. J. Atmos. Sci. 36, pp. 1663-1680.
73. Hoskins, B. J. (1982) The mathematical-theory of frontogenesis. Ann. Rev. Fluid Mech. 14, pp. 131-151.
74. Hoskins, B. J., McIntyre, M. E. and Robertson, A. W. (1985) On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteorol. Soc. 111, pp. 877-946. Also 113, pp. 402-404.
75. Kantorovich, L. (1942) On the Translocation of Masses. C. R. (Doklady) Acad. Sci. URSS (N. S.) 37, pp. 199-201.
76. Kushner, P. J. and Shepherd, T. G. (1995a) Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: Part 1. Pseudomomentum based theory. J. Fluid Mech. 290, pp. 67-104.
77. Kushner, P. J. and Shepherd, T. G. (1995b) Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: Part 2. Pseudo-energy based theory. J. Fluid Mech. 290, pp. 105-129.
78. Larichev, V. D. and McWilliams, J. C. (1991) Weakly decaying turbulence in an equivalent-barotropic fluid. Phys. Fluids A, 3(5), pp. 938-950.
79. Leith, C. E. and Kraichnan, R. E., (1972) Predictablity of turbulent flows. J. Atmos. Sci. 29, pp. 1041-1052
80. Lions, J.-L., Temam, R. and Wang, S. (1992) On the equations of the large-scale ocean. Nonlinearity 5, pp. 237-288.
81. Loeper, G. (2004) The semi-geostrophic equations. Preprint, EPFL, SB, IMA Lausanne.
82. Lorenz, E. N. (1963) Deterministic non-periodic flow. J. Atmos. Sci. 20, pp. 131-141.
83. Lorenz, E. N. (1963) The slow manifold-What is it? J. Atmos. Sci. 49, pp. 2449-2451.
84. Lynch, P. (1989) The slow equations. Quart. J. Roy. Meteorol. Soc. 115, pp. 201-219.
85. McCann, R. J. (1995) Existence and uniqueness of monotone measure preserving maps. Duke Math. J. 80, pp. 309-323.
86. McCann, R. J. (1997) A convexity principle for interacting gases. Adv. Math. I, pp. 153-179.
87. McCann, R. J. (2001) Polar factorisation of maps on Riemannian manifolds. Geom. Fund. Anal. 11, pp. 589-608.
88. McIntyre, M. E. and Roulstone, I. (2002) Are there higher-accuracy analogues of semi-geostrophic theory. In Large-Scale Atmosphere-Ocean Dynamics, J. Norbury and I. Roulstone eds., Cambridge University Press, vol. II, pp. 301-364.
89. McWilliams, J. C. and Yavneh, I. (1998) Fluctuation growth and instability associated with a singularity of the balance equations. Phys. Fluids 10, pp. 2587-2596.
90. McWilliams, J. C., Yavneh, I., Cullen, M. J. P. and Gent, P. R. (1999) The breakdown of large-scale flows in rotating, stratified fluids. Phys. Fluids 10, pp. 3178-3184.
91. Majda, A. J. (1984) Compressible fluid flow, and systems of conservation laws in several space variables. Applied Mathematical Sciences, 53, Springer, New York.
92. Majda, A. J. (2003) Introduction to PDEs and waves for the atmosphere and ocean. Courant Lecture Notes, 9, American Math. Society.
93. Magnusdottir, G. and Schubert, W. H. (1991) Semi-geostrophic theory on the hemisphere. J. Atmos. Sci. 48, pp. 1449-1456.
94. Malardel, S., Thorpe, A. J. and Joly, A. (1997) Consequences of the geostrophic momentum approximation on barotropic instability. J. Atmos. Sci. 54, pp. 103-112.
95. Mawson, M. H. (1996) A shallow water semi-geostrophic model on a sphere. Quart. J. Roy. Meteorot. Soc. 122, pp. 267-290.
96. Mohebalhojeh, A. R. and Dritschel, D. G. (2001) Hierarchies of balance conditions for the f-plane shallow water equations. J. Atmos. Sci., 58, pp. 2411-2426.
97. Monge, G. (1781) Mémoire sur la théorie des déblais et de remblais. Memoires de l'Academie des Sciences, pp. 686-704.
98. Muraki, D. J., Snyder C., and Rotunno R. (1999) The next-order corrections to quasigeostrophic theory. J. Atmos. Sci. 56, pp. 1547-1560.
99. Nakamura, N. and Held, I. M. (1989) Nonlinear equilibriation of two-dimensional Eady waves. J. Atmos. Sci. 46, pp. 3055-3064.
100. Nakamura, N. (1994) Nonlinear equilibriation of two-dimensional Eady waves: simulations with viscous geostrophic momentum equations. J. Atmos. Sci. 51, pp. 1023-1035.
101. Neumann, C. J. (1993) 1993 Global overview. Chapter 1 in Holland, G. J. (ed.) Global guide to tropical cyclone forecasting. WMO/TD 560, TCP Report 31.
102. Norbury, J. and Roulstone, I. (2002) Large-scale atmosphere-ocean dynamics, Vols. I and II, Cambridge University Press, 2002.
103. Ostdiek, V. and Blumen, W. (1997) A dynamic trio: inertial oscillation, deformation frontogenesis, and the Ekman-Taylor boundary layer. J. Atmos. Sci. 54, pp. 1490-1502.
104. Parsons, A. T. (1969) A two-layer model of Gulf Stream separation. J. Fluid Mech. 39, pp. 511-528.
105. Pedder, M. A. and Thorpe, A. J. (1999) The semi-geostrophic diagnosis of vertical motion. I: Formulation and coordinate transformations. Quart. J. Roy. Meteorol. Soc. 125, pp. 1231-1256.
106. Pedlosky, J. (1987) Geophysical fluid dynamics. Springer-Verlag.
107. Phillips, N. A. (1963) Geostrophic motion. Rev. Geophysics, 1, pp. 123-176.
108. Phillips, N. A. (2000) The start of numerical weather prediction in the United States. Proc. 50th Anniversary of Numerical Weather Prediction., Deutsche Meteorologische Gesellschaft, pp. 13-28.
109. Pogorelov, A. V. (1964) Monge-Ampère equations of elliptic type. Noordhoff, Groningen, 114pp.
110. Preparata, F. P., and Hong, S. J. (1977) Convex hulls of finite sets of points in two and three dimensions. Comm. A. C. M. 20, pp. 87-93.
111. Purser, R. J. and Cullen, M. J. P. (1987) A duality principle in semi-geostrophic theory. J. Atmos. Sci. 44, pp. 3449-3468.
112. Purser, R. J. (2002) Legendre-transformable semi-geostrophic theories. In Large-Scale Atmosphere-Ocean Dynamics, J. Norbury and I. Roulstone eds., Cambridge University Press, vol. II, pp. 224-250.
113. Rasmussen, E. (1985) A case study of a polar low development over the Barents Sea. Tellus 37A, pp. 407-418.
114. Reed, R. J. and Albright, M. D. (1986) A case study of explosive cyclogenesis in the Eastern Pacific. Mon. Weather Rev. 114, pp. 2297-2319.
115. Ren, S. (2000a) Finite-amplitude wave-activity invariants and nonlinear stability theorems for shallow water semi-geostrophic dynamics. J. Atmos. Sci. 57, pp. 3388-3397.
116. Reiser, H. The development of numerical weather prediction in Deutsche Wetter-dienst. Proc. 50th Anniversary of Numerical Weather Prediction., Deutsche Meteorologische Gesellschaft, pp. 51-80.
117. Richardson, L. F. (1922) Weather prediction by numerical process. Cambridge University Press. 236pp (also from Dover Publications Inc., New York, 1965).
118. Robert, R. and Sommeria, J. (1991) Statistical equilibrium states for twodimensional flows. J. Fluid Mech. 229, pp. 291-310.
119. Rockafellar, R. T. (1970) Convex analysis. Princeton University Press, 451pp.
120. Roulstone, I. and Norbury, J. (1994) A Hamiltonian structure with contact geometry for the semi-geostrophic equations. J. Fluid Mech. 272, pp. 211-233.
121. Roulstone, I. and Sewell, M. J. (1996) Potential vorticities in semi-geostrophic theory. Quart. J. Roy. Meteorol. Soc. 122, pp. 983-992.
122. Roulstone, I. and Sewell, M. J. (1996) The mathematical structure of theories of semi-geostrophic type. Phil. Trans. R. Soc. London A, pp. 2489-2517.
123. Ryff, J. V (1970) Measure preserving transformations and rearrangements. J. Math. Anal, and Applies. 30, pp. 431-437.
124. Salmon, R. (1985) New equations for nearly geostrophic flow. J. Fluid Mech. 153, pp. 461-477.
125. Schar, C. and Wernli, H. (1993) Structure and evolution of an isolated semi-geostrophic cyclone. Quart. J. Roy. Meteorol. Soc. 119, pp. 57-90.
126. Schubert, W. H. and Hack, J. J. (1985) Transformed Eliassen balanced vortex model. J. Atmos. Sci. 40, pp. 1571-1583.
127. Schubert, W. H. (1985) Semi-geostrophic theory. J. Atmos. Sci. 42, pp. 1770-1772.
128. Schubert, W. H., Ciesieleski, P. E., Stevens, D. E. andKuo, H-C. (1991) Potential vorticity modelling of the ITCZ and the Hadley circulation. J. Atmos. Sci. 48, pp. 1493-1509.
129. Schubert, W. H. and Magnusdottir, G. (1994) Vorticity coordinates, transformed primitive equations, and a canonical form for balanced models. J. Atmos. Sci. 51, pp. 3309-3319.
130. Schwerdtfeger, W. (1975) The effects of the Antarctic peninsula on the temperature regime of the Weddell Sea. Mon. Weath. Rev. 103, pp. 45-51.
131. Sewell, M. J. (2002) Some applications of transformation theory in mechanics. In 'Large-scale Atmosphere-Ocean Dynamics,' J. Norbury and I. Roulstone eds., Cambridge University Press, vol. II, pp. 143-223.
132. Shapiro, M. A. and Thorpe, A. J. (2004) Thorpex science plan. Available from http: //www. mmm. ucax. edu/uswrp/thorpex. html
133. Shutts, G. J. (1987) The semi-geostrophic weir: a simple model of flow over mountain barriers. J. Atmos. Sci. 44, pp. 2018-2030.
134. Shutts, G. J. (1987) Balanced flow states resulting from penetrative, slant-wise convection. J. Atmos. Sci. 44, pp. 3363-3376.
135. Shutts, G. J., Booth, M. W. and Norbury, J. (1988) A geometric model of balanced, axisymmetric flow with embedded penetrative convection. J. Atmos. Sci. 45, pp. 2609-2621.
136. Shutts, G. J. (1989) Planetary semi-geostrophic theory. J. Fluid Mech. 208, pp. 545-573.
137. Shutts, G. J. and Cullen, M. J. P. (1987) Paxcel stability and its relation to semi-geostrophic theory. J. Atmos. Sci. 44, pp. 1318-1330.
138. Shutts, G. J. and Gray, M. E. B. (1994) A numerical modelling study of the geostrophic adjustment process following deep convection. Quart. J. Roy. Meteorol. Soc. 120, pp. 1145-1178.
139. Shutts, G. J. (1995) An analytical model of the balanced flow created by localised convective mass transfer in a rotating fluid. Dyn. Atmos. Oceans 22, pp. 1-17.
140. Shutts, G. J. (1998) Idealised models of the pressure drag force on mesoscale mountain ridges. Contr. Atmos. Phys. 71, pp. 303-313.
141. Snyder, C., Skamarock, W. C. and Rotunno, R. (1991) A comparison of primitive-equation and semi-geostrophic simulations of baroclinic waves. J. Atmos. Sci. 48, pp. 2179-2194.
142. Thomson, W. (Lord Kelvin) (1910) Maximum and minimum energy in vortex motion. Mathematical and Physical Papers 4, pp. 172-183. Cambridge University Press.
143. Thorpe, A. J. and Pedder, M. A. (1999) The semi-geostrophic diagnosis of vertical motion. II: Results for an idealized baxoclinic wave life cycle. Quart. J. Roy. Meteorol. Soc. 125, pp. 1257-1276.
144. Thuburn, J. and Li, Y. (2000) Numerical simulations of Rossby-Haurwitz waves. Tellus A 52, pp. 181-189.
145. Thuburn, J., Wood, N. and Staniforth, A. (2002) Normal modes of deep atmospheres. I: spherical geometry. Quart. J. Roy. Meteorol. Soc. 128, pp. 1771-1792.
146. Van Meighem, J. M. (1952) Hydrodynamic stability. Compendium of meteorology Amer. Met. Soc., pp. 434-453.
147. Veitch, G. and Mawson, M. H. (1993) A comparison of inertial stability conditions in the planetary semi-geostrophic and quasi-equilibrium models. U. K. Met. Office Short Range Forecasting Tech. Report no. 60.
148. Villani, C. (2003) Topics in optimal transportation. Vol. 58 of Graduate Studies in Mathematics, Amer. Math. Soc., Providence, RI.
149. Wakefield, M. A. and Cullen, M. J. P. (2005) Modelling the response of the atmosphere to equatorial forcing. Int. J. Numer. Meth. Fluids, 47, pp. 1345-1351.
150. Wang, X.-J. (1995) Some counter-examples to the regularity of Monge-Ampère equations. Proc. A. M. S. 123, pp. 841-845.
151. Warn, T., Bokhove, O., Shepherd, T. G. and Vallis, G. K. (1995) Rossby-number expansions, slaving principles, and balance dynamics. Quart. J. Roy. Meteorol. Soc. 121, pp. 723-739.
152. White, A. A. (2002) The equations of meteorological dynamics and various approximations. In 'Large-scale Atmosphere-Ocean Dynamics,' J. Norbury and I. Roulstone eds., Cambridge University Press, vol. I, pp. 1-100.
153. White, A. A., Hoskins, B. J., Roulstone, I. and Staniforth, A. (2005) Consistent approximate models of the globed atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic. Quart. J. Roy. Meteorol. Soc., 131, pp. 2081-2108.
154. Wiin-Nielsen, A. (2000) Numerical weather prediction: the early development with emphasis on Europe. Proc. 50th Anniversary of Numerical Weather Prediction., Deutsche Meteorologische Gesellschaft, pp. 29-50.
155. Winkler, C. R., Newman, M., Sardeshmukh, P. D. (2001) A linear model of wintertime low frequency variability, Part 1: formulation and forecast skill. J. Climate 14, pp. 4474-4494.
156. Wood, N. and Staniforth, A. (2003) The deep atmosphere Euler equations with a mass-based vertical coordinate. Quart. J. Roy. Meteorol. Soc. 129, pp. 1289-1300.