Balance and the slow quasimanifold: Some explicit results

Journal of the Atmospheric Sciences

Volumn 57, Issue 9, 2000, Pages 1236-1254

  Ford, Rupert ^a,c   McIntyre, Michael E ^c   Norton, Warwick A ^b,c  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC RADIATION; ENERGY DISSIPATION; FLOW OF WATER; GRAVITY WAVES; SPONTANEOUS EMISSION; UNSTEADY FLOW; VORTEX FLOW;

FROUDE NUMBER; LIGHTHILL RADIATION; POTENTIAL VORTICITY INVERSION; ROSSBY NUMBER;

ATMOSPHERIC MOVEMENTS;

ATMOSPHERIC DYNAMICS; FLUID DYNAMICS; FROUDE NUMBER; LIMIT ANALYSIS; ROSSBY NUMBER;

EID: 0034087979     PISSN: 00224928     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0469(2000)057<1236:BATSQS>2.0.CO;2     Document Type: Article

References (47)

1. Abramowitz, M., and I. A. Stegun, 1964: A Handbook of Mathematical Functions. Dover, 1046 pp.
2. Aref, H., and N. Pomphrey, 1982: Integrable and chaotic motions of four vortices: I. The case of identical vortices. Proc. Roy. Soc. London, 380A, 359-387.
3. Armi, L., D. Hebert, N. Oakey, J. Price, P. L. Richardson, T. Rossby, and B. Ruddick, 1988: The history and decay of a Mediterranean salt lens. Nature, 333, 649-651.
4. Batchelor, G. K., 1967: An Introduction to Fluid Dynamics. Cambridge University Press, 615 pp.
5. Berry, M. V., 1978: Regular and irregular motion. Proc. AIP Conf. on Topics in Nonlinear Dynamics, Vol. 46, La Jolla, CA. American Institute of Physics, 16-120.
6. Bishop, C. H., and A. J. Thorpe, 1994: Potential vorticity and the electrostatics analogy: Quasi-geostrophic theory. Quart. J. Roy. Meteor. Soc., 120, 713-731.
7. Bokhove, O., and T. G. Shepherd, 1996: On Hamiltonian balanced dynamics and the slowest invariant manifold. J. Atmos. Sci., 53, 276-297.
8. Chang, K. M., and I. Orlanski, 1993: On the dynamics of storm tracks. J. Atmos. Sci., 50, 999-1015.
9. Charney, J. G., 1948: On the scale of atmospheric motions. Geofys. Publ., 17 (2), 3-17.
10. Crighton, D. G., 1981: Acoustics as a branch of fluid mechanics. J. Fluid Mech., 106, 261-298.
11. Crow, S. C., 1970: Aerodynamic sound generation as a singular perturbation problem. Stud. Appl. Math., 49, 21-44.
12. Errico, R. M., 1981: An analysis of interactions between geostrophic and ageostrophic modes in a simple model. J. Atmos. Sci., 38, 544-553.
13. Ford, R., 1993: Wave generation by vortical motion. Ph.D. thesis, University of Cambridge, 269 pp. [Available from Superintendent of Manuscripts, University Library, West Rd., Cambridge CB3 9DR, United Kingdom.]
14. _, 1994a: The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water. J. Fluid Mech., 280, 303-334.
15. _, 1994b: The response of a rotating ellipse of uniform potential vorticity to gravity wave radiation. Phys. Fluids, 6A, 3694-3704.
16. Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.
17. Gough, D. O., and M. E. McIntyre, 1998: Inevitability of a magnetic field in the sun's radiative interior. Nature, 394, 755-757.
18. Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, 1985: On the use and significance of isentropic potential-vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877-946.
19. Kambe, T. 1986: Acoustic emissions by vortex motions. J. Fluid Mech., 173, 643-666.
20. Kleinschmidt, E., 1950a: Über Aufbau und Entstehung von Zyklonen (1 Teil). Meteor. Rundsch., 3, 1-6.
21. _, 1950b: Über Aufbau und Entstehung von Zyklonen (2 Teil). Meteor. Rundsch., 3, 54-61.
22. _, 1951: Über Aufbau und Entstehung von Zyklonen (3 Teil). Meteor. Rundsch., 4, 89-96.
23. Lamb, H., 1932: Hydrodynamics. 6th ed. Cambridge University Press, 738 pp.
24. Leith, C. E., 1980: Nonlinear normal mode initialization and quasi-geostrophic theory. J. Atmos. Sci., 37, 958-968.
25. Lighthill, M. J., 1952: On sound generated aerodynamically. I. General theory. Proc. Roy. Soc. London, 211A, 564-587.
26. _, 1958: An Introduction to Fourier Analysis and Generalised Functions. Cambridge University Press, 79 pp.
27. Lorenz, E. N., 1980: Attractor sets and quasi-geostrophic equilibrium. J. Atmos. Sci., 37, 1685-1699.
28. _, 1992: The slow manifold - What is it? J. Atmos. Sci. 49, 2449-2451.
29. _, and V. Krishnamurthy, 1987: On the nonexistence of a slow manifold. J. Atmos. Sci., 44, 2940-2950.
30. Manney, G. L., R. W. Zurek, A. O'Neill, and R. Swinbank, 1994: On the motion of air through the stratospheric polar vortex. J. Atmos. Sci., 51, 2973-2994.
31. McIntyre, M. E., 1993: Isentropic distributions of potential vorticity and their relevance to tropical cyclone dynamics. Proc. ICSU/ WMO Int. Symp. on Tropical Cyclone Disasters. Beijing, China, ISCU/WMO, 143-156.
32. _, and W. A. Norton, 2000: Potential vorticity inversion on a hemisphere. J. Atmos. Sci., 57, 1214-1235.
33. Norton, W. A., 1988: Balance and potential vorticity inversion in atmospheric dynamics. Ph.D. thesis, University of Cambridge, 167 pp. [Available from Superintendent of Manuscripts, University Library, West Rd., Cambridge CB3 9DR, United Kingdom.]
34. Obukhov, A. M., 1962: On the dynamics of a stratified liquid. Sov. Phys. Dokl., 7, 682-684. First published in Dokl. Akad. Nauk SSSR, 145, 1239-1242.
35. Obukhov, A. M., 1962: On the dynamics of a stratified liquid. Sov. Phys. Dokl., 7, 682-684. First published in Dokl. Akad. Nauk SSSR, 145, 1239-1242.
36. Polvani, L. M., and R. A. Plumb, 1992: Rossby wave breaking, microbreaking, filamentation, and secondary vortex formation: The dynamics of a perturbed vortex. J. Atmos. Sci., 49, 462-476.
37. Simmons, A. J., and B. J. Hoskins, 1979: The downstream and upstream development of unstable baroclinic waves. J. Atmos. Sci., 36, 1239-1254.
38. Thorncroft, C. D., B. J. Hoskins, and M. E. McIntyre, 1993: Two paradigms of baroclinic-wave life-cycle behaviour. Quart. J. Roy. Meteor. Soc., 119, 17-55.
39. van Dyke, 1964: Perturbation Methods in Fluid Mechanics. Academic Press, 229 pp.
40. Vautard, R., and B. Legras, 1986: Invariant manifolds, quasi-geostrophy and initialization. J. Atmos. Sci., 43, 565-584.
41. Warn, T., 1997: Nonlinear balance and quasigeostrophic sets. Atmos.-Ocean, 35, 135-145 (originally written in 1983).
42. _, and R. Ménard, 1986: Nonlinear balance and gravity-inertial wave saturation in a simple atmosperic model. Tellus, 38A, 285-294.
43. _, O. Bokhove, T. G. Shepherd, and G. K. Vallis, 1995: Rossby number expansions, slaving principles, and balance dynamics. Quart. J. Roy. Meteor. Soc., 121, 723-739.
44. Webster, R. B., 1970: Jet noise simulation on shallow water. J. Fluid Mech., 40, 423-432.
45. Whitaker, J. S., 1993: A comparison of primitive and balance equation simulations of baroclinic waves. J. Atmos. Sci., 50, 1519-1530.
46. Zeitlin, V., 1988: Acoustic radiation from distributed vortex structures. Sov. Phys. Dokl., 34, 199-191.
47. _, 1991: On the backreaction of acoustic radiation for two-dimensional vortex structures. Phys. Fluids, 3A, 1677-1680.