On resonant Rossby-Haurwitz triads

Tellus, Series A: Dynamic Meteorology and Oceanography

Volumn 61, Issue 3, 2009, Pages 438-445

  Lynch, Peter ^a  

^a UNIVERSITY COLLEGE DUBLIN   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

BAROTROPIC INSTABILITY; RESONANCE; ROSSBY WAVE; SPHERICAL HARMONICS; VORTICITY;

EID: 64349083791     PISSN: 02806495     EISSN: 16000870     Source Type: Journal    
DOI: 10.1111/j.1600-0870.2009.00395.x     Document Type: Article

References (35)

1. Baines, P. G. 1976. The stability of planetary waves on a sphere. J. Fluid Mech. 73, 193-213.
2. Burzlaff, J., DeLoughry, E. and Lynch, P. 2008. Generation of zonal flow by resonant Rossby-Haurwitz wave interactions. Geophys. Astro. Fluid Dyn. 102, 165-177.
3. Charney, J. G., Fjørtoft, R. and von Neumann, J. 1950. Numerical integration of the barotropic vorticity equation. Tellus 2, 237-254.
4. Chen, Q., Chen, S., Eyink, G. L. and Holm, D. D. 2005. Resonant interactions in rotating homogeneous three-dimensional turbulence. J. Fluid. Mech. 542, 139-164.
5. Craig, R. A. 1945. A solution of the nonlinear vorticity equation for atmospheric motion. J. Meteorol. 2, 175-178.
6. Craik, A. D. D. 1985. Wave Interactions and Fluid Flows. Cambridge University Press, Cambridge. 322 pp.
7. Eliasen, E., Machenhauer, B. and Rasmussen, E. 1970. On a numerical method for integration of the hydrodynamical equations with a spectral representation of the horizontal fields, Technical Report 2, Department of Meteorology, Copenhagen University, 35pp.
8. Ellsaesser, H. W. 1966. Evaluation of spectral versus grid methods of hemispheric numerical weather prediction. J. Appl. Meteorol. 5, 246-262.
9. Fjørtoft, R. 1953. On the changes in the spectral distribution of kinetic energy in two-dimensional, non-divergent flow. Tellus 5, 225-230.
10. Gill, A. E. 1974. The stability of planetary waves on an infinite beta-plane. Geophys. Fluid Dyn. 6, 29-47.
11. Haurwitz, B. 1940. The motion of atmospheric disturbances on the spherical earth. J. Mar. Res. 3, 254-267.
12. Hobson, E. W. 1931. The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press, Cambridge. 500 pp.
13. Holm, D. and Lynch, P. 2002. Stepwise precession of the resonant swinging spring. SIAM J. Appl. Dyn. Sys. 1, 44-64.
14. Holton, J. R. and Mass, C. 1976. Stratospheric vacillation cycles. J. Atmos. Sci. 33, 2218-2225.
15. Hoskins, B. J. 1973. Stability of the Rossby-Haurwitz wave. Q. J. R. Meteorol. Soc. 99, 723-745.
16. José, J. V. and Saletan, E. J. 1998. Classical Dynamics: A Contemporary Approach. Cambridge University Press, Cambridge. 670 pp.
17. Kartashova, E. and L'vov, V. S. 2007. Model of intraseasonal oscillations in earth's atmosphere. Phys. Rev. Lett. 98, doi:.
18. Longuet-Higgins, M. S. 1968. The eigenfunctions of Laplace's tidal equations over a sphere. Phil. Trans. Roy. Soc., London A262, 511-607.
19. Lorenz, E. N. 1960. Maximum simplification of the dynamic equations. Tellus 12, 243-254.
20. Lorenz, E. N. 1972. Barotropic instability of Rossby wave motion. J. Atmos. Sci. 29, 258-269.
21. Lynch, P. 2003. Resonant Rossby wave triads and the swinging spring. Bull. Am. Meteorol. Soc. 84, 605-616.
22. Lynch, P. and Houghton, C. 2004. Pulsation and precession of the resonant swinging spring. Physica D 190, 38-62.
23. Machenhauer, B. 1979. The spectral method, Numerical Methods Used in Atmospheric Models Volume II. WMO/GARP Publ. Ser. 17, WMO, 121-275.
24. Miles, J. 1985. Resonantly forced Rossby waves. J. Phys. Oceanogr. 15, 467-474.
25. Neamtan, S. M. 1946. The motion of harmonic waves in the atmosphere. J. Meteorol. 3, 53-56.
26. Newell, A. C., Nazarenko, S. and Biven, L. 2001. Wave turbulence and intermittency. Physica D 152-153, 520-550.
27. Orszag, S. A. 1970. Transform method for calculation of vector-coupled sums: Application to the spectral form of the vorticity equation. J. Atmos. Sci. 27, 890-895.
28. Orszag, S. A. 1974. Fourier series on spheres. Mon. Wea. Rev. 102, 56-75.
29. Pedlosky, J. 1987. Geophysical Fluid Dynamics 2nd Edition. Springer, Berlin. 710 pp.
30. Platzman, G. W. 1960. The spectral form of the vorticity equation. J. Atmos. Sci. 17, 635-644.
31. Platzman, G. W. 1962. The analytical dynamics of the spectral vorticity equation. J. Atmos. Sci. 19, 313-328.
32. Reznik, G. M., Piterbarg, L. I. and Kartashova, E. A. 1993. Nonlinear interactions of spherical Rossby modes. Dyn. Atmos. Oceans 18, 235-252.
33. Rossby, C.-G. et al. 1939. Relations between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semipermanent centers of action. J. Mar. Res. 2, 38-55.
34. Silberman, I. 1954. Planetary waves in the atmosphere. J. Meteorol. 11, 27-34.
35. Thuburn, J. and Li, Y. 2000. Numerical simulation of Rossby-Haurwitz waves. Tellus 52A, 181-189.