On the normal mode instability of harmonic waves on a sphere

Geophysical and Astrophysical Fluid Dynamics

Volumn 92, Issue 2, 2000, Pages 115-127

  Skiba, Yu N ^a  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

Legendre polynomial flow; Normal mode instability; Rossby Haurwits wave

Indexed keywords

HARMONICS; INSTABILITY; ROTATING FLOW;

HARMONIC ANALYSIS; INSTABILITY; ROTATING FLOW;

EID: 0033750014     PISSN: 03091929     EISSN: None     Source Type: Journal    
DOI: 10.1080/03091920008203713     Document Type: Article

References (26)

1. Anderson, J. L., "The instability of finite amplitude Rossby waves on the infinite β-plane," Geophys. Astrophys. Fluid Dynam. 63, 1-27 (1992).
2. Baines, P. G., "The stability of planetary waves on a sphere," J. Fluid Mech. 73, 193-213 (1976).
3. Gill, A. E.,"The stability of planetary waves on an infinite beta plane," Geophys. Fluid Dyn. 6, 29-47 (1974).
4. Haarsma, R. J. and Opsteegh, J. D., "Barotropic instability of planetary-scale flows," J. Atmos. Sci. 45, 2789-2810 (1988).
5. Haurwitz, B., "The motion of atmospheric disturbances on the spherical earth," J. Marine Res. 3, 254-267 (1940).
6. Hoskins, B. J., "Stability of the Rossby-Haurwitz wave," Quart. J. Roy. Met. Soc. 99, 723-745 (1973).
7. Hoskins, B. J. and Hollingsworth, A., "On the simplest example of the barotropic instability of Rossby wave motion," J. Atmos. Sci. 30, 150-153 (1973).
8. Karunin, A. B., "On Rossby waves in barotropic atmosphere in the presence of zonal flow," Izvestiya, Atmos. Ocean. Physics 6, 1091-1100 (1970).
9. Kuo, H.-L., "Dynamic instability of two-dimensional non-divergent flow in a barotropic atmosphere," J. Meteorology 6, 105-122 (1949).
10. Liapunov, A. M., Stability of motion. Academic Press, New York (1966).
11. Lorenz, E. N., "Barotropic instability of Rossby wave motion," J. Atmos. Sci. 29, 258-264 (1972).
12. Platzman, G. W., "The analytical dynamics of the spectral vorticity equation," J. Atmos. Sci. 19, 313-328 (1962).
13. Ripa, P., "Positive, negative and zero wave energy and the flow stability problem in the Eulerian and Lagrangian-Eulerian descriptions," Pure and Applied Geophysics 133, 713-732 (1990).
14. Rosenbluth, M. N. and Simon, A., "Necessary and sufficient condition for the stability of plane parallel inviscid flow," Phys. Fluids 7, 557-558 (1964).
15. Shepherd, T. G., "Symmetries, conservation laws, and Hamiltonian structure in Geophysical Fluid Dynamics," Advances in Geophysics 32, 287-338 (1990).
16. Silberman, I., "Planetary waves in the atmosphere," J. Meteorology 11, 27-34 (1954).
17. Skiba, Yu. N., The Dynamics of Perturbations of Solutions of a Vorticity Equation for an Ideal Fluid on a Sphere. Dept. Numer. Mathematics, AN SSSR, Moscow, 246, 1-46 (1989a).
18. Skiba, Yu. N., Mathematical Problems of the Dynamics of Viscous Barotropic Fluid on a Rotating Sphere. Dept. Comput. Mathematics, USSR Academy of Sciences, Moscow, pp. 1-178 (1989b)
19. (English transl.: Indian Institute of Tropical Meteorology, Pune, 1990).
20. Skiba, Yu. N., "Dynamics of perturbations of the Rossby-Haurwitz wave and the Verkley modon," Atmósfera. 6, 87-125 (1993).
21. Skiba, Yu. N., "On the long-time behavior of solutions to the barotropic atmosphere model," Geophys. Astrophys. Fluid Dynam. 78, 143-167 (1994).
22. Skiba, Yu. N., "On dimension of attractive sets of viscous fluids on a sphere under quasiperiodic forcing," Geophys. Astrophys. Fluid Dynam. 85, 233-242 (1997).
23. Skiba, Yu. N., "Spectral approximation in the numerical stability study of non-divergent viscous flows on a sphere," Numerical Methods for Partial Differential Equations 14(2), 143-157 (1998).
24. Skiba, Yu. N. and Adem, J., "On the linear stability study of zonal incompressible flows on a sphere," Numerical Methods for Partial Differential Equations 14(5), 649-665 (1998).
25. Tung, K. K., "Barotropic instability of zonal flows," J. Atmos. Sci. 38, 308-321 (1981).
26. Thuburn, J. and Haynes, P. H., "Bounds on the growth rate and phase velocity of instabilities in non-divergent barotropic flow on a sphere: A semicircle theorem," Quart. J. Roy. Met. Soc. 122, 779-787 (1996).