Baines , P. G. 1976 . The stability of planetary waves on a sphere . J. Fluid Mech . 73 , 193 – 213 .
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 .
Charney , J. G. , Fjortoft , R. and von Neumann , J. 1950 . Numeri-cal integration of the barotropic voracity equation . Tellus 2 , 237 – 254 .
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 .
Craig , R. A. 1945 . A solution of the nonlinear voracity equation for atmospheric motion . J. Meteorol . 2 , 175 – 178 .
Craik , A. D. D. 1985 . Wave Interactions and Fluid Flows . Cambridge University Press , Cambridge . 322 pp .
Eliasen , E. , Machenhauer , B. and Rasmussen , E. 1970 . On a nu-merical method for integration of the hydrodynamical equations with a spectral representation of the horizontal fields, Techni-cal Report 2, Department of Meteorology, Copenhagen University, 35 pp .
Ellsaesser , H. W. 1966 . Evaluation of spectral versus grid methods of hemispheric numerical weather prediction . J. AppL Meteorol . 5 , 246 – 262 .
Fjørtoft , R. 1953 . On the changes in the spectral distribution of ki-netic energy in two-dimensional, non-divergent flow . Tellus 5 , 225 – 230 .
Gill , A. E. 1974 . The stability of planetary waves on an infinite beta-plane . Geophys. Fluid Dyn . 6 , 29 – 47 .
Haurwitz , B. 1940 . The motion of atmospheric disturbances on the spherical earth . J. Mar Res . 3 , 254 – 267 .
Hobson , E. W. 1931 . The Theory of Spherical and Ellipsoidal Harmon-ics . Cambridge University Press , Cambridge . 500 pp .
Holm , D. and Lynch , P. 2002 . Stepwise precession of the resonant swing-ing spring. SIAM J. AppL Dyn. Sys . 1 , 44 - 64 .
Holton , J. R. and Mass , C. 1976 . Stratospheric vacillation cycles . J. Atmos. Sci . 33 , 2218 – 2225 .
Hoskins , B. J. 1973 . Stability of the Rossby-Haurwitz wave . Q. J. R. Meteorol. Soc . 99 , 723 – 745 .
José , J. V. and Saletan , E. J. 1998 . Classical Dynamics: A Contemporary Approach . Cambridge University Press , Cambridge . 670 pp .
Kartashova , E. and L’vov , V. S. 2007. Model of intrasea-sonal oscillations in earth’s atmosphere. Phys. Rev. Lett . 98 , doi: https://doi.org/10.1103/PhysRevLett.98.198501 .
Longuet-Higgins , M. S. 1968 . The eigenfunctions of Laplace’s tidal equations over a sphere. Phil. Trans. Roy. Soc ., London A 262 , 511 – 607 .
Lorenz , E. N. 1960 . Maximum simplification of the dynamic equations . Tellus 12 , 243 – 254 .
Lorenz , E. N. 1972 . Barotropic instability of Rossby wave motion . J. Atmos. Sci . 29 , 258 – 269 .
Lynch , P. 2003 . Resonant Rossby wave triads and the swinging spring . Bull. Am. Meteorol. Soc . 84 , 605 – 616 .
Lynch , P. and Houghton , C. 2004 . Pulsation and precession of the reso-nant swinging spring . Physica D 190 , 38 – 62 .
Machenhauer , B. 1979 . The spectral method, Numerical Methods Used in Atmospheric Models Volume II . WMO/GARP Publ. Ser. 17, WMO , 121 – 275 .
Miles , J. 1985 . Resonantly forced Rossby waves . J. Phys. Oceanogr 15 , 467 – 474 .
Neamtan , S. M. 1946 . The motion of harmonic waves in the atmosphere . J. Meteorol . 3 , 53 – 56 .
Newell , A. C. , Nazarenko , S. and Biven , L. 2001 . Wave turbulence and intermittency. Physica D 152 – 153 , 520-550 .
Orszag , S. A. 1970 . Transform method for calculation of vector-coupled sums: application to the spectral form of the voracity equation . J. Atmos. Sci . 27 , 890 – 895 .
Orszag , S. A. 1974 . Fourier series on spheres . Mon. Wea. Rev . 102 , 56 – 75 .
Pedlosky , J. 1987 . Geophysical Fluid Dynamics 2nd Edition . Springer, Berlin . 710 pp .
Platzman , G. W. 1960 . The spectral form of the voracity equation . J. Atmos. Sci . 17 , 635 – 644 .
Platzman , G. W. 1962 . The analytical dynamics of the spectral voracity equation . J. Atmos. Sci . 19 , 313 – 328 .
Reznilc , G. M. , Piterbarg , L. I. and Kartashova , E. A. 1993 . Nonlinear interactions of spherical Rossby modes . Dyn. Atmos. Oceans 18 , 235 – 252 .
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 .
Silberman , I. 1954 . Planetary waves in the atmosphere . J. Meteorol . 11 , 27 – 34 .
Thuburn , J. and Li , Y. 2000 . Numerical simulation of Rossby-Haurwitz waves . Tellus 52A , 181 – 189 .