
AIMS Mathematics, 2019, 4(2): 279298. doi: 10.3934/math.2019.2.279
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Elementary properties of nonLinear RossbyHaurwitz planetary waves revisited in terms of the underlying spherical symmetry
Mathematical Physics, EEMCS, Delft University of Technology, The Netherlands
Received: , Accepted: , Published:
Topical Section: Mathematical Analysis in Fluid Dynamics
References
1.D. Brink and G. Satchler, Angular Momentum, Oxford Library of the Physical Sciences, Oxford University Press, Oxford, 1962.
2.E. Butkov, Mathematical Physics, AddisonWesley Publishing Company, 1968.
3.S. Chandrasekhar, Ellipsoidal Figures of Equilibrium, Yale University Press, 1969.
4.J. Cornwell, Group Theory in Physics An Introduction, Academic Press, San Diego, 1997.
5.R. Craig, A solution for the nonlinear vorticity equation for atmospheric motion, J. Meteor., 2 (1945), 175178.
6.P. J. Dellar, Variations on a betaplane: derivation of nontraditional betaplane equations from Hamilton's principle on a sphere, J. Fluid Mech., 674 (2011), 174195.
7.B. A. Dubrovin, A. T. Fomenko and S. P. Novikov, Modern Geometry, Methods and Applications, Part 1, Graduate Texts in Mathematics, SpingerVerlag, New York, 1992.
8.H. Flanders, Differential Form with Applications to the Physical Sciences, Mathematics in Science and Engineering, Academic Press, New York, 1963.
9.B. Haurwitz, The motion of atmospheric disturbances on a spherical earth, Journal of Marine Research, 3 (1940).
10.M. C. Hendershott, Long waves and ocean tides, in Evolution of Physical Oceanography (eds. B. A. Warren and C. Wunsch), MIT Press, Cambridge, Massac, 1981, 292341.
11.J. R. Holton, An Introduction to Dynamic Meteorology, vol. 48 of International Geophysics Series, 3rd edition, Academic Press, 1992.
12.S. S. Hough, On the application of harmonic analysis to the dynamical theory of the tides  Part I. On Laplace's "Oscillations of the first species", and on the dynamics of ocean currents, Phil. Trans. R. Soc. London. Ser. A., 189 (1897), 201257.
13.S. S. Hough, On the application of harmonic analysis to the dynamical theory of the tides  Part II. On the general integration of Laplace's dynamical equations, Phil. Trans. R. Soc. London. Ser. A., 191 (1898), 139185.
14.M. S. LonguetHiggins, Planetary waves on a rotating sphere, Proc. Roy. Soc. London, A, 279 (1964), 446473.
15.P. Lynch, On resonant RossbyHaurwitz triads, Tellus, 61A (2009), 438445.
16.J. Pedlosky, Geophysical Fluid Dynamics, SpingerVerlag, New York, 1987.
17.G. W. Platzman, The spectral form of the vorticity equation, Journal of Meteorology, 17 (1960), 635644.
18.G. W. Platzman, The analytical dynamics of the spectral vorticity equation, J. Atmos. Sci., 19 (1962), 313327.
19.M. Rose, Elementary Theory of Angular Momentum, John Wiley & Sons, New York, 1957.
20.C. Rossby, Relations between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semipermanent centers of action, Journal of Marine Research, 2 (1939), 3855.
21.I. S. Sokolnikoff, Tensor Analysis; Theory and Applications to Geometry and Mechanics of Continua, 2nd edition, John Wiley and Sons, Inc., 1964,
22.P. D. Thompson, A generalized class of exact timedependent solutions of the vorticity equation for nondivergent barotropic flow, Monthly Weather Review, 110 (1982), 13211324.
23.R. van der Toorn and J. T. F. Zimmerman, On the spherical approximation of the geopotential in geophysical fluid dynamics and the use of a spherical coordinate system, Geophys. Astrophys. Fluid Dyn., 102 (2008), 349371.
24.R. Van der Toorn and J. T. F. Zimmerman, Angular momentum dynamics and the intrinsic drift of monopolar vortices on a rotating sphere, J. Math. Phys., 51 (2010), 83102.
25.W. Verkley, The construction of barotropic modons on a sphere, J. Atmos. Sci., 40 (1984), 24922504.
26.A. White, B. Hoskins, I. Roulstone, et al. Consistent approximate models of the global atmosphere: Shallow, deep hydrostatic and nonhydrostatic, Quar. J. Roy. Met. Soc., 131 (2005), 20812107.
27.E. P. Wigner, Group Theory, Academic Press, New York, 1959.
28.Wolfram Research, Inc., Mathematica, Version 11.3, Champaign, IL, 2018.
29.R. Zhang, L. Yang, Q. Liu, et al. Dynamics of nonlinear Rossby waves in zonally flow with spatialtemporal varying topography, Appl. Math. Comput., 346 (2019), 666679.
30.R. Zhang, L. Yang, J. Song, et al. (2+1) dimensional nonlinear Rossby solitary waves under the effects of generalized beta and slowly varying topography, Nonlinear Dynamics, 90 (2017), 815822.
31.R. Zhang, L. Yang, J. Song, et al. (2+1) dimensional Rossby waves with complete coriolis force and its solution by homotopy perturbation method, Comput. Math. Appl., 73 (2017), 19962003.
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