Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 1, 2013
Harmonic analysis
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Page(s) | 1 - 17 | |
DOI | https://doi.org/10.1051/mmnp/20138101 | |
Published online | 28 January 2013 |
- R.F. Anderson, S. Ali, L.L. Brandtmiller, S.H.H. Nielsen, M.Q. Fleisher. Wind-driven upwelling in the Southern Ocean and the deglacial rise in atmospheric CO2. Science. (2006) 323, 1443-1448. [Google Scholar]
- G.K. Bachelor. An Introduction to Fluid Dynamics. Cambridge University Press, (1967) Cambridge. [Google Scholar]
- S. Balasuriya. Vanishing viscosity in the barotropic β–plane J. Math.Anal. Appl., (1997) 214, 128-150. [Google Scholar]
- O.M. Belotserkovskii, I.V. Mingalev, O.V. Mingalev. Formation of large-scale vortices in shear flows of the lower atmosphere of the earth in the region of tropical latitudes. Cosmic Research, (2009) 47, (6), 466-479. [CrossRef] [Google Scholar]
- G. Ben-Yu. Spectral method for vorticity equations on spherical surface. Math. Comput. (1995) 64, 1067-1079. [CrossRef] [Google Scholar]
- E.N. Blinova. A hydrodynamical theory of pressure and temperature waves and of centres of atmospheric action. C.R. (Doklady) Acad. Sci USSR, (1943) 39, 257-260. [Google Scholar]
- E.N. Blinova. A method of solution of the nonlinear problem of atmospheric motions on a planetary scale. Dokl. Acad. Nauk USSR, (1956) 110, 975-977. [Google Scholar]
- C. Cenedese, P.F. Linden. Cyclone and anticyclone formation in a rotating stratified fluid over a sloping bottom. J. Fluid Mech., (1999) 381, 199-223. [CrossRef] [Google Scholar]
- A. Furnier, H. Bunger, R. Hollerbach, I. Vilotte. Application of the spectral-element method to the axisymetric Navier-Stokes equations. Geophys. J. Int. 156, (2004) 682-700. [CrossRef] [Google Scholar]
- H. Golovkin. Vanishing viscosity in Cauchy’s problem for hydromechanics equation. Proc. Steklov Inst. Math. (1966) 92, 33-53. [Google Scholar]
- E. Herrmann. The motions of the atmosphere and especially its waves. Bull. Amer. Math. Soc. 2 (9), 285-296. [Google Scholar]
- P.A. Hsieh. Application of modflow for oil reservoir simulation during the Deepwater Horizon crisis. Ground Water. (2011) 49 (3), 319-323. [CrossRef] [PubMed] [Google Scholar]
- R.N. Ibragimov. Nonlinear viscous fluid patterns in a thin rotating spherical domain and applications. Phys. Fluids. (2011) 23, 123102. [CrossRef] [Google Scholar]
- R.N. Ibragimov, M. Dameron. Spinning phenomena and energetics of spherically pulsating patterns in stratified fluids. Physica Scripta. (2011) 84, 015402. [Google Scholar]
- N.H. Ibragimov, R.N. Ibragimov. Intergarion by quadratures of the nonlinear Euler equations modeling atmoaspheric flows in a thin rotating spherical shell. Phys. Letters A. (2011) 375, 3858. [Google Scholar]
- N.H. Ibragimov, R.N. Ibragimov. Applications of Lie Group Analysis in Geophysical Fluid Dynamics. (2011) Series on Complexity, Nonlinearity and Chaos, Vol 2, World Scientific Publishers, ISBN : 978-981-4340-46-5. [Google Scholar]
- N.H. Ibragimov, R.N. Ibragimov. Conservation laws and invariant solutions for a model of nonlinear atmospheric zonal flows in a thin rotatimng spherical shell. (2012) Archives of ALGA, vol. 9, pp.27-38. [Google Scholar]
- R.N. Ibragimov, D.E. Pelinovsky. Effects of rotation on stability of viscous stationary flows on a spherical surface. Phys. Fluids. (2010) 22, 126602. [CrossRef] [Google Scholar]
- R.N. Ibragimov. Mechanism of energy transfers to smaller scales within the rotational internal wave field . Springer. Mathematical Physics, Analysis and Geometry, (2010) 13 (4), 331-355. [CrossRef] [Google Scholar]
- R.N. Ibragimov, D.E. Pelinovsky. Incompressible viscous fluid flows in a thin spherical shell. J. Math. Fluid. Mech. (2009) 11, 60-90. [Google Scholar]
- R.N. Ibragimov. Shallow water theory and solutions of the free boundary problem on the atmospheric motion around the Earth. Physica Scripta. (2000) 61, 391-395. [Google Scholar]
- N.H. Ibragimov. A new conservation theorem. Journal of Mathematical Analysis and Applications, (2007) 333 (1), 311–328. [Google Scholar]
- D. Iftimie, G. Raugel. Some results on the Navier-Stokes equations in thin 3D domains. J. Diff. Eqs. (2001) 169, 281-331. [Google Scholar]
- H. Lamb. Hydrodynamics. Cambridge University Press, 5th edition (1924) . [Google Scholar]
- J.L. Lions, R. Teman, S. Wang. On the equations of the large-scale ocean. Nonlinearity. (1992) 5, 1007-1053. [CrossRef] [MathSciNet] [Google Scholar]
- J.L. Lions, R. Teman, S. Wang. New formulations of the primitive equations of atmosphere and applications. Nonlinearity, (1992) 5, 237-288. [CrossRef] [MathSciNet] [Google Scholar]
- E. Noether. Invariante Variationsprobleme. Konigliche Gessellschaft der Wissenschaften, Gottingen Math. Phys. K1., (1918) English transl. : Transport Theory and Statistical Physics 1(3) (1971) 186-207. [Google Scholar]
- D.T. Shindell, G.A. Schmidt. Southern Hemisphere climate response to ozone changes and greenhouse gas increases. Res. Lett., (2004) 31, L18209. [Google Scholar]
- J. Shen. On pressure stabilization method and projection method for unsteady Navier-Stokes equations, in : Advances in Computer Methods for Partial Differential Equations, (1992) 658-662, IMACS, New Brunswick, NJ. [Google Scholar]
- C.P. Summerhayes, S.A. Thorpe. Oceanography, An Illustrative Guide. (1996) New York : John Willey & Sons. [Google Scholar]
- P.N. Swarztrauber. Shallow water flow on the sphere. Mon. Wea. Rev. (2004) 132, 3010-3018. [CrossRef] [Google Scholar]
- P.N. Swarztrauber. The approximation of vector functions and their derivatives on the sphere. SIAM J. Numer. Anal. (1981) 18, 181-210. [CrossRef] [Google Scholar]
- R. Temam, M. Ziane. Navier-Stokes equations in thin spherical domains. Contemp. Math. (1997) 209, 281-314. [CrossRef] [Google Scholar]
- J.R. Toggweiler, J.L. Russel. Ocean circulation on a warming climate. Nature. (2008) 451, 286-288. [CrossRef] [PubMed] [Google Scholar]
- W. Weijer, F. Vivier, S.T. Gille, H. Dijkstra. Multiple oscillatory modes of the Argentine Basin. Part II : The spectral origin of basin modes. J. Phys. Oceanogr., (2007) 37, 2869-2881. [CrossRef] [Google Scholar]
- D. Williamson. A standard test for numerical approximation to the shallow water equations in spherical geometry. J. Comput. Physics., (1992) 102, 211-224. [CrossRef] [MathSciNet] [Google Scholar]
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