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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Sources and Sinks of Energy Balance for Nonlinear Atmospheric Motion Perturbed by West-to-east Winds Progressing on a Surface of a Rotating Spherical Shell

Discontinuity, Nonlinearity, and Complexity 1(1) (2012) 41--55 | DOI:10.5890/DNC.2012.02.002

Ranis N. Ibragimov$^{1}$; Michael Dameron$^{1}$; Chamath Dannangoda$^{2}$

$^{1}$ Department of Mathematics, University of Texas at Brownsville, Brownsville, TX 78520, USA.

$^{2}$ Department of Physics and Astronomy, University of Texas at Brownsville, Brownsville, TX 78520, USA.

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We study the asymptotic behavior of sources and sinks associated with the effects of rotation and nonlinearity of the energy balance of atmospheric motion perturbed by west-to-east winds progressing on the surface of a rotating spherical shell. The model uses nonlinear viscous and nonviscous incompressible fluid flows on a rotating spherical domain with infinitely small thickness. The energy density and associated sources and sinks were determined and visualized by means of elementary functions that provide the exact solutions of the nonviscous baratropic vorticity equation on the rotating sphere. It is shown that there exists a particular form of west-to east flows for which the source and sink terms associated with the energy balance vanishes providing thus the energy conservation law. Moreover, this particular form of atmospheric perturbation preserves the exact solutions for the case of viscous flows.


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