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Explicit invariant solutions associated with nonlinear atmospheric flows in a thin rotating spherical shell with and without west-to-east jets perturbations

Ibragimov, Ranis, Jefferson, Grace and Carminati, John 2013, Explicit invariant solutions associated with nonlinear atmospheric flows in a thin rotating spherical shell with and without west-to-east jets perturbations, Analysis and mathematical physics, vol. 3, no. 4, pp. 375-391, doi: 10.1007/s13324-013-0062-9.

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Title Explicit invariant solutions associated with nonlinear atmospheric flows in a thin rotating spherical shell with and without west-to-east jets perturbations
Author(s) Ibragimov, Ranis
Jefferson, Grace
Carminati, John
Journal name Analysis and mathematical physics
Volume number 3
Issue number 4
Start page 375
End page 391
Total pages 17
Publisher Springer
Place of publication Berlin, Germany
Publication date 2013-12
ISSN 1664-2368
Summary A class of non-stationary exact solutions of two-dimensional nonlinear Navier–Stokes (NS) equations within a thin rotating spherical shell were found as invariant and approximately invariant solutions. The model is used to describe a simple zonally averaged atmospheric circulation caused by the difference in temperature between the equator and the poles. Coriolis effects are generated by pseudoforces, which support the stable west-to-east flows providing the achievable meteorological flows. The model is superimposed by a stationary latitude dependent flow. Under the assumption of no friction, the perturbed model describes zonal west-to-east flows in the upper atmosphere between the Ferrel and Polar cells. In terms of nonlinear modeling for the NS equations, two small parameters are chosen for the viscosity and the rate of the earth’s rotation and exact solutions in terms of elementary functions are found using approximate symmetry analysis. It is shown that approximately invariant solutions are also valid in the absence of the flow perturbation to a zonally averaged mean flow.
Language eng
DOI 10.1007/s13324-013-0062-9
Field of Research 010504 Mathematical Aspects of General Relativity
010207 Theoretical and Applied Mechanics
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1.1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2013, Springer
Persistent URL http://hdl.handle.net/10536/DRO/DU:30071662

Document type: Journal Article
Collection: School of Information Technology
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