Geodesic
Conserved Vectors for a Model of Nonlinear Atmospheric Flows Around The Rotating Spherical Surface
A.M. Araslanov1 ; L.R. Galiakberova1 ; N.H. Ibragimov1 ; R. N. Ibragimov2
1 Laboratory “Group analysis of mathematical models in natural and engineering sciences” Ufa State Aviation Technical University 12, K. Marx, Str., 450000 Ufa, Russia
2 Department of Mathematics University of Texas at Brownsville Brownsville, TX 78520, USA
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 1, pp. 1-17

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We derive the conserved vectors for the nonlinear two-dimensional Euler equations describing nonviscous incompressible fluid flows on a three-dimensional rotating spherical surface superimposed by a particular stationary latitude dependent flow. Under the assumption of no friction and a distribution of temperature dependent only upon latitude, the equations in question can be used to model zonal west-to-east flows in the upper atmosphere between the Ferrel and Polar cells. As a particualr example, the conserved densities are analyzed by visualizing the exact invariant solutions associated with the given model for the particular form of finite disturbances for which the invariant solutions are also exact solutions of Navier-Stokes equations.
DOI : 10.1051/mmnp/20138101

A.M. Araslanov 1 ; L.R. Galiakberova 1 ; N.H. Ibragimov 1 ; R. N. Ibragimov 2

1 Laboratory “Group analysis of mathematical models in natural and engineering sciences” Ufa State Aviation Technical University 12, K. Marx, Str., 450000 Ufa, Russia
2 Department of Mathematics University of Texas at Brownsville Brownsville, TX 78520, USA 
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A.M. Araslanov; L.R. Galiakberova; N.H. Ibragimov; R. N. Ibragimov. Conserved Vectors for a Model of Nonlinear Atmospheric Flows Around The Rotating Spherical Surface. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 1, pp. 1-17. doi: 10.1051/mmnp/20138101

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