Math. Model. Nat. Phenom.
Volume 8, Number 1, 2013Harmonic analysis
|Page(s)||1 - 17|
|Published online||28 January 2013|
Conserved Vectors for a Model of Nonlinear Atmospheric Flows Around The Rotating Spherical Surface
1 Laboratory “Group analysis of
mathematical models in natural and engineering sciences” Ufa State Aviation Technical
University 12, K. Marx, Str., 450000
2 Department of Mathematics University of Texas at Brownsville Brownsville, TX 78520, USA
∗ Corresponding author. E-mail: Ranis.Ibragimov@utb.edu
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.
Mathematics Subject Classification: 35A20
Key words: nonlinear Navier-Stokes equations / atmospheric waves / exact solutuons / nonlinear conservation laws
© EDP Sciences, 2013
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