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Conserved Vectors for a Model of Nonlinear Atmospheric Flows Around The Rotating Spherical Surface

Published online by Cambridge University Press:  28 January 2013

A.M. Araslanov ,
L.R. Galiakberova ,
N.H. Ibragimov  and
R. N. Ibragimov
A.M. Araslanov
Affiliation:
Laboratory “Group analysis of mathematical models in natural and engineering sciences” Ufa State Aviation Technical University 12, K. Marx, Str., 450000 Ufa, Russia
L.R. Galiakberova
Affiliation:
Laboratory “Group analysis of mathematical models in natural and engineering sciences” Ufa State Aviation Technical University 12, K. Marx, Str., 450000 Ufa, Russia
N.H. Ibragimov
Affiliation:
Laboratory “Group analysis of mathematical models in natural and engineering sciences” Ufa State Aviation Technical University 12, K. Marx, Str., 450000 Ufa, Russia
R. N. Ibragimov*
Affiliation:
Department of Mathematics University of Texas at Brownsville Brownsville, TX 78520, USA
*
∗ Corresponding author. E-mail: Ranis.Ibragimov@utb.edu
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Abstract

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.

Keywords

nonlinear Navier-Stokes equationsatmospheric wavesexact solutuonsnonlinear conservation laws
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 1: Harmonic analysis , 2013 , pp. 1 - 17
Copyright
© EDP Sciences, 2013

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