Journal
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
Volume 8, Issue 1, Pages 1-17Publisher
EDP SCIENCES S A
DOI: 10.1051/mmnp/20138101
Keywords
nonlinear Navier-Stokes equations; atmospheric waves; exact solutuons; nonlinear conservation laws
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Funding
- Government of Russian Federation [11.G34.31.0042]
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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.
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