Mathematical Physics, Analysis and Geometry

, Volume 17, Issue 1, pp 27–47

Asymptotic Analysis of Conserved Densities Evaluated on Invariant Solutions Associated with Large Scale Nonlinear Zonal Flows Around the Rotating Sphere

  • Ranis N. Ibragimov
  • Michael Dameron
  • Chamath Dannangoda

DOI: 10.1007/s11040-014-9139-4

Cite this article as:
Ibragimov, R.N., Dameron, M. & Dannangoda, C. Math Phys Anal Geom (2014) 17: 27. doi:10.1007/s11040-014-9139-4


We study the asymptotic behavior of the conserved densities deduced form the Lagrangian corresponding to 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. The conserved densities were analyzed and visualized by using 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.


Navier Stokes equations Conservation laws Lagrangian Euler equations Atmospheric modeling 

Mathematics Subject Classifications (2010)

35Q30 35Q86 35L65 

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Ranis N. Ibragimov
    • 1
  • Michael Dameron
    • 1
  • Chamath Dannangoda
    • 2
  1. 1.Department of MathematicsUniversity of Texas at BrownsvilleBrownsvilleUSA
  2. 2.Department of Physics and AstronomyUniversity of Texas at BrownsvilleBrownsvilleUSA

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