Mathematical Physics, Analysis and Geometry

, Volume 17, Issue 1, pp 27-47

First online:

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

  • Ranis N. IbragimovAffiliated withDepartment of Mathematics, University of Texas at Brownsville Email author 
  • , Michael DameronAffiliated withDepartment of Mathematics, University of Texas at Brownsville
  • , Chamath DannangodaAffiliated withDepartment of Physics and Astronomy, University of Texas at Brownsville

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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