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Analysis of Barotropic Model

  • Valentin P. Dymnikov
  • Aleksander N. Filatov
Chapter
  • 322 Downloads
Part of the Modeling and Simulation in Science, Engineering, & Technology book series (MSSET)

Abstract

In this chapter we shall consider the following equations of the barotropic atmosphere on rotating sphere S2R3 with radius a:
$$\frac{\partial }{{\partial t}}\Delta \psi + J\left( {\psi ,\Delta \psi + l} \right) = - \sigma \Delta \psi + v\mathop \Delta \nolimits^2 \psi + f,\quad \psi \left| {_{t = 0} } \right.\; = \;\psi _0 ,$$
(3.1)
and
$$\frac{\partial }{{\partial t}}\Delta \psi + J\left( {\psi ,\Delta \psi + l} \right) = - \sigma \Delta \psi + v\mathop {\left( { - \Delta \,} \right)}\nolimits^{s + 1} \psi + f,\quad \psi \left| {_{t = 0} } \right.\; = \;\psi _0 ,$$
(3.2)
where ψ is the stream-function, J(a,b) is the Jacobian, l = 2Ω sin φ, s ≥ 1, while the parameters Ω > 0 and σ ≥ 0 have the dimensions [Ω] = T−1, [σ] = T−1, respectively.

Keywords

Probability Measure Invariant Measure Variation Equation Hausdorff Dimension Global Attractor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 1997

Authors and Affiliations

  • Valentin P. Dymnikov
    • 1
  • Aleksander N. Filatov
    • 2
  1. 1.Institute of Numerical Mathematics of the Russian Academy of SciencesMoscowRussia
  2. 2.Hydrometeorological Center of RussiaMoscowRussia

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