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Two-Layer Baroclinic Model

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

Abstract

Let us consider the baroclinic atmosphere equations in p-system of coordinates:
$${{du} \over {dt}} - lv = - {{\partial \varphi } \over {\partial x}} + {\partial \over {\partial p}}v{{\partial u} \over {\partial p}} + \mu \Delta u, $$
$${{du} \over {dt}} + lv = - {{\partial \varphi } \over {\partial y}} + {\partial \over {\partial p}}v{{\partial u} \over {\partial p}} + \mu \Delta v, $$
$${{d\Phi } \over {dp}} = - {{RT} \over p}{{\partial u} \over {\partial x}} + {{\partial u} \over {\partial y}} + {{\partial \tau } \over {\partial y}} = 0, $$
$${{dT} \over {dt}} = {{RT} \over {pc_p }}\tau + {\partial \over {\partial p}}v_1 {{\partial T} \over {\partial p}} + \mu _1 \Delta T + \varepsilon /c_p ,$$
$${d \over {dt}} = {\partial \over {\partial t}} + u{\partial \over {\partial x}} + v{\partial \over {\partial y}} + \tau {\partial \over {\partial p}},$$
or if we set \(T = T' + \bar T\left( p \right):\)
$${{dT'} \over {dt}} = {{R\bar T} \over {pg}}\left( {\gamma _a - \bar \gamma } \right)\tau + {\partial \over {\partial _p }}v_1 {{\partial T'} \over {\partial _P }} + \mu \Delta T' + {\varepsilon /c_p }.$$
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Keywords

Attractor Dimension Lyapunov Exponent Global Attractor Baroclinic Instability Positive Lyapunov Exponent 
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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