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 \(T = T' + \bar T\left( p \right):\)
$${{dT'} \over {dt}} = {{R\bar T} \over {pg}}\left( {\gamma _a - \bar \gamma } \right)\tau + {\partial \over {\partial _p }}v_1 {{\partial T'} \over {\partial _P }} + \mu \Delta T' + {\varepsilon /c_p }.$$
.

Keywords

Entropy Vorticity Sorb 

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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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