# Two-Layer Baroclinic Model

• Valentin P. Dymnikov
• Aleksander N. Filatov
Chapter
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.