Assignment 3, Fall 2022

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Revision as of 10:10, 1 November 2022 by Etone (talk | contribs) (Created page with "Held-Hou(1980) 讨论了当外部强迫的经向分布呈二次勒让德多项式,即<math>\dfrac{\Theta_E(\phi,z)}{\Theta_o}=1-\dfrac{2}{3}\Delta_H P_2(\sin \phi)+\Delta_v(\dfrac{z}{H}-\dfrac{1}{2})</math>的情况下,哈德莱环流内的风场、温度场、环流的空间范围等将怎样随纬度和外力强迫的强度而变化。 如果将外力强迫的空间分布改为<math>\dfrac{\Theta_E(\phi,z)}{\Theta_o}=1-\Delta_H(\sin^3 \phi - \dfrac{1}{4})+\Delta_v...")
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Held-Hou(1980) 讨论了当外部强迫的经向分布呈二次勒让德多项式,即[math]\displaystyle{ \dfrac{\Theta_E(\phi,z)}{\Theta_o}=1-\dfrac{2}{3}\Delta_H P_2(\sin \phi)+\Delta_v(\dfrac{z}{H}-\dfrac{1}{2}) }[/math]的情况下,哈德莱环流内的风场、温度场、环流的空间范围等将怎样随纬度和外力强迫的强度而变化。

如果将外力强迫的空间分布改为[math]\displaystyle{ \dfrac{\Theta_E(\phi,z)}{\Theta_o}=1-\Delta_H(\sin^3 \phi - \dfrac{1}{4})+\Delta_v(\dfrac{z}{H}-\dfrac{1}{2}) }[/math]


  1. 请推导出哈德莱环流内的高空风场和垂直平均位温场[math]\displaystyle{ \dfrac{\tilde{\Theta}}{\Theta_o} }[/math]将如何随纬度分布;
  2. 同样利用小角度假设,请推导出环流的空间范围[math]\displaystyle{ \phi_H }[/math] 的表达式。如果设 [math]\displaystyle{ r \equiv \dfrac{gH}{\Omega^2a^2} }[/math], 请分别画出当 [math]\displaystyle{ \Delta_H=1/3 }[/math][math]\displaystyle{ \Delta_H=1/6 }[/math] 时, 与Held-Hou的情况相比,[math]\displaystyle{ \phi_H }[/math] 怎样随 [math]\displaystyle{ r }[/math] 而变化。
  3. 选做题目:在此情况下,近地面风场的分布有怎样变化。