# 地轉風

## 關係式

${D\boldsymbol{U} \over Dt} = -2\boldsymbol{\Omega} \times \boldsymbol{U} - {1 \over \rho} \nabla p + \boldsymbol{g} + \boldsymbol{F}_r$

Fr 代表摩擦力，g 代表標準重力（9.81 m.s−2）。

${Du \over Dt} = -{1 \over \rho}{\partial P \over \partial x} + f \cdot v$

${Dv \over Dt} = -{1 \over \rho}{\partial P \over \partial y} - f \cdot u$

$0 = -g -{1 \over \rho}{\partial P \over \partial z}$

$f = 2 \Omega \sin{\phi}$科里奧利頻率（大約是10−4 s−1，隨緯度改變）。

$f \cdot v = {1 \over \rho}{\partial P \over \partial x}$

$f \cdot u = -{1 \over \rho}{\partial P \over \partial y}$

$f \cdot v = g\frac{\partial P / \partial x}{\partial P / \partial z} = g{\partial Z \over \partial x}$

$f \cdot u = -g\frac{\partial P / \partial y}{\partial P / \partial z} = -g{\partial Z \over \partial y}$

Z 是指固定氣壓表面的高度（滿足 ${\partial P \over \partial x}dx + {\partial P \over \partial y}dy + {\partial P \over \partial z} dZ = 0$）。

$u_g = - {g \over f} {\partial Z \over \partial y}$

$v_g = {g \over f} {\partial Z \over \partial x}$

$\overrightarrow{V_g} = {\hat{k} \over f} \times \nabla_p \Phi$

## 參考資料

1. ^ Holton, J.R., 'An Introduction to Dynamic Meteorology', International Geophysical Series, Vol 48 Academic Press.