# 地轉風

## 關係式

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

Fr 代表摩擦力，g 代表標準重力（9.81 m.s−2）。

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

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

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

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

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

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

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

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

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

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

${\displaystyle v_{g}={g \over f}{\partial Z \over \partial x}}$

${\displaystyle {\overrightarrow {V_{g}}}={{\hat {k}} \over f}\times \nabla _{p}\Phi }$

## 参考文献

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