# 埃克曼层

## 数学表述

${\displaystyle \ -fv=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial x}}+K_{m}{\frac {\partial ^{2}u}{\partial z^{2}}}}$

${\displaystyle \ fu=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial y}}+K_{m}{\frac {\partial ^{2}v}{\partial z^{2}}}}$

${\displaystyle \ 0=-{\frac {1}{\rho _{o}}}{\frac {\partial p}{\partial z}}}$

### 边界条件

${\displaystyle \ z=0:\rho \nu {\frac {\partial u}{\partial z}}=\tau _{x};\rho \nu {\frac {\partial v}{\partial z}}=\tau _{y}}$

${\displaystyle \ z\to \infty :u=u_{g},v=v_{g}}$

### 解法

${\displaystyle \ u=u_{g}+{\frac {\sqrt {2}}{\rho fd}}e^{z/d}\left[\tau _{x}cos(z/d-\pi /4)-\tau _{y}sin(z/d-\pi /4)\right]}$  ${\displaystyle \ v=v_{g}+{\frac {\sqrt {2}}{\rho fd}}e^{z/d}\left[\tau _{x}sin(z/d-\pi /4)-\tau _{y}cos(z/d-\pi /4)\right].}$

## 参考文献

1. ^ Cushman-Roisin, Benoit. Chapter 5 - The Ekman Layer. Introduction to Geophysical Fluid Dynamics 1st. Prentice Hall. 1994: 76–77 [2009-08-06]. （原始内容存档于2009-07-26） （英语）.
2. Vallis, Geoffrey K. Chapter 2 - Effects of Rotation and Stratification. Atmospheric and Oceanic Fluid Dynamics 1st. Cambridge, UK: Cambridge University Press. 2006: 112–113 [2009-08-06]. （原始内容存档于2009-01-23） （英语）.
3. ^ Ekman, V.W. On the influence of the earth's rotation on ocean currents. Ark. Mat. Astron. Fys. 1905, 2 (11): 1–52.
4. Holton, James R. Chapter 5 - The Planetary Boundary Layer. Dynamic Meteorology. International Geophysics Series 88 4th. Burlington, MA: Elsevier Academic Press. 2004: 129–130 [2009-08-06]. （原始内容存档于2016-10-16） （英语）.
5. ^ Rudnick, Daniel. Observations of Momentum Transfer in the Upper Ocean: Did Ekman Get It Right?. Near-Boundary Processes and their Parameterization (Manoa, Hawaii: School of Ocean and Earth Science and Technology). 2003.
6. ^ Weller, R.A.; Davis, R.E. A vector-measuring current meter. Deep-Sea Res. 1980, 27: 565–582.
7. ^ Davis, R.E.; R. de Szoeke, and P. Niiler. Part II: Modelling the mixed layer response. Deep-Sea Res. 1981, 28: 1453–1475.