# 埃克曼层

## 数学表述

$\ -fv = -\frac{1}{\rho_o} \frac{\part p}{\part x}+K_m \frac{\part^2 u}{\part z^2}$

$\ fu = -\frac{1}{\rho_o} \frac{\part p}{\part y}+K_m \frac{\part^2 v}{\part z^2}$

$\ 0 = -\frac{1}{\rho_o} \frac{\part p}{\part z}$

### 边界条件

$\ z = 0 : A \frac{\part u}{\part z} = \tau^x; A \frac{\part v}{\part z} = \tau^y$

$\ z \to \infty : u = u_g, v = v_g$

### 解法

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

## 参考文献

1. ^ [Benoit] Check |authorlink= value (帮助). Chapter 5 - The Ekman Layer. Introduction to Geophysical Fluid Dynamics 1st. Prentice Hall. 1994: 76–77 （English）.
2. ^ 2.0 2.1 [Geoffrey K.] Check |authorlink= value (帮助). Chapter 2 - Effects of Rotation and Stratification. Atmospheric and Oceanic Fluid Dynamics 1st. Cambridge, UK: Cambridge University Press. 2006: 112–113 （English）.
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. ^ 4.0 4.1 [James R.] Check |authorlink= value (帮助). Chapter 5 - The Planetary Boundary Layer. Dynamic Meteorology. International Geophysics Series 4th. Burlington, MA: Elsevier Academic Press. 2004: 129–130 （English）.
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.