THE NEAR-SURFACE LAYER OF THE OCEAN
The analysis of the velocity structure of the ocean surface boundary
layer, or Ekman layer, is similar to the atmospheric layer (except for the
boundary conditions). The surface boundary layer is also called the surface
mixed layer, because temperature and salinity are often well mixed.
equations (1.134) apply equally well to the ocean mixed layer, and
definitions (1.131) are also applicable.
For the analysis of the ocean surface boundary layer, we choose a
coordinate system with the x-axis aligned with the surface stress and with z
being positive upwards. Change of variables,
g
u u
u
o and
g
v v
v
o ,
transforms (1.134) into:
0,
0
m
m
u
v
K
f v
K
f u
z
z
z
z
w
w
w
w
§
·
§
·
¨
¸
¨
¸
w
w
w
w
©
¹
©
¹
.
(1.142)
The boundary conditions for the oceanic side of the interface differ from
those for the atmosphere side. First, shear stress is imposed on the sea
surface by the wind, so that in the oceanic coordinate system:
2
0
0
and
0
m
m
z
z
u
v
K
u
K
z
z
o
o
w
w
§ ·
§ ·
¨ ¸
¨ ¸
w
w
© ¹
© ¹
,
(1.143)
whereas, in deeper water, the velocity asymptotes to zero:
0 and
0
u
v
o
o as z o f .
(1.144)
In equations (1.142) and (1.143), m
K and u refer to their ocean values
(where the surface stress, 0
W , has been expressed via atmospheric and
oceanic friction velocities as follows):
2
2
0
a a
u
u
W U
U
(1.145)
Solutions to (1.142) with boundary conditions (1.143)-(1.144) are as
follows:
1/ 2
2
cos
/ 4
E z
m
E
u u K f
e
z
J
J
S
ª
º
¬
¼ ,
(1.146)
1/ 2
2
sin
/ 4
E z
m
E
v
u K f
e
z
J
J
S
ª
º
¬
¼ .
(1.147)
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