Geography Reference
In-Depth Information
where K is the eddy viscosity in the ocean (assumed constant). As a lower
boundary condition assume that u, v
10
−
3
m
2
s
−
1
,
what is the depth of the surface Ekman layer at 43˚N latitude?
→
0asz
→−∞
.IfK
=
5.7.
Show that the vertically integrated mass transport in the wind-driven oceanic
surface Ekman layer is directed 90˚ to the right of the surface wind stress in
the Northern Hemisphere. Explain this result physically.
5.8.
A homogeneous barotropic ocean of depth H
3 km has a zonally sym-
metric geostrophic jet whose profile is given by the expression
=
U exp
(y/L)
2
u
g
=
−
1m s
−
1
=
=
where U
200 km are constants. Compute the vertical
velocity produced by convergence in the Ekman layer at the ocean bottom
and show that the meridional profile of the secondary cross-stream motion
forced in the interior is the same as the meridional profile of u
g
. What are
the maximum values of
and L
10
-
3
m
2
s
-
1
v in the interior and
¯
w if K
¯
=
and
10
−
4
s
−
1
(Assume that w and the eddy stress vanish at the surface.)
f
=
5.9.
Using the approximate zonally averaged momentum equation
∂
u
∂t
=
¯
f
v
¯
compute the spin-down time for the zonal jet in Problem 5.8.
5.10.
Derive a formula for the vertical velocity at the top of the plane
ta
ry boundary
layer using the mixed layer expression (5.22). Assume that
5ms
−
1
|
V
|=
is independent of x and y and that
0.05,
what value must K
m
have if this result is to agree with the vertical velocity
derived from the Ekman layer solution at 43˚ latitude with De
u
g
=¯
¯
u
g
(y).Ifh
=
1kmandκ
s
=
=
1 km?
5.11.
Show that K
m
=
kzu
∗
in the surface layer.
MATLAB EXERCISES
M5.1.
The MATLAB script
mixed layer wind1.m
uses a simple iterative tech-
nique to solve for u and v in (5.22) with u
g
in the range 1-20 m s
−
1
for
0.05 m
−
1
s. If you run the script, you will
observe that this iterative technique fails for u
g
greater than 19 m s
−
1
.An
alternative method, which works for a wide range of specified geostrophic
winds, utilizes the natural coordinate system introduced in Section 3.2.1.
the case v
g
=
0 and κ
s
=
