Arctic Ocean Circulation
361
x
x e
y
R
w
E < 0
w
E
> 0
(a)
(b)
(c)
Figure 15.6. (a) Sketch of the situation of localized Ekman pumping within a disk of radius R.
(b) Isolines of ˆ
q2 for the case y0 =2 , R =1 . (c) Same for y0 =0 .25 and R =1(from Pedlosky
(1996)).
The critical value of the forcing which is required to have closed contours is
determined by the condition y 0 ≤ R, which is equivalent to
β 2
0 D
γf 0 ˆ
F
≤ R → γ ≥
β 2
0 D
f 0 ˆ
FR
.
(15.17)
When γ = W 0 /R, where W 0 is a typical amplitude of the Ekman pump velocity,
then by defining a mean Rossby deformation radius L d using ˆ
F =1/L 2
d ,wefind
W 0 ≥
β 2
0 L 2
d D
f 0
.
(15.18)
With typical values f 0 =1 0 −4 s −1 , β 0 =1 0 −11 (ms) −1 , D = 1000 ma n d
L d =5 0km, we find as critical value W 0 ≈ 2.5 × 10 −6 ms −1 = 0.2 m/day,
which is well within the realistic range of high latitude Ekman pump velocities
(Fig. 5.13) observed.
361
x
x e
y
R
w
E < 0
w
E
> 0
(a)
(b)
(c)
Figure 15.6. (a) Sketch of the situation of localized Ekman pumping within a disk of radius R.
(b) Isolines of ˆ
q2 for the case y0 =2 , R =1 . (c) Same for y0 =0 .25 and R =1(from Pedlosky
(1996)).
The critical value of the forcing which is required to have closed contours is
determined by the condition y 0 ≤ R, which is equivalent to
β 2
0 D
γf 0 ˆ
F
≤ R → γ ≥
β 2
0 D
f 0 ˆ
FR
.
(15.17)
When γ = W 0 /R, where W 0 is a typical amplitude of the Ekman pump velocity,
then by defining a mean Rossby deformation radius L d using ˆ
F =1/L 2
d ,wefind
W 0 ≥
β 2
0 L 2
d D
f 0
.
(15.18)
With typical values f 0 =1 0 −4 s −1 , β 0 =1 0 −11 (ms) −1 , D = 1000 ma n d
L d =5 0km, we find as critical value W 0 ≈ 2.5 × 10 −6 ms −1 = 0.2 m/day,
which is well within the realistic range of high latitude Ekman pump velocities
(Fig. 5.13) observed.