318
DYNAMICAL OCEANOGRAPHY
Having identified these two different length scales, we know that the ratio δ D /δ a
provides a guideline for investigating the different balances that can occur in the
flow. The possible cases are systematically discussed below; we will indicate the
scale D of the thermocline below (don’t confuse this with the total layer thickness
as used in earlier chapters).
(A) First we consider the case where δ D /δ a ≫ 1, which corresponds to small W E
according to (Fig. 13.6a)
δ D
δ a
≈ W
−3/2
E
.
(13.92)
and hence the Ekman pumping is relatively weak.
δ
D
δ
a
surface
Ekman
layer
W
E
(A1)
(A2a)
(A2b)
D
(a)
δ
D
δ
a
surface
Ekman
layer
W
E
(B2)
(B1)
D
(b)
Figure 13.6. Sketch to help understand the different cases in the scales of the thermocline depth.
(a) Case A with δD/δa ≫ 1. (b) Case B with δD/δa ≪ 1.
There are now several choices that can be made for the characteristic vertical
length scale of the flow D:
(A1) If we choose D = δ a then it follows that
λ V =
K V r 0
UD 2 =
K V
W E D
=
δ D
D
=
δ D
δ a
≫ 1,
(13.93)
and because ρ = ρ s according to (13.89), the surface density extends
(because of large vertical mixing) to the deep sea which is not what is
observed.