346
DYNAMICAL OCEANOGRAPHY
sea level height (in a high-resolution ocean model) as in Fig. 14.12 shows the
signatures of these eddies, in particular in the ACC region.
Figure 14.12. Snapshot of the global sea-level height field from a high-resolution ocean model
(NLOM, 1/32
◦ , see http://www7320.nrlssc.navy.mil/html/7320-home.html).
These type of flows are complex and the flow field is usually decomposed into
a time mean (u) and a deviation (˜ u) from this time mean as follows,
u = u + ˜
u → ˜
u =0.
(14.30)
As an example, consider the zonal momentum balance in local Cartesian coordinates, i.e.,
∂u
∂t
+
∂(uu)
∂x
+
∂(vu)
∂y
+
∂(wu)
∂z
− fv = −
1
ρ 0
∂p
∂x
+ A H ∇
2 u + A V
∂ 2 u
∂z 2 . (14.31)
We cannot neglect inertia in these flows as it determines the interaction between
the eddies. Substitution of (14.30) for all fields, and then taking an average gives
∂(uu + ˜
u˜ u)
∂x
+
∂(vu + ˜
v˜ u)
∂y
+
∂(wu + ˜
w˜ u)
∂z
− f v =
−
1
ρ 0
∂p
∂x
+ A H ∇
2 u + A V
∂ 2 u
∂z 2 .
(14.32)
Additional Material
B: The JEBAR concept is worked out in more detail in Mertz and Wright (1992).
Further discussion on the effects of eddies on the Southern Ocean flow can
be found in section 4.6 of WOCE (2001).