Antarctic Circumpolar Current
341
topography on the water is given by
F s =
p ∇Hd
2 x
and points in the example in the negative x-direction providing a effective drag
(the ‘form drag’, although it is not a real drag). This drag induces a reduction in
the volume transport as in Fig. 14.5.
Additional Material
B: There are several interesting papers on the concept of ‘form stress’ which
clarify many more aspects of it (Warren et al., 1997; Olbers, 1998). Further
discussion on the role of the ‘bottom form stress’ in relation to the Antarctic
Circumpolar Current can be found in section 4.6 of WOCE (2001).
14.3. Stratification
There are two basic effects caused by the presence of stratification:
(i) through baroclinic pressure gradients a flow is generated according to the thermal wind balance.
(ii) the zonal currents are susceptible to baroclinic instability, which leads to eddies whose dominant size is the scale of the internal Rossby deformation radius
L = ND/f, where N is the buoyancy frequency.
We will consider these two special cases in the next subsections.
14.3.1. Stationary baroclinic flows
Near the Antarctic continent the water is strongly cooled by the atmosphere
increasing its density. Sea-ice formation can also contribute to a density increase
of the ocean water. So, apart from an increase in density with depth, there is also
a meridional density gradient; the density increase poleward (Fig. 14.3c).
To study the effect of the presence of stratification on the flow in the zonal
channel, we consider a situation in which the bottom topography is piecewise
linear (Fig. 14.9). The channel has a zonal extent [x w ,x e ] and a meridional extent
[y 0 ,y 1 ] and in the region without topography, the layer depth is equal to D.O v e r
the interval [x 0 , (x 0 + x 1 )/2] the height of the topography increases linearly up to
a height h 0 and over the interval [(x 0 + x 1 )/2,x 1 ] it decreases to zero. The total
depth of the layer H is
H(x, y)=
⎧
⎨
⎩
D : x ∈ [x w ,x 0 ] ∧ x ∈ [x 1 ,x e ]
D − α b (x − x 0 ):x ∈ [x 0 ,
x0+x1
2 ]
D + α b (x − x 1 ):x ∈ [
x0+x1
2 ,x 1 ]
341
topography on the water is given by
F s =
p ∇Hd
2 x
and points in the example in the negative x-direction providing a effective drag
(the ‘form drag’, although it is not a real drag). This drag induces a reduction in
the volume transport as in Fig. 14.5.
Additional Material
B: There are several interesting papers on the concept of ‘form stress’ which
clarify many more aspects of it (Warren et al., 1997; Olbers, 1998). Further
discussion on the role of the ‘bottom form stress’ in relation to the Antarctic
Circumpolar Current can be found in section 4.6 of WOCE (2001).
14.3. Stratification
There are two basic effects caused by the presence of stratification:
(i) through baroclinic pressure gradients a flow is generated according to the thermal wind balance.
(ii) the zonal currents are susceptible to baroclinic instability, which leads to eddies whose dominant size is the scale of the internal Rossby deformation radius
L = ND/f, where N is the buoyancy frequency.
We will consider these two special cases in the next subsections.
14.3.1. Stationary baroclinic flows
Near the Antarctic continent the water is strongly cooled by the atmosphere
increasing its density. Sea-ice formation can also contribute to a density increase
of the ocean water. So, apart from an increase in density with depth, there is also
a meridional density gradient; the density increase poleward (Fig. 14.3c).
To study the effect of the presence of stratification on the flow in the zonal
channel, we consider a situation in which the bottom topography is piecewise
linear (Fig. 14.9). The channel has a zonal extent [x w ,x e ] and a meridional extent
[y 0 ,y 1 ] and in the region without topography, the layer depth is equal to D.O v e r
the interval [x 0 , (x 0 + x 1 )/2] the height of the topography increases linearly up to
a height h 0 and over the interval [(x 0 + x 1 )/2,x 1 ] it decreases to zero. The total
depth of the layer H is
H(x, y)=
⎧
⎨
⎩
D : x ∈ [x w ,x 0 ] ∧ x ∈ [x 1 ,x e ]
D − α b (x − x 0 ):x ∈ [x 0 ,
x0+x1
2 ]
D + α b (x − x 1 ):x ∈ [
x0+x1
2 ,x 1 ]