6.8 The Wind-Driven Circulation of the Ocean
141
6.8.7 The Sverdrup Balance
On the β plane, the divergence of lateral volume transport inherent with geostrophic
fl w is given by:
∂ Q
geo
x
∂ x
+
∂ Q
geo
y
∂ y
= −
β
f
Q
geo
y
(6.46)
On the large scale, this divergence (or convergence) of the geostrophic f ow balances the convergence (or divergence) of the drift in the surface Ekman layer. Effects
associated with bottom friction are irrelevant here. Under the assumption of purely
zonal wind (τ
wind
y
= 0), the steady-state balance leading to an equilibrium sea-level
distribution is given by:
β Q
geo
y ≈ −
1
ρ o
∂τ
wind
x
∂ y
(6.47)
This balance is called the Sverdrup relation (Sverdrup, 1947) and allows for
calculation of the meridional geostrophic volume transport (also called Sverdrup
transport) from knowledge of the average zonal wind-stress distribution. The corresponding zonal volume transport can be estimated from:
∂ Q
geo
x
∂ x
+
∂ Q
geo
y
∂ y
≈ 0
(6.48)
where the β effect can be ignored since this equation is used for diagnostic purposes only. It is important to note that the Sverdrup balance can only establish with
existence of a meridional boundary. The dynamics of unbounded fl ws, such as the
Antarctic Circumpolar Current, is more complex.
6.8.8 Interpretation of the Sverdrup Relation
First and foremost, the Sverdrup relation implies that latitudes of vanishing windstress curl (∂τ
wind
x
/∂ y = 0) coincide with regions of vanishing meridional geostrophic f ow. Hence, these regions form natural boundaries that, for instance,
separate subtropical from subpolar gyres in the ocean.
In the midlatitude ocean of the northern hemisphere, the main wind pattern consists of trades to the south and westerlies to the north. This wind pattern provides
∂τ
wind
x
/∂ y > 0 and produces a convergence of volume transport in the surface
Ekman layer. Hence, equatorward Sverdrup transport is required to balance this
convergence.
Since no geostrophic f ow is possible across the natural boundaries marked by
the maximum trade winds and the maximum westerlies, this equatorward fl w must
141
6.8.7 The Sverdrup Balance
On the β plane, the divergence of lateral volume transport inherent with geostrophic
fl w is given by:
∂ Q
geo
x
∂ x
+
∂ Q
geo
y
∂ y
= −
β
f
Q
geo
y
(6.46)
On the large scale, this divergence (or convergence) of the geostrophic f ow balances the convergence (or divergence) of the drift in the surface Ekman layer. Effects
associated with bottom friction are irrelevant here. Under the assumption of purely
zonal wind (τ
wind
y
= 0), the steady-state balance leading to an equilibrium sea-level
distribution is given by:
β Q
geo
y ≈ −
1
ρ o
∂τ
wind
x
∂ y
(6.47)
This balance is called the Sverdrup relation (Sverdrup, 1947) and allows for
calculation of the meridional geostrophic volume transport (also called Sverdrup
transport) from knowledge of the average zonal wind-stress distribution. The corresponding zonal volume transport can be estimated from:
∂ Q
geo
x
∂ x
+
∂ Q
geo
y
∂ y
≈ 0
(6.48)
where the β effect can be ignored since this equation is used for diagnostic purposes only. It is important to note that the Sverdrup balance can only establish with
existence of a meridional boundary. The dynamics of unbounded fl ws, such as the
Antarctic Circumpolar Current, is more complex.
6.8.8 Interpretation of the Sverdrup Relation
First and foremost, the Sverdrup relation implies that latitudes of vanishing windstress curl (∂τ
wind
x
/∂ y = 0) coincide with regions of vanishing meridional geostrophic f ow. Hence, these regions form natural boundaries that, for instance,
separate subtropical from subpolar gyres in the ocean.
In the midlatitude ocean of the northern hemisphere, the main wind pattern consists of trades to the south and westerlies to the north. This wind pattern provides
∂τ
wind
x
/∂ y > 0 and produces a convergence of volume transport in the surface
Ekman layer. Hence, equatorward Sverdrup transport is required to balance this
convergence.
Since no geostrophic f ow is possible across the natural boundaries marked by
the maximum trade winds and the maximum westerlies, this equatorward fl w must