Etudes et évaluation de processus océaniques par des hiérarchies ...

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52 CHAPTER 9. ABYSSAL AND OVERTURNING CIRCULATION
Only in the beginning of the 20 th century Chamberlain (1906) considered the possibility
of variability or even a reversal of the deep ocean currents and its effects on climate. The
vulnerability of the overturning circulation to changes in the freshwater forcing at the ocean
surface is today seen as a likely candidat for the abrupt (several decades) Dansgaard-Oeschger
climate change events.
9.1 The Stommel Arons Theory
tel-00545911, version 1 - 13 Dec 2010
The picture presented in the previous section led Stommel and Aarons to consider the dynamics
of the deep layer in the ocean, which is subject to a localized injection of water in the northern
part and an upwelling, from the deep layer into the surface layer, through out the rest of
the thermocline. In the simplest geometry our ocean is a slice of the earth confined between
longitudes φ w , φ e and in the south by the equator. The injection happens at the North Pole
and has a strength S N (measured in Sv). As the total volume of the deep layer is conserved
the upwelling velocity w up = S/A where A is the surface of our slice, A = R 2 (φ e − φ w ). This
positive vertical velocity leads to a stretching of the deep layer and thus by conservation of
potential vorticity (eq. 5.57 or actually planetary potential vorticity) to a northward velocity
which is given by v sv = fw up /(Hβ) = w up R tan(θ)/H. But north-ward velocity means towards
the source! Conservation of mass imposes a southward transport somewhere in the fluid, and
knowing Sverdrup theory we suspect this transport to occur on the western boundary.
✗
✍
✕
North Atlantic
SN
✻
✻
✻
❑
▼
❖
Figure 9.2: Stommel-Arons Model
The north-ward interior (Sverdrup) transport as a function of latitude is
T sv = v sv H(φ e − φ w )Rcos(θ) = w up R 2 (φ e − φ w ) sin(θ) = S N sin(θ). (9.1)
The vertical transport into the deep layer north of the latitude θ (it actually goes out of the
deep layer it has a minus sign!) is equal to minus the upward velocity times the surface,
T up = −w up R 2 (φ e − φ w )
∫ π/2
For a slice north of θ we have,
θ
cos(θ ′ )dθ ′ = −w up R 2 (φ e − φ w )(1 − sin(θ)) = S N (sin(θ) − 1).(9.2)
S N + T sv + T b + T up = 0 (9.3)