5.7 The Thermohaline Circulation
147
to a depth of 1,500–2,000 m. In the sole presence of vertical diffusion of heat, the
permanent thermocline would gradually deepen and the abyssal oceans would gradually become warmer until a thermodynamic equilibrium is being established. Since
this does not happen, there must be another process that overrides the downward
diffusive heat flux.
Based on earlier suggestions of Stommel (1958), Stommel and Arons (1960)
proposed a model for the abyssal circulation of the world ocean that is still subject
to intense debate by the scientific community. A key ingredient of this analytical
model, commonly called the Stommel-Arons model, is the assumption that largescale upwelling induced by geostrophic flow in the abyssal ocean balances vertical
diffusion of heat, such that the structure of the permanent thermocline is maintained.
Consider a two-layer ocean for illustration of this mechanism. For simplicity, the
deep layer is assumed to have uniform thickness h and density. Using the betaplane approximation (Eq. 4.7) gives a relationship between the vertical speed at the
top of bottom layer and the meridional geostrophic flow component v that can be
written as:
w =
βh
f
v
(5.16)
Consequently, upwelling at the top of the bottom layer is associated with a poleward geostrophic flow in this layer. A meridional flow of a speed of v = 1 mm/s with
h = 2,000 m, for instance, would create a vertical upward displacement of isotherms
at a rate of 14 m per year.
A further ingredient of the Stommel-Arons model is the prescription of two separate regions of dense-water formation that operate as volume sources for the deep
layer; that is, the Greenland Sea/Labrador Sea and the Weddell Sea (ignoring the
Ross Sea contribution to Antarctic Bottom Water formation). Volume conservation
implies that poleward flow in deeper layers of the north Atlantic Ocean must be
returned southward by a narrow DWBC. Nevertheless, the volume carried by this
boundary current must be greater than that introduced at the source region given
that it also has to return the volume inherent with the poleward flow. To this end, the
DWBC carries some surplus volume across the equator and into the south Atlantic
Ocean.
Figure 5.17 illustrates the analytical result of the Stommel-Arons Model for
the Atlantic Ocean. Several inconsistencies of this model have been identified in
recent years. These include: (a) observed deep-ocean values of eddy diffusivity are
much less than those required to reproduce the Western Boundary Current with
the Stommel-Arons model; (b) the model does not include any dynamics actually
driving poleward deep flows, (c) variable bathymetry, such as mid-ocean ridges,
are not included, despite their control on the possible pathways of deep flows.
Despite these shortcomings, the Stommel-Arons model, proposed half a century
ago, is still the backbone of many present-day research projects undertaken in the
deep sea.
147
to a depth of 1,500–2,000 m. In the sole presence of vertical diffusion of heat, the
permanent thermocline would gradually deepen and the abyssal oceans would gradually become warmer until a thermodynamic equilibrium is being established. Since
this does not happen, there must be another process that overrides the downward
diffusive heat flux.
Based on earlier suggestions of Stommel (1958), Stommel and Arons (1960)
proposed a model for the abyssal circulation of the world ocean that is still subject
to intense debate by the scientific community. A key ingredient of this analytical
model, commonly called the Stommel-Arons model, is the assumption that largescale upwelling induced by geostrophic flow in the abyssal ocean balances vertical
diffusion of heat, such that the structure of the permanent thermocline is maintained.
Consider a two-layer ocean for illustration of this mechanism. For simplicity, the
deep layer is assumed to have uniform thickness h and density. Using the betaplane approximation (Eq. 4.7) gives a relationship between the vertical speed at the
top of bottom layer and the meridional geostrophic flow component v that can be
written as:
w =
βh
f
v
(5.16)
Consequently, upwelling at the top of the bottom layer is associated with a poleward geostrophic flow in this layer. A meridional flow of a speed of v = 1 mm/s with
h = 2,000 m, for instance, would create a vertical upward displacement of isotherms
at a rate of 14 m per year.
A further ingredient of the Stommel-Arons model is the prescription of two separate regions of dense-water formation that operate as volume sources for the deep
layer; that is, the Greenland Sea/Labrador Sea and the Weddell Sea (ignoring the
Ross Sea contribution to Antarctic Bottom Water formation). Volume conservation
implies that poleward flow in deeper layers of the north Atlantic Ocean must be
returned southward by a narrow DWBC. Nevertheless, the volume carried by this
boundary current must be greater than that introduced at the source region given
that it also has to return the volume inherent with the poleward flow. To this end, the
DWBC carries some surplus volume across the equator and into the south Atlantic
Ocean.
Figure 5.17 illustrates the analytical result of the Stommel-Arons Model for
the Atlantic Ocean. Several inconsistencies of this model have been identified in
recent years. These include: (a) observed deep-ocean values of eddy diffusivity are
much less than those required to reproduce the Western Boundary Current with
the Stommel-Arons model; (b) the model does not include any dynamics actually
driving poleward deep flows, (c) variable bathymetry, such as mid-ocean ridges,
are not included, despite their control on the possible pathways of deep flows.
Despite these shortcomings, the Stommel-Arons model, proposed half a century
ago, is still the backbone of many present-day research projects undertaken in the
deep sea.