Theory for the Deep Circulation
What are the important ingredients?
Theory for the Deep Circulation
after Stommel, Arons, and Faller (1958 to 1960)
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Cold, deep water is supplied by deep convection at a few high­latitude locations in the Atlantic, notably in the Irminger and Greenland Seas in the north and the Weddell Sea in the south.
Mixing in the ocean brings the cold, deep water back to the surface.
The abyssal circulation is strictly geostrophic in the interior of the ocean, and therefore potential vorticity is conserved.
Theory for the Deep Circulation
after Stommel, Arons, and Faller (1958 to 1960)
their ideas start with considering bottom currents of thickness H in the interior of an ocean with constant depth
Theory for the Deep Circulation
(I) abyssal interior flow below the thermocline
Theory for the Deep Circulation
(II) a DWBC connects the streamlines of the flow
DWBC transport in a basin with source (S0):
without source (S comes from other basin):
Theory for the Deep Circulation
What drives the deep circulation?
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Notice that the deep circulation is driven by mixing, not by the sinking of cold water at high latitudes.
Munk and Wunsch (1998) point out that deep convection by itself leads to a deep, stagnant, pool of cold water. In this case, the “deep” circulation is confined to the upper layers of the ocean.
Tides and winds are the primary source of energy driving the mixing.
Theory for the Deep Circulation
flat bottom approximation vs. topography
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Note that the Stommel­Arons theory assumes a flat bottom.
The mid­ocean ridge system divides the deep ocean into a series of basins connected by sills through which the water flows from one basin to the next.
As a result, the flow in the deep ocean is not as simple as that sketched by Stommel.
The vertical mixing is not homogeneous.
Theory for the Deep Circulation
convection and mixing
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Convection is a very localized process, mixing can occur over far larger areas.
Convection reduces the potential energy of the water column, and it is self powered.
Mixing in a stratified fluid increases the potential energy, and it must be driven by an external process.
Theory for the Deep Circulation
numerical models show that:
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the meridional overturning circulation is very sensitive to the assumed value of vertical eddy diffusivity in the thermocline, recent results indicate sensitivity especially near side boundaries.
the transport is not limited by the rate of deep convection.
Theory for the Deep Circulation
Where is cold water mixed upward?
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Recent measurements of vertical mixing suggest mixing is concentrated above seamounts and mid­
ocean ridges, and along strong currents such as the Gulf Stream.
Because we do not know very well the value of vertical eddy diffusivity, and because we do not know where vertical mixing in the ocean is important, the deep circulation calculated from numerical models probably has large errors.
Observation of the Deep Circulation
What are its time scales and how to best measure it?
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abyssal transport through the basins takes O[100 – 1000 years] ­> mean flow has O[1 mm/s]
Observing this small mean flow in the presence of typical deep currents having variable velocities of up to 10 cm/s or greater, is very difficult.
Most of our knowledge of the deep circulation is inferred from measured distribution of temperature, salinity, oxygen, silicate, tritium, fluorocarbons and other tracers.
Observation of the Deep Circulation
Water masses: a point, better a cluster on a T­S­plot
Upper: Mixing of two water masses produces a line on a T­S plot. Lower: Mixing among three water masses produces intersecting lines on a T­S plot, and the apex at the intersection is rounded by further mixing. From Tolmazin (1985).
Observation of the Deep Circulation
Water masses in the South Atlantic
Observation of the Deep Circulation
following local extrema ­ the core method
Contour plot of salinity as a function of depth in the western basins of the Atlantic from the Arctic Ocean to Antarctica. The plot clearly shows extensive cores, one at depths near 1000 m extending from 50°S to 20°N, the other at is at depths near 2000m extending from 20°N to 50°S. The upper is the Antarctic Intermediate Water, the lower is the North Atlantic Deep Water. The arrows mark the assumed direction of the flow in the cores. The Antarctic Bottom Water fills the deepest levels from 50°S to 30°N. See also Figures 10.16 and 6.11. From Lynn and Reid (1968).
Observation of the Deep Circulation
Examples of conservative and dynamical tracers
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Salinity and Temperature are dynamical tracers.
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Fluorocarbons (Freon) and Sulphur hexafluoride (SF6) are conservative tracers
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Tritium, Oxygen, Silicates, Phosphates are non­
conservative tracers (decay, respiration and oxidation, used by organisms)
Antarctic Circumpolar Current
”mix­master ” between all Oceans
Cross section of neutral density across the Antarctic Circumpolar Current in the Drake Passage from the World Ocean Circulation Experiment section A21 in 1990. The current has three streams associated with the three fronts (dark shading): SF = Southern acc Front, PF = Polar Front, and SAF = Sub­antarctic Front. Hydrographic station numbers are given at the top, and transports are relative to 3,000dbar. Circumpolar deep water is indicated by light shading. From Orsi (2000).
Antarctic Circumpolar Current
”mix­master ” between all Oceans (cont.)
Distribution of the Sub­
antarctic and Polar Fronts and associated currents in the Antarctic. From Orsi (1995).
Antarctic Circumpolar Current
”mix­master ” between all Oceans (cont.)
Tave = 125 Sv
Variability of the transport in the Antarctic Circumpolar Current as measured by an array of current meters deployed across the Drake Passage. The heavier line is smoothed, time­averaged transport. From Whitworth (1988).
Equatorial Processes & El Niño
What is left?
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Numerical modelling
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Waves (esp. off­equatorial)
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Coastal processes and tides
Equatorial Processes & El Niño
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EUC phenomenon and dynamics
ENSO phenomenon and historical background
Rossby and Kelvin waves