E 60e 90e 120e 150e 180 150w 120w 90w 60w 30w 0

Fig. 5.4 Deep water formation sites in the world's oceans, with the 5 km depth contours; squares indicate water mass formation in the open ocean, and circles indicate formation in marginal seas.

Formation in the open ocean

Deep water can be formed through the so-called chimney formation. Water formed in the open ocean directly sinks to the bottom, and spreads to other parts of the oceans, at sites shown by the lettered squares in Figure 5.4. The following list was compiled with the help of B. Warren.

A. Gulf of Lions in the Mediterranean Sea (MEDOC Group, 1970);

B. The Weddell chimney (Gordon, 1978); the Weddell polynya (Martinson et al., 1981; Gordon, 1982);

C. The Norwegian/Greenland Seas;

D. The Labrador Sea (Lazier, 1973; Clarke and Gascard, 1983; Pickart et al., 2002);

In addition, there is deepwater formation in the Bransfield Strait; however, the deep water formed in this location may not be exported to other part of the world's oceans (Gordon andNowlin, 1978).

Formation along the margins of the sea

Strong cooling along the edge of a continent creates favorable conditions for dense water mass formation in the marginal sea. Water formed in this way moves down along the continental slope and eventually reaches the bottom of the oceans (numbered circles in Fig. 5.4), including:

1. The western and southwestern Weddell Sea (Foster and Carmack, 1976);

2. The Ross Sea (Jacobs et al., 1970; Warren, 1981);

3. The Wilkes Land (Carmack and Killworth, 1978);

4. The Adelie coast (Gordon and Tchernia, 1972);

5. The Enderly Land (Jacobs and Georgi, 1977);

6. The eastern coast of Greenland.

It is notable that deep/bottom water formation is not a continuous process. In fact, dense water formation tends to happen episodically, depending on the anomalous atmospheric conditions.

Although dense water is formed in the Mediterranean Sea during winter-time, under current climate conditions it cannot sink to the deep ocean. Instead, through strong entrainment, it becomes lighter and eventually spreads into the North Atlantic Ocean at the depth range of slightly below 1 km.

There is also dense water formation in the Red Sea due to excessive evaporation. However, dense water formed in the Red Sea is mostly confined to the Indian Ocean, so it will not be discussed here.

5.1.2 Bottom/deepwaterformation

Antarctic Bottom Water (AABW) formation

The bottom layer of the world's oceans is filled with a thick layer of very cold water with potential temperature lower than 2°C, as shown in Figure 5.5.

The origin of this water mass is clearly from the edge of Antarctic (thus, it is called AABW), whose origin can be traced back to a few sites along the continental margin of Antarctica where cold water is formed during the Southern Hemisphere winter. The cold temperature of this water mass is directly linked to the strong cooling in winter-time when very cold wind from glacial ice on Antarctica blows over the coastal ocean adjacent to the ice edge, driving sea ice away from the coasts and thus creating coastal polynyas (small open water areas surrounded by sea ice). Owing to the increase in concentration of oxygen at low temperature, the newly formed bottom water is normally associated with very high oxygen concentration, about 200 ^mol/kg (Fig. 5.2).

Strong cooling over polynyas produces more sea ice, and salt rejection during sea ice formation creates cold dense water with higher salinity. This dense water overflows the continental slope. The offshore transport of the newly formed bottom water is compensated by the onshore flow of water in the subsurface layer. However, flow pathways in the ocean are

Fig. 5.5 Meridional distribution of potential temperature in a the Atlantic Ocean; b the Pacific Ocean; c the Indian Ocean.

Cold wind from Antarctica

Cold wind from Antarctica

Fig. 5.6 Formation of AABW (redrawn from Gordon, 2002).

much more complicated due to many dynamical factors, including wind stress and surface thermohaline forcing, stratification and rotation; thus, the arrows in the two-dimensional sketch (Fig. 5.3) should not be taken as being the real trajectories of water parcels.

The formation of AABW involves many complicated physical processes (Fig. 5.6), including the formation of dense and salty water within the coastal polynyas, the transport of this water by the gyre circulation within the coastal area, the overflow from the marginal sea to the open ocean, and the entrainment during the descent of the gravity current along the continental slope. During the descent along the slope, it entrains the water in the environment; thus, it is slightly warmed up from —2°C to — 1°C. Eventually, it sinks to the bottom with a temperature of nearly 0°C. Due to vigorous entrainment during the overflow from the marginal sea to the open ocean, the total volume flux of the final product is greatly increased (Gordon, 2002). In addition, cabbeling may further increase the density of the newly formed bottom water; thus, it may play a vital role in setting the properties of the final product.

Deep convection

Another form of bottom/deep water formation in the oceans is the deep convection taking place in the open ocean (Fig. 5.7). The major sites of deep convection include the northwestern Mediterranean, the Labrador Sea, and the Greenland Sea.

Deep Convection

c Lateral exchange/spreading d Final stage

Fig. 5.7 Sketch of open ocean deep convection: a preconditioning, b deep convection, c lateral exchange/spreading, d final stage (redrawn from Marshall and Schott, 1999).

Basic processes

Deep convection in the open ocean involves dynamical processes of rather broad spectra in both spatial and temporal scales. As a concise description, it can be roughly classified into the following major processes (Marshall and Schott, 1999).

• Preconditioning: Strong cyclonic wind stress curl in early winter enhances the Ekman upwelling in the center of the cyclonic gyre, leading to a dome-shaped isopycnal structure. Within the center of the cyclonic gyre, stratification is very weak, and this weak stratification can facilitate deep convection (Fig. 5.7a).

• Deep convection: Strong buoyancy loss due to cooling and evaporation further reduces the stratification in the upper ocean within the central regime of the cyclonic gyre. Further cooling eventually sets in the deep convection, which consists of clusters of small-scale downward plumes (with a horizontal scale of 1 km or less) and eddies (with a horizontal scale of 10 km). Water in the small plumes moves downward with vertical velocity on the order of 0.1 m/s (Fig. 5.7b). Plumes and eddies form the mixed patch (this is also called a "chimney" in some early articles) with a horizontal scale on the order of 100 km.

• Lateral exchange and spreading: A few days after the onset of cooling, the dominating mode of heat exchange is shifted from vertical to horizontal through eddy activities on the geostrophic scale (Fig. 5.7c).

• Final stage: The chimney-like density structure associated with deep convection is gradually closed up and leaves behind a dome-shaped isopycnal structure, with a layer of cold water which settles at depth (Fig. 5.7d).

Two basic parameters play crucial roles in the establishment of deep convection. First, the buoyancy (Brunt-Vaisala frequency, N2 = - gdp;), which is also a measure of the frequency of internal gravity waves. The ocean is normally stably stratified, i.e., N2 > 0; however, owing to strong buoyancy forcing, there are small areas in the upper ocean where the stratification may become temporarily unstable, i.e., N2 < 0, and convection ensues.

The second parameter is the Rossby deformation radius, defined as Rd = NH/f0, where H is the thickness of the convective layer. Since the buoyancy frequency can be rewritten as N = y/g'/H, the speed of gravity waves is c0 = y/g'H; thus, Rd = c0/f0 is a measure of how far gravity waves can travel over an inertial period. For the mid-latitude ocean, the typical scale of the Rossby deformation radius is on the order of 30 km. However, at high latitudes, weak stratification gives rise to a much smaller deformation radius, on the order of 10 km. Owing to strong cooling in winter-time it can be further reduced to a few kilometers. For horizontal scales on the order of the deformation radius or larger, geostrophic and hydrostatic balance dominate; however, for horizontal scales much smaller than the deformation radius, geostrophic and hydrostatic balances break down (Marshall etal, 1997).

Scales of the plumes

Dimensional analysis can be used to predict the basic scales involved in deep convection (Marshall and Schott, 1999). Assume the surface buoyancy flux is B0 and there is a layer of homogenized fluid with a depth of h. During the initial stage of the onset of convection, t ^ 1/f, rotation is unimportant; thus, both B0 and t work as the only parameters controlling the formation of plumes. With these two parameters, dimensional analysis gives rise to the following scales for the horizontal length, velocity, and buoyancy of the plumes l - (B0t3)V2 (5.1a)

For time scales that are long enough, the plumes evolve and reach to the bottom of the mixed layer. As the time scale approaches 1/f, the role of rotation becomes dominating, and the corresponding scales are lrot - (B0/f 3)V2 (5.2a)

Assume the flux of heat loss is 500 W/m2, the corresponding buoyancy flux is B0 = 2.25 x 10-7m2/s3, and the scales of plumes are: lrot - 0.47 km, urot = wrot - 0.05 m/s.

North Atlantic Deep Water formation North Atlantic Deep Water primarily consists of two parts: the overflow from the Norwegian Sea, and deep water formed in the Labrador Sea.

Deep water overflow from the Norwegian Sea may come from two sources (Mauritzen, 1996). The classical theory has been the following: winter deep convection in the Iceland and Greenland Seas produces cold and dense water that sinks to the deep part of the Norwegian Basin. As deep water accumulates and fills up to a level higher than the sills connecting the Norwegian Basin with the open northern North Atlantic Ocean, deep water overflows the sills and becomes the source of NADW.

However, such a scenario of deepwater formation in the North Atlantic Ocean has some potential problems. First, the existing estimates of deepwater formation rate are much smaller than the estimates of dense water overflows through the Greenland-Scotland Ridge. Second, this scenario implies that the overflow rate may have noticeable seasonal and interannual cycles. For example, observations indicate that the production of deep water in the Greenland Sea was greatly reduced in the 1980s (Schlosser et al, 1991). However, there are no clear indications that the overflow rate changes much over such time scales.

Another source of deepwater overflow from the Norwegian Sea originates from the cooling-induced convection in the boundary currents flowing around the edge of the Norwegian Sea. In fact, Atlantic Water in the northward flowing Norwegian Atlantic Current becomes gradually denser due to heat loss, filling up the shallow and intermediate depths along the rim of the basin. This water mass flows over the sills and becomes the source of the NADW.

On the other hand, although cooling in the Norwegian Sea can produce Deep Norwegian Sea Water, this water mass is too cold and is denser than the overflow water. Tritium concentration analysis indicates that overflow water should come from a depth shallower than 1,000 m. As a matter of fact, three sills connecting the Norwegian Sea to the North Atlantic Ocean are relatively shallow: the Faroe-Shetland Channel (850 m), the Denmark Strait (600 m), and the Iceland-Faroe Ridge (500 m). Therefore, deep water overflowing these sills should be primarily from the relatively shallow sources along the rim of the basin. Thus, cooling-induced convection along the rim current in the Norwegian-Greenland Sea may be the major source of NADW.

Similarly, deep convection in the Labrador Sea contributes very little to the overall meridional overturning in the North Atlantic Ocean, and the most important pathway of water mass formation in the Labrador Sea is the gradual transition of water properties within the boundary current around the basin (Pickart and Spall, 2007).

5.1.3 Overflow of deep water

Topographic control of deep flow

The world's oceans are characterized by many basins separated by major ridge systems. Due to the existence of these ridges, bottom water movement and distribution of water properties are strongly confined by complicated dynamical laws. Basically, deepwater flows from one basin to the others must go over sills which exist as the lowest passages in these otherwise tall topographic barriers.

When water moves over a sill, it behaves very much like a deep waterfall. In many cases, a deep waterfall involves a volume flux on the order of 1-10 Sv (106-107 m3/s), and an elevation change on the order of several hundreds of meters. Many people have visited the Niagara Falls, one of the largest land-based waterfalls in the world, which has a maximal volume flux of 3,000 m3/s and elevation drop of 56 m. In comparison, deep waterfalls are much more powerful than any land-based waterfall on Earth, with a volume flux of more than 1,000 times and elevation drop of more than 10 times that of the Niagara Falls.

The meaning of rotating hydraulics

An essential feature common to the overflow associated with deepwater formation is that the overflow goes through the transition from subcritical to critical, and then to supercritical. Whether a flow is subcritical or not is defined in terms of the Froude number. Using the waterfall as an example, the concept of hydraulics for a non-rotating fluid can be explained as follows. For water flowing in an open channel, signals propagate with the velocity of the surface wave, i.e., c = y/gh, where h is the depth of water. The Froude number is defined as F = U/c, where U is the horizontal velocity of the fluid. For most cases of flow through a channel, F < 1, so the fluid motion is subcritical, i.e., fluid travels at a speed slower than the speed of signals.

If the mean slope of the channel is gradually increased, fluid speed increases. At a critical value of slope, water travels so fast that its speed exactly matches the speed of surface waves. Generally, the bottom of the channel is not flat, and there is a place in the channel where the depth is the shallowest. This is called a sill, and depth both upstream and downstream from the sill is greater, as shown in Figure 5.8.

Assume that water motion upstream from the sill is subcritical and the depth of the sill is gradually reduced. The Froude number at the sill gradually increases, while flow in the

Subcritical flow Critical flow Supercritical flow

Signal speed

Flow speed

Signal speed

Flow speed

Fig. 5.8 Sketch of overflow from a marginal sea to the open ocean, involving rotating hydraulics.

whole channel remains subcritical. When the sill depth reaches a critical value, fluid motion at the sill becomes exactly critical, i.e., U = c at this section. Although fluid motion upstream remains subcritical, fluid motion downstream becomes supercritical, i.e., fluid velocity is larger than the signal velocity. One of the major differences in supercritical and subcritical flows is that, in a supercritical flow, field signals cannot propagate upstream because the speed of the signals is slower than the flow speed.

If we stand by a waterfall, we realize that no matter how hard we disturb water in the fall, nothing happens upstream - signals cannot go upstream. What happens in the oceans is more complicated because we have to deal with stratification and rotation; thus, the study of overflow is called rotating hydraulics. As a first step in this direction, we can treat the oceanic flow with continuous stratification as a system with two density layers. In addition, we can assume that the upper layer moves so slowly that it can be assumed to be stagnant. Under such assumptions, the problem is reduced to the framework of the inverse reduced-gravity model discussed previously. The equivalent signal speed is c = ^Jgh, where g' = gAp/p is the reduced gravity and h is the thickness of the moving layer. Thus, the corresponding Froude number is defined as F = u/sigh.

Similar to the case of the hydraulic problem in an open channel, the supercritical flow downstream from the sill is not very stable, and hydraulic jump-like phenomena and mixing with the environmental fluid ensue.

Another crucial phenomenon associated with deepwater overflow is that the newly formed cold and dense overflow water is piled up on the right-side bank of the channel (if we look in the downstream direction) because of the Coriolis force (Fig. 5.9). Of course, if the channel

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