Lecture 1. A survey of oceanic circulation theory 3/14/2006 7:21 AM

I. Introduction It is well known that oceanic circulation is driven by a) Wind stress, b) Heat flux, c) Freshwater flux (associated with evaporation, precipitation, and river runoff), d) Tidal force. Although mankind started to observe the oceanic circulation many centuries ago, the development of the theory of the oceanic circulation is relatively new. On the other hand, the theory about atmospheric circulation has been developed to a much more complete stage during the past half century.

In his famous monograph about atmospheric general circulation, Lorenz (1967) reviewed the historical development of the relevant theory. The Hadley cell and the Jet Stream in both the North and South Hemispheres characterize circulation in the atmosphere. In a crude way, the circulation in the atmosphere can be described in terms of an axisymmetric circulation.

On the other hand, circulation in the oceans is much more complicated. Due to the existence of continents, individual basins are bounded by the coastal lines. As a result, there are many gyres and meridional overturning cells in the world oceans. There is only one current system in the modern ocean that resembles the circulation in the atmosphere -- the Antarctic Circumpolar Currents.

The existence of the meridional boundaries in each basin creates east-west pressure gradient, making the existence of meridional geostrophic current in each possible. As we will see that the existence of the eastern/western boundary is the major difference between atmospheric and oceanic circulation. The main focus of our course is on the structure of the circulation illustrated in Fig. 1. The circulation system in the Atlantic can be separated into the combination of meridional cells and horizontal gyres. There are three gyres in the Atlantic, two subtropical gyres and a subpolar gyre in the North Atlantic. The existence of these gyres is primarily due to wind stress applied to the ocean, and the structure of these gyres is the main focus of our study. In addition, there are also two tropical gyres near the equator. These two tropical gyres are coupled to the so-called tropical cells (in the y-z plane), and they play vitally important role in regulating the equatorial circulation in the ocean and climate. However, due to the limitation of time this part of the oceanic circulation will not be the focus of our course. There are two meridional overturning cells in the Atlantic -- the main cell driven by Atlantic Deep Water and a bottom cell driven by the Antarctic Bottom Water. Finally, there is the Antarctic Circumpolar Currents, which is the global artery and plays the most important role in the global oceanic circulation and climate.

Although we have seen great progresses along the line of understanding the structure of the global oceans, many important aspects of this global picture remain unclear, and it is one of the most important and exciting research frontiers.

Fig. 1.1. Sketch of the circulation system in the world oceans, using the Atlantic basin as an example. Our knowledge about the oceanic circulation has evolved in a much slower pace, due to the difficulties associated with observing the oceanic general circulation, a turbulent system with extremely broad spatial and temporal scales. In the early stage, our knowledge of oceanic general circulation was mostly observational. For example, "The Oceans" written by Sverdrup, Johnson and Fleming (1942) has been one of the classical books in oceanography, which is an amazing summary of the state of the art of oceanography in the early 1940's. Ekman (1905) discussed the structure of the wind-driven circulation in the surface boundary layer, which has been the theoretical foundation of modern circulation theories. However, it took four decades before Sverdrup (1947) proposed the theory of wind-driven circulation. At the time "The Oceans" was published, it seemed that a lot was known about the oceanic circulation. Thus, the book was a rather intimidate collection of knowledge. However, at that time our knowledge of oceanic circulation theory was confined to simple dynamical calculations of currents based on the so-called “level of no motion”, the Ekman layer, waves, and tides. During the past twenty years there have been many major breakthroughs in the theory of oceanic general circulation. Henry Stommel (1957) wrote a wonderful review on the same subject 49 years ago. Now it is time to review the progress along these lines. II. Thermal structure and circulation in the upper ocean

Motions in the ocean are driven by wind stress, heat flux, and freshwater flux from above. In addition, the tidal force works as a body force. Traditionally, tides have been studied in separation from the general circulation in the ocean. Recent studies indicate there is a strong connection between tidal dissipation and the oceanic general circulation.

Circulation in the upper kilometer of the ocean is dominated by the wind stress forcing, so it is called the wind-driven circulation. The circulation over the whole depth of the ocean is driven by the density difference due to the redistribution of heat and salt through mixing processes, and it is called the thermohaline circulation (a new trend in this direction is to treat thermohaline circulation as a system driven by external mechanical energy, this will be discussed in detail later). Separating the circulation into these two types is only conceptual. In fact, upper ocean circulation is also

Strong Jet Stream drives the ACC

affected by the density difference, and the circulation below the top kilometer is also affected by the wind stress through the setting of the surface conditions and subsurface mixing.

Thermocline is one of the most outstanding features in the oceans, and one can easily identify the main thermocline from hydrographic sections. As an example, the structure of both temperature and density for the upper ocean along 158.5oE are shown in Fig. 2.1. By definition, thermocline is a thin layer where the vertical gradient of temperature is a local maximum. There are many types of thermocline, including the diurnal thermocline, the seasonal thermocline, the main thermocline, and the abyssal thermocline. The diurnal thermocline exists in the upper ocean, and it is closely related to the diurnal cycle there. The seasonal thermocline exists in the upper hundred meters of the ocean, and it is closely related to the seasonal cycle in the upper ocean. The main thermocline exists within the depth range of 100m to 800m. Because it is far away from the sea surface and shaded from the direct forcing in the seasonal cycle, it is also called the permanent thermocline. The abyssal thermocline exists in the deep ocean, which will be discussed in the Lecture about deep circulation later. The main thermocline can be readily identified from the top panel of Fig. 2.1. It is close to the 20oC isothermal surface in the equatorial ocean, and it gradually shifts to lower temperature of 11-12oC at middle latitudes. The main thermocline is clearly asymmetric with respect to the Equator, which indicates that forcing and boundary conditions for the wind-driven circulation are asymmetric. On the other hand, the main pycnocline is not clearly defined in this section.

Since motions in the oceans are intimately related to density, the pycnocline, defined as the local maximum of vertical density gradient, may be more important dynamically. However, salinity contribution to the density in most cases is much smaller than that due to temperature; therefore, the thermocline and the pycnocline are closely linked to each other, and in many studies people use the term of thermocline, although it would be more accurate to use the term of pycnocline. Since thermal (or the density) structure is intimately associated with the circulation, the theory of the thermocline is also a theory for the circulation in the upper ocean.

Fig. 2.1. Thermal structure (a) and stratification (b) along 158.5oE, overlaid with the vertical gradient, based on Levitus 1998 climatology.

The depth of the main thermocline varies greatly with the geographic location, Fig. 2.2. It is rather shallow near the eastern boundary of the equatorial ocean due to equatorial upwelling driven by the easterlies at low latitudes. It is also shallow along the eastern boundaries of the Southern Hemisphere due to the along-shore wind. The shallowness of the main thermocline is associated with the relatively cold temperature at the surface, and these areas are called the cold tongues in the oceans.

The main thermocline in the western part of the equatorial oceans is deeper than that in the eastern part because warm water is piled up under the easterlies. In the Pacific this body of warm water is called the Warm Water Pool. Both the Warm Water Pool and the cold tongue play very vitally important role in the global climate system, especially the ENSO dynamics.

Thermocline is much deeper at middle latitudes, primarily due to the downward pushing of the negative wind stress curl. In the subtropical gyre of the North Atlantic (North Pacific), it can reach to the depth of 800 m (550 m), Fig. 2.2. The thermocline in the Southern Hemisphere is relatively shallower, and it is about 500 m (450 m) for the South Atlantic (South Pacific). The difference in thermocline depth reflects the difference in wind stress forcing and the stratification in different oceans. As will be explained shortly, the thermocline depth is inversely proportional to the stratification. In the North Atlantic stratification is relatively weak due to high salinity induced by strong evaporation; thus, thermocline there is much deeper than in other oceans.

The isopycnal surfaces representing the main thermocline outcrop along the boundary between the subtropical and subpolar gyres; thus, there is no main thermocline in subpolar basins.

Fig. 2.2. Depth of the main thermocline (in m) for the Pacific and Atlantic.

Temperature on the main thermocline varies depending on the location. For example, temperature on the thermocline is about 21oC at the western part of the Equatorial Pacific, and it gradually shifts toward 18oC near the eastern Equatorial Pacific where the cold tongue exists, see Fig. 2.3. At middle latitudes, the main thermocline corresponds to a much lower temperature, about 8-10oC for the subtropical North Pacific and about 10-12oC for the subtropical North Atlantic.

Fig. 2.3. The temperature, in oC, on the main thermocline of the Pacific and Atlantic Oceans.

Vertical temperature gradient on the main thermocline also varies greatly over the world oceans. Within the subtropical gyres, the gradient is on the order of 2-4oC/100m; however, it is much larger in the equatorial ocean, varies from 10oC/100m in the western part to 20oC/100m in the eastern part of the Equatorial Pacific, see Fig. 2.4. If wind stress changes, the thermocline should move vertically in response, and the subsurface temperature anomaly should appear near the time-mean depth of the main thermocline.

Fig. 2.4. The temperature gradient (lower panel, in oC/100m) on the main thermocline of the Pacific and Atlantic Oceans. 1. Simple models for the wind-driven circulation Our knowledge about the oceanic circulation has evolved in a rather slow pace, due to the difficulties associated with observing the oceanic general circulation, a turbulent system with extremely broad spatial and temporal scales. In the early stage, our knowledge of oceanic general circulation was mostly observational.

The first milestone is the paper by Ekman (1905), in which he discussed the structure of the wind-driven circulation in the surface boundary layer. According to his theory, the velocity in the boundary layer should have a spiral structure, and the vertically integrated volume transport is

0/ fτ ρ and 90o to the right of the wind stress. This layer is now called the Ekman layer and the flux in this layer is called the Ekman flux, which has been the theoretical foundation of modern wind-driven circulation theories.

The Ekman layer and its associated spiral velocity profile in the atmospheric boundary layer can be readily observed. I still remember vividly the beautiful Ekman spiral demonstrated by sending a line with many blooms during a field trip in Seattle organized by the late Welander in the early 1980s.

It took a long time before the theory can be verified in the ocean. The major difficulties in the ocean are the strong surface waves in the upper ocean. Only after a long time delay, the Ekman spiral on the upper ocean was confirmed through in-site measurement (Price et al., 1987). The structure of the stratified Ekman layer is much more complicated. For the most updated information, the reader is referred to Price and Sundermeyer (1999).

Before 1940s our knowledge of oceanic circulation theory was confined to simple dynamical calculations of currents based on a level of no motion, the Ekman layer, waves, and tides. For example, "The Oceans" written by Sverdrup, Johnson and Fleming (1942) has been one of the classical books in oceanography, which is an amazing summary of the state of the art of oceanography in the early 1940's. At the time "The Oceans" was published, it seemed that a lot was known about the oceanic circulation. Thus, the book was a rather intimidate collection of knowledge, as Stommel recalled in his autobiography.

During the past 60 years there have been many major breakthroughs in our understanding of the oceanic general circulation. In fact, many simple models have been developed in order to explain the wind-driven circulation and the structure of the thermocline.

The second milestone in wind-driven circulation theory is the work by Sverdrup (1947), in which he established the simple relation between the wind stress curl and the circulation. In order to maintain a relatively steady rotation of the Earth, the globally integrated frictional torque exerted by the atmosphere on the solid earth should be zero; thus, both westerlies and easterlies are the necessary components of the atmospheric circulation.

Westerlies at middle latitudes, and easterlies at low latitudes and polar regime drive a poleward Ekman flow in both low and high latitudes and an equatorward Ekman flow at middle latitudes. As a result, the meridional convergence of Ekman flux gives rise to the Ekman pumping/upwelling. In the basin interior, the relative vorticity is negligible, so potential vorticity for a water column is f/h. Ekman pumping compresses the water column height h. In order to conserve the potential vorticity f/h, water columns move toward the equator where the Coriolis parameter f is smaller. Thus, Ekman pumping drives an equatorward flow in the ocean interior. Similarly, the Ekman upwelling in the subpolar basin drives a poleward flow in the ocean interior.

Shortly afterward Sverdrup's seminal paper, simple theories about western boundary currents were proposed to close the circulation, including the western intensification theory by Stommel (1948), using a model with bottom friction; the western boundary layer with lateral friction by Munk (1950); and the inertial western boundary layer theory by Charney (1955).

Since seawater is nearly incompressible, the simplest way to simulate the ocean circulation is assuming that the ocean is homogeneous in density. Such an ocean would have no vertical structure. Early studies were based on the homogeneous ocean models, such as Stommel (1948). Other studies, such as Sverdrup (1947) and Munk (1950), used baroclinic models for the ocean. By assuming wind-driven circulation is confined to the upper layer of the ocean, the density structure is not explicitly included in the vertically integrated volume flux of the wind-driven circulation.

Wind-driven circulation has also been described in terms of the quasi-geostrophic model derived from the shallow water equation in many existed textbooks, e.g., Pedlosky (1987). However, quasi-geostrophic theory is not suitable for gyre-scale circulation problems because within the north-south direction the vertical displacement of isopycnal surfaces is the same order of magnitude as the layer depth. The strong nonlinearity due to the meridional change of the stratification can be handled much more accurately by layered models, such as the reduced gravity model.

The essence of a reduced gravity model is to treat the main thermocline (or the pycnocline) in the oceans as a step function in density, so density in the upper layer equals to a constant ρ and density in the lower layer is ρ ρ+ Δ . Furthermore, the lower layer is assumed infinitely deep, so pressure gradient in the lower layer is infinitely small and the mass flux negligible. As a good assumption, we can assume that the lower layer is motionless; thus, we actually deal with a single moving layer. The pressure gradient in the upper layer is in forms of / 'p g hρ∇ = ∇ , where h is

the upper layer depth and 'g g ρρΔ

= is called a reduced gravity, which is on the order of 1-

2cm/s2. The basic idea is demonstrated in Fig. 2.5, where the structure of the water column is

depicted. The seasonal thermocline (pycnocline) near the upper surface is clearly seen. The main thermocline and the main pycnocline locate at about the same depth (800 m), this is due to the fact that salinity contribution to the density is relatively small at this location (and many other locations). The density structure is now represented in terms of two layers of constant density as shown in Fig. 2.5b. The advantage of reduced gravity model is its ability to capture the first baroclinic mode of the circulation, and the depth of the main thermocline.

Fig. 2.5. Temperature and stratification at a station (70.5oW, 30.5oN). a) Temperature, in oC; b) Stratification, in θσ , and the heavy lines indicate the equivalent stratification used in a reduced gravity model; c) -dT/dz , in 0.01oC/m ; d) /d dzσ , in 0.01 θσ /m . 2. Equatorial thermocline and ENSO

ENSO events are manifestations of the strong atmosphere-ocean interaction, which are primarily concentrated in the Equatorial Pacific. Many theories have been proposed for explaining or predicting ENSO. The book by Philander (1990) is highly recommended as a good introduction to the reader. For the most updated and comprehensive review on the relative issues, the reader is referred to a special issue of J. of Geophysical Research Vol. 103, No. 7, 1998, especially the review by McPhaden et al. (1999), Neelin et al. (1999), and Latif et al. (1999).

Historically, El Nino was first observed in terms of anomalous sea surface temperature along the coast of Peru near the time of Christmas, so came the name of El Nino. As people started to investigate the relevant problems, the source of these events were gradually traced back to the Equatorial Pacific, and largest sea surface temperature anomaly is found in the eastern part of the Equatorial Pacific. The practical need for predicting El Nino leads to the discovery that strong temperature anomaly actually appears much earlier in the subsurface layer. A large-scale observation net was specially designed and put in operation during the Tropical Ocean-Atmosphere (TOGA) program. The strong subsurface temperature anomaly associated with El Nino was observed and discussed in many papers, for the comprehensive list of information the reader is referred to the special issue of J. Geophys. Res..

Fig. 2.6. Structure of the equatorial thermocline. The vertical temperature gradient is color-coded in units of 0.01oC/m .

As the wind stress changes, the thermocline moves vertically in response. Thus, in addition to the sea surface temperature anomaly map, the depth of the 20oC isotherm has been used as an indicator for the El Nino events. Kessler (1990) constructed a map of the 20oC isotherm depth anomaly for the Equatorial Pacific. His map clearly showed how the anomalous signals propagated in forms of Rossby waves and Kelvin waves. For a more complete list of paper along this line the reader is referred to McPhaden et al. (1999) and the references cited there.

Assuming that most isotherms move the same distance vertically, the largest temperature anomaly should appear near the main thermocline; thus, tracing the temperature anomaly on the climatological location of main thermocline may provide an early warning of incoming El Nino. As

shown in Fig. 2.6, however, the equatorial thermocline is very close to the 20oC isotherm, so both of them can be used as the preferred surface for search. Chao et al. (2002) came up with another interesting approach. By processing the subsurface temperature data over the past several decades, a Surface of Maximal Temperature Anomaly (SMTA) is defined. Although the SMTA is rather close to the main thermocline, it is a much more practical way for tracing the temperature anomaly. Using this approach, they are able to show that strong temperature anomalies normally start several months ahead of El Nino, and propagate eastward along the equatorial wave-guide. At the eastern boundary the signals turn poleward. At 10oN the signals turn westward and move toward the western boundary. Thus, this technique may be very useful in predicting El Nino. Similar ideas of tracing the subsurface temperature anomaly have been pursued by other investigators previously, such as Zhang et al. (1999), Li and Mu (1999).

It is to note that equatorial thermocline in three oceans has similar structure, as shown in Fig. 2.6. Thus, the connection between surface wind stress and the subsurface temperature anomaly exists, so this approach may also apply to the study of the thermal structure in the Indian and Atlantic Oceans. In particular, the Indian Ocean Warm Pool is closely related to the Warm Pool in the Pacific Ocean, through both the wind stress and the Indonesian Throughflow. III. Theories of the barotropic circulation (1947-1960)

The development of oceanic general circulation theory consists of two major phases. First, starting by Sverdrup's (1947) seminal work on the wind-driven circulation theory, the theory for the barotropic circulation was developed during the 1950's, including the following contributions: 1) Wind-driven circulation in a homogeneous ocean by Sverdrup (1947); 2) Western intensification and bottom-frictional western boundary layer by Stommel (1948); 3) Lateral-frictional western boundary layer by Munk (1950); 4) Inertial western boundary layer by Stommel (1954), Charney (1955), and Morgan (1956); and 5) Abyssal circulation by Stommel (1957), and Stommel and Arrons (1960 a,b).

Most theories developed at this stage were devoted to the stationary circulation. At the same time the theory of time-dependent circulation was also advanced by Stommel and others.

One of the most outstanding features in the oceans is the existence of the main thermocline. Theory of the thermocline was first proposed in by Welander (1959), Stommel and Robinson (1959). There have been many attempts to find solutions to the thermocline equations; however, most of these solutions are similarity solutions that cannot satisfy some essential boundary conditions. The most serious deficit of these solutions is their inability in satisfying the Sverdrup constraint. Without satisfying this constraint, these solutions are incapable of describing the basin-wise structure of the wind-driven gyre.

During the 1960's and 1970's, the development of oceanic circulation was relatively slow due to lack of understanding of the circulation physics. Numerical models had been developed; however, without physical insight obtained from observations or theoretical studies, results from numerical experiments proved as hard to understand as data from the oceans.

The backbone of the barotropic circulation is the barotropic potential vorticity constraint. Hough (1897) devoted a minor portion of his tidal study to the currents produced by a zonally distributed evaporation and precipitation, ignoring friction. He found that a uniformly accelerated system of purely east-west geostrophic currents would exist. His model has several important limitations. First, there is no friction in his model, so he was unable to obtain a steady solution, nor had he been able to discern the effect of evaporation and precipitation. Second, his model has no meridional boundary, which is an important constraint on the oceanic circulation. Hough published

his results without even a figure to show the structure of the solution; thus, his solution remained unnoticed, till Stommel (1957) publicized this solution with a beautiful illustration.

Fig. 3.1. Two successive stages of the Hough-type circulation pattern, driven by precipitation distributed over the northern hemisphere (P) and evaporation distributed over the Southern hemisphere (E). The hovering arrows indicate the distribution of precipitation-evaporation. The arrows drawn on the surface of the spheres are velocity components. The zonal currents grow with time. The central solid portion of the earth is shown as shaded in cut-away mid-section (Hough, 1897; Stommel, 1957). Goldsbrough (1933) discussed a model ocean forced by evaporation and precipitation. By choosing a rather special form of precipitation and evaporation pattern (the zonally-integrated evaporation and precipitation along each latitude vanishes), he was able to obtain a steady circulation, even though his model also has no friction. Goldsbrough's solution requires a special form of precipitation and evaporation that makes his solution quite unrealistic. The major reason why the Goldsbrough theory has been largely ignored is due to the small size of the barotropic current predicted by his theory. As we will discuss later, another major shortcoming in his theory is the lack of salinity in the model. Were the salt added into his model, the baroclinic velocity driven by the freshwater flux could be hundred times stronger than the barotropic velocity predicted by his original theory.

Fig. 3.2. Goldsbrough's solution for the North Atlantic, with precipitation and evaporation balanced for each latitudinal circle.

Nevertheless, the theories of Hough and Goldsbrough are more general than they first appear. The general nature of their theories can be explained more clearly with the aid of two basic mechanisms.

First, Ekman (1905) showed that the frictional stress of the wind is confined to a thin layer on the upper surface, so the motion below the sea surface can be treated as frictionless.

Second, the frictional or inertial western boundary layers provide an important dynamic component that can help to close the circulation in terms of the conservation of mass, energy, and momentum or vorticity (in more specialized terminology, conservation of potential vorticity.) The interior flow field can therefore be patched with some kind of western boundary layer (Stommel, 1948; Munk, 1950; Charney, 1955). Thus, the boundary layer theory that was developed in traditional fluid dynamics found its use in dynamical oceanography. In mathematical terms, the problem is treated by the perturbation method. In the interior ocean the flow is described by low-order dynamics, (essentially inviscid and linear); within the western boundary layer, the high-order terms such as frictional or inertial terms play important roles.

Fig. 3.3. Left panel: The Goldsbrough gyre driven by evaporation-precipitation and presented by him in 1933 as a model of the North Atlantic; right panel: Effects of using a more realistic distribution of evaporation-precipitation, and including western boundary currents. (Stommel, 1985).

In modern dynamical language, the wind stress creates the Ekman layer, which is driven by friction between the atmosphere and oceans. The horizontal convergence of Ekman flux generates an Ekman pumping which drives the interior flow equatorward in the subtropical basin and poleward in the subpolar basin.

In terms of potential vorticity dynamics, the lowest-order balance for the oceanic interior is: negative wind stress curl (or precipitation) input is balanced by equatorward motion, so that the potential vorticity of the water column is conserved.

Mass conservation requires a return flow, accomplished by western boundary currents. Thus, flow driven by an arbitrary pattern of wind stress, or evaporation minus precipitation, can be very well described by the theory. Similarly, the same argument has been applied to the abyssal circulation by Stommel and his colleagues. Thus, the wind-driven circulation can be interpreted in terms of potential vorticity balance and mass balance.

Although people tried very hard to work out theories about the vertical structure of the oceanic circulation during the following years, the theories about the oceanic circulation remained primarily two-dimensional. We will discuss the many puzzles and difficulties people faced during that period.

Fig. 3.4. Connections between different paths during the early development of the oceanic general circulation. IV. Theories of the baroclinic circulation (1979-2020?) The second phase of development of theory of oceanic circulation began in the 1980's. This new phase is characterized by combining observations, theory and numerical models. 1) Three-dimensional structure of the wind-driven circulation:

As our understanding of the oceanic circulation deepened, we realized that the ocean can be described as an ideal fluid system to a very good approximation. (As results from recent field observations indicated, diapycnal mixing rate is on the order of 10-5m2/s ). A major theoretical difficulty in the 1970s was the puzzle of how the subsurface layers in an ideal-fluid model ocean could be in motion. Since interfacial friction is assumed infinitely small, it might appear that the lower layers should be stagnant. This puzzle was solved by Rhines and Young (1982 a,b). Using a quasi-geostrophic model, they were able to show that closed geostrophic contours formed due to strong interfacial deformation. As a result, there could be infinitely many possible non-stagnant solutions to the problem, instead of the solution of no motion as was thought previously. Furthermore, they showed, subject to assumptions about the effects of eddies on the mean flow, that potential vorticity should be homogenized within these closed geostrophic contours; thus, the system should possess a unique solution that is stable to small perturbations. Their theory provided a theoretical background for the subsurface motions in the unventilated thermocline.

A second way of getting the subsurface water in motion was proposed by Luyten, Pedlosky and Stommel (1983); in their model the isopycnal outcropping effectively bypasses the blocking due to the eastern boundary. In some sense, their model is a very nice extension of the classical conceptual model of ventilation through outcropping proposed by Iselin (1939) more than 40 years ago. Of course, such an extension included many conceptual breakthroughs, such as formulating the model in a solid dynamical framework, and introducing the conceptions of the ventilated zone, the pool regime and the shadow zone.

Although Iselin proposed his conceptual model of ventilation, it was not clear why the ocean should pick up only the late winter properties for ventilation. To explain this phenomenon, Stommel (1979) analyzed the physical processes involved and showed that there are indeed some processes in the oceans that select only the late winter properties for ventilation. This mechanism is now called the Stommel demon. Accordingly, in order to study the climatological mean circulation it is possible to avoid the complexity of the seasonal cycle by simply choosing the late winter properties, such as the mixed layer depth and density. To date, the Stommel demon has remained a main theoretical backbone of the modern theory of wind-driven ocean circulation.

Another classical approach to the thermocline theory is the ideal-fluid thermocline theory proposed by Welander (1959, 1971). His theory is basically to treat the wind-driven circulation as a perturbation to the background stratification set up by an external thermohaline circulation (which is not explicitly studied in the model). Welander (1971) showed that the ideal-fluid thermocline problem can be reduced to solving a second-order ordinary differential equation; however, his solution can only satisfy two boundary conditions in the vertical direction. Thus, for a long time it was not clear how to improve his theory to accommodate more boundary conditions as required by the physics.

The connections between these seemingly different approaches were unified into a theory of the three-dimensional structure of the wind-driven circulation in the continuously stratified oceans by Huang (1988). It was demonstrated that the problem can be reduced to solving a free-boundary problem of a second-order ordinary differential equation in density coordinates. This theory was further extended to incorporate a mixed layer on top (Huang, 1990a), and the model is now capable of providing a quite realistic description of the three-dimensional structure of the wind-driven circulation in the oceans. 2) The baroclinic structure of the inertial western boundary currents

Although theories of western boundary currents associated with the barotropic circulation have been simple, elegant, and successful, the corresponding part associated with the baroclinic circulation is not. The trouble associated with multi-layer inertial western boundary currents was first discussed by Blandford (1965). Basically, he searched for solutions with two moving layers, but failed to find any continuous solutions. Instead, he found that the solutions break down before they get to the place where the Gulf Stream separates from the coast. The difficulties associated with the discontinuity of the inertial western boundary current have been discussed by Luyten and Stommel (1985) in terms of virtual control.

Using a streamfunction coordinates transformation, Huang (1990b) has shown that continuous solutions for the two-moving-layer inertial western boundary currents do exist, and these solutions can be matched to the multi-layer ventilated thermocline solution in the ocean interior (Huang, 1990c). However, the continuity of the inertial western boundary currents does impose certain dynamical constraints on the thermocline structure of the interior oceans. 3) The baroclinic structure of the abyssal circulation.

Although the Stommel-Arons theory about the abyssal circulation was very successful in interpreting some of the early deep ocean observations, the theory had to be improved to explain new observational data; thus the time-dependent and baroclinic structure of the deep circulation were developed.

First, Kawase (1987) studied the spin-up process of an inverse reduced-gravity model, in which he assumed that the interfacial upwelling is linearly proportional to the interfacial

displacement from the mean. His solution clearly demonstrated the critical role of the coastal Kelvin waves in setting up the deep circulation, especially the deep western boundary currents. Rhines and MacCready (1989) noted that the bottom of the oceans is far from being flat. In fact, the oceans' bottom has a bowl shape, more like a Chinese wok. Since the horizontal area of the deep oceans increases upward, the deep circulation in the interior oceans may be clockwise, instead of counterclockwise as suggested by the classical Stommel and Arons theory.

Stommel and Arons (1960a) assumed the upwelling velocity was basin-wide uniform; such an assumption was a way to simplify the model and it is not necessarily true. There is much evidence suggesting that upwelling is not uniform. Using a two-level model, Huang (1993a) was able to show that upwelling is very strong along the equator and the eastern boundary.

The baroclinic structure of the abyssal circulation with continuous stratification has been discussed by Pedlosky (1992) in a series of papers with his coworkers. For a model with flat bottom and given stratification, it was shown that the vertical and meridional velocity can have alternate signs because the basic equation has eigenfunctions that oscillate.

These theories are based on simple assumptions about the bottom topography and mixing. However, the situation in the oceans is much more complicated. As field experiments indicated, mixing is highly inhomogeneous in both space and time. As a result of the nonlinear interaction between stratification, flow over topography, and mixing, the abyssal circulation is very complicated, as it is one of the most exciting research frontiers. 4) The baroclinic structure of the haline circulation

Although in theory we know that fresh water is one of the primary driving forces of the oceanic general circulation, the dynamical role of freshwater flux has been neglected most of the time. Before 1990, there were only very few papers in which freshwater-driven barotropic circulation was discussed, such as those by Hough (1897), Goldsbrough (1933), and Stommel (1957, 1984).

Huang (1993b) discussed the suitable upper boundary conditions for the salinity balance, and showed that freshwater flux does drive a haline circulation. As shown in the Appendix to this section, the Goldsbrough-Stommel theory is still valid for the more general case with continuous stratification, but a flat bottom. Although the barotropic component of such a haline circulation is relatively weak, the baroclinic component has a strength that is comparable with the circulation driven by heat flux or wind stress. 5) The multiple equilibria and variability of the thermohaline circulation

The multiple equilibria for the thermohaline circulation were first discussed in a seminal paper by Stommel (1961). Like many of Hank's papers, this paper was thought to be too simple and people could not appreciate its physical meaning for two decades. However, this was changed rapidly in the 1980s. Due to a very strong demand for understanding the climate system, people started to seek possible multiple equilibrium states of the climate, including multiple solutions of the thermohaline circulation.

Major contributions include F. Bryan's (1986) work on the multiple states of the model Atlantic Ocean and the associated change in the poleward heat flux. He also introduced the use of the so-called mixed boundary conditions, which have since gained wide spread acceptance by most modelers. Manabe and Stouffer (1988) found multiple states in an air-sea coupled general circulation model. Marotzke (1990) found many more multiple states of the thermohaline circulation, especially the so-called flushing phenomenon associated with the halocline catastrophe.

Weaver and Sarachik (1991) discussed the critical role of virtual salt flux in controlling the thermohaline catastrophe and its variability on the decadal time scale. One of the most interesting topics is the thermohaline variability on decadal or longer time scales.

The flux condition for the salinity balance seems to be the essential ingredient for the thermohaline variability, as shown by many studies, such as Weaver et al. (1991). Furthermore, Huang and Chou (1994) have shown that freshwater flux alone can give rise to haline oscillation on decadal time scale. Thus, freshwater flux due to evaporation and precipitation may be the essential ingredient for climate variability.

The rapid development of the theories during this period is primarily due to the very strong demand for understanding the oceanic circulation in order to understand the environment we are living in, especially the climate system. With the completion of many major international observational programs, such as the WOCE, TOGA, our understanding of the oceanic general circulation will deepen, and the theories of the oceanic circulation will be developed rapidly. We hope that within the next 15 years we may be able to build a more complete theoretical framework for the oceanic general circulation. V. Energetics of the oceanic circulation

Classical work along this line including "Abyssal recipe" (Munk, 1966), and "Source of energy for the ocean circulation" (Faller, 1966). The most important issues are: a) Vertical mixing requires external sources of mechanical energy

Vertical (diapycnal) mixing in a stratified fluid increases gravitational potential energy of the mean state. Thus, in contrast to the common wisdom that turbulence kinetic energy is completely lost and becomes dissipation heat, turbulence in stratified fluid actually converses part of their kinetic energy into the gravitational potential energy. Thus, in sustaining the turbulence external source of mechanical energy is required. Therefore, sources of external mechanical energy and their distribution within the ocean are critically important for oceanic circulation and climate. b) Mixing is non-uniform in space and time. 1) Energetics of oceanic circulation, Huang (1998a), Munk and Wunsch (1999).

Oceanic circulation requires energy sources for supporting, so energy balance for the oceanic circulation is one of the most fundamental aspects of the oceanic circulation. Unfortunately, energetics of the oceanic circulation has been overlooked so far. As a result, there are only a few papers devoted to this important issue. Most people talk about the oceanic circulation in terms of potential vorticity conservation or tracer conservations only. 2) Sandstrom (1905) theorem

The fundamental difference between the atmospheric circulation and the oceanic circulation is that the atmospheric circulation is a heat engine, but the oceanic circulation is not a heat engine; instead, the oceanic circulation is a conveyor belt driven by external sources of mechanical energy.

The classical Sandstrom (1905) theorem: There is no circulation if the heating source is located at a level higher than the cooling source. Sandstrom theorem is based on thermodynamics, so it is not very accurate. Recently, this has been examined in details, such as the new theorem by Paparella and Young (2002).

The meridional differential heating is only a precondition for the oceanic thermohaline circulation, and the external mechanical energy available for vertical mixing is the dominating factor controlling the oceanic circulation. On the other hand, mixing is not so fundamentally

important for the atmospheric circulation, but other issues, such as radiation and moist are more important. For a theoretical case with no wind stress, the strength of the meridional overturning rate is directly controlled by the amount of external energy available for mixing. Since mixing requires external source of mechanical energy, mechanical energy sources and their transform in the ocean is critically important for understanding the circulation, Munk and Wunsch (1999). 3) Circulation driven by mechanical energy input through the surface geostrophic current

For the world oceans, the situation is quite different. Under the modern geometry with the Drake Passage open, strong Southern Jet Stream induces a strong upwelling of the cold deep water and thus contributes to the formation of the meridional overturning cells in the world oceans. In particular, Toggweiler and Samuels (1995) have demonstrated that in the theoretical limit of no vertical mixing, the existence of wind stress force is capable of maintaining sizable meridional overturning cells and poleward heat flux in the world ocean. 4) Available potential energy and oceanic circulation

The commonly used definition of available potential energy is based on the quasi-geostrophic approximation; it is not suitable for basin-scale thermohaline circulation. One of the major pitfalls of this Q-G definition is the excluding of the mixing energy required for supporting the circulation. Thus, the classical definition of available potential energy is a better choice for the energetics analysis for the oceanic circulation. For basin-scale circulation problem the original definition of available potential energy is more appropriate, Huang (1998, 2005) 5) Recent observations indicate that mixing in the oceanic interior is highly inhomogeneous because mixing is very weak in the interior (about 10-5m2/s), it can be very strong near the bottom and close to the mid-ocean ridge (on the order of 10-3m2/s). Abyssal circulation in the presence of complicated bottom topography and driven by such non-uniform mixing is expected to be drastically different from the classical theory of Stommel and Arrons (1962). However, the new theory of abyssal circulation remains rudimentary at this time because currents in the abyss tend to be rather slow and difficult to observe and we do not have enough data. Thus, this is a grand challenge for us. 6) Abyssal circulation driven by non-uniform mixing;

Circulation driven by bottom-intensified mixing has been studied by many investigators. Phillips (1960) and Wunsch (1960) studied the uphill flow induced by bottom mixing. In a rotating fluid mixing-induced horizontal pressure gradient gives rise to geostrophic flow along slope. Garrett (1991) reviewed the circulation induced by bottom-intensified mixing.

Recent numerical study about abyssal circulation induced by bottom-intensified mixing can be found in Cummins and Forman (1998), Huang and Jin (2001). VI. Climate variability related to oceanic circulation on different time scales (1990-present)

Although most studies in our field have been focused on quasi-steady circulation, climate variability on short time scales, from interannual to decadal, is very important for the understanding of climate changes and variability. We are in the very beginning to understand such phenomena. 1) Decadal variability observed in the oceans.

Deser et al. (1996) described the decadal variability of the thermocline, and identified the southward propagation of the thermal anomaly.

Pathways of the connection between subtropical and tropical oceans: Interior communication window, western boundary current, Kelvin waves and Rossby waves. 2) Simple theories about decadal variability in the thermocline (1) Treat the climate variability as the difference between two steady states.

Huang and Pedlosky (1999) showed that climate variability induced by buoyancy forcing anomaly appears in the forms of the second dynamical thermocline mode. This was also extended to the case of multi-layer model and continuous model. In general climate variability due to buoyancy forcing anomaly appears in the forms of dynamical thermocline modes. (2) The wave process: Rossby waves and Kelvin waves. The time-evolution of the thermocline is carried out in forms of waves, including both Rossby waves and Kelvin waves. Two primary sources of climate variability: a) Surface forcing anomaly in the subtropical basin interior. This includes wind stress and buoyancy forcing. Climate anomalies produced then propagate in forms of Rossby and coastal-(equatorial-) trapped waves. The adjustment process has been discussed by Kawase (1987), Liu (1999). b) Change in deep water formation at high latitudes. The wave process is similar to case discussed above, except that the perturbations may be very close to the northern boundary, so that the perturbations move equatorward right after their formation. Discussion along this line can be found in: Yang (1999), Johnson and Marshall (2001). The solution for centennial time scale was discussed by Huang et al. (1999), and More updated discussion can be found in Cessi et al. (2004). VII. Some of the research frontiers for large-scale circulation 1) Parameterization of the sub-grid-scale processes In numerical models, the spatial and temporal resolutions are limited by computer power; thus, many processes with scale smaller than the grid size have to be parameterized in order to simulate their contribution to oceanic circulation. Typical problems include the vertical/horizontal coefficients for momentum dissipation and tracer mixing. Currently, parameterization of vertical mixing coefficient of tracers has received much attention because the meridional overturning rate is rather sensitive to vertical (or diapycnal) mixing coefficient. However, in the near future parameterization of vertical momentum mixing and horizontal mixing of tracer and momentum will become important research topics as well. 2) Surface boundary layer Planetary boundary layers at the air-sea interface are important components in the climate system. Most of currently used numerical models are based on rather simple bulk formulae for the parameterization of these boundary layers. In particular, surface waves and other processes have been parameterized in rather rudimentary ways. Air-sea fluxes of momentum, heat and other tracers must be improved to meet the challenge of providing better simulation of climate. 3) Bottom boundary layer Simulating the bottom boundary layer remains a challenge as well.