j~web-static-aws.seas.harvard.edu/climate/pdf/huang_2004.pdf · 498 ocean, energy flows in 1.2...

Ocean, Energy Flows inRUI XIN HUANGWoods Hole Oceanographic InstitutionWoods Hole, Massachusetts, United States

-- ~-_Ti'_,Ti'-,_-1. Basic Conservation Laws for Ocean Circulation

2. Energetics of the Oceanic Circulation3. Heat Flux in the Oceans

4. The Ocean Is Not a Heat Engine5. Mechanical Energy Flows in the Ocean

6. Major Challenge Associated with Energetics, OceanicModeling, and Climate Change

7. Conclusion

Glossary

Ekman layer A boundary layer within the top 20 to 30 mof the ocean where the wind stress is balanced byCoriolis and frictional forces.

mixed layer A layer of water with properties that arealmost vertically homogenized by wind stirring andconvective overturning due to the unstable stratificationinduced by cooling or salinification.

thermocline A thin layer of water at the depth range of300 to 800 m in the tropicallsubtropical basins, wherethe vertical temperature gradient is maximum.

thermohaline circulation An overturning flow in the oceandriven by mechanical stirring/mixing, which transportsmass, heat, freshwater, and other properties. In addi-tion, the surface heat and freshwater fluxes arenecessary for setting up the flow.

wind-driven circulation A circulation in the upper kilo-meter of the ocean, which is primarily controlled bywind stress. In addition, this circulation also depends onbuoyancy forcing and mixing.

Oceanic circulation plays an important role in theclimate system because it transports heat and fresh-water fluxes meridionally. There is a huge heat fluxthrough the upper surface of the ocean, but the oceanis not a heat engine; instead, the ocean is driven byexternal mechanical energy, including wind stressand tides. Although mechanical energy flux is 1000times smaller than the heat flux, it controls the

Encyclopedia of Energy, Volume 4. iQ 2004 Elsevier Inc. All rights reserved.

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strength of the oceanic general circulation. Inparticular, energy input through wind stress is themost important source of mechanical energy indriving the oceanic circulation.

1. BASIC CONSERVATION LAWSFOR OCEAN CIRCULATION

Oceanic circulation is a mechanical system, so itobeys many conservation laws as other mechanicalsystems do, such as the conservation of mass, angularmomentum, vorticity, and energy. It is well knownthat these laws should be obeyed when we study theoceanic circulation either observationally, theoreti-cally, or numerically. However, this fundamental rulehas not always been followed closely in previousstudies of the oceanic circulation. As a result, ourknowledge of the energetics of the ocean circulationremains preliminary.

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1.1 Mass Conservation Law

This is one of the most important laws of nature.However, mass conservation has not been applied inmany existing numerical models. In fact, mostmodels are based on the Boussinesq approximations,which consist of three terms: mass conservation isreplaced by a volume conservation, in situ density inthe horizontal momentum equations is replaced by aconstant reference density, and tracer prognosticequations are based on volume conservation insteadof mass conservation. For models based on theBoussinesq approximations, heating (cooling) caninduce an artificial loss (gain) of gravitationalpotential energy. Furthermore, precipitation (eva-poration) is often simulated in terms of the equiva-lent virtual salt flux out of (into) the ocean; thus, anartificial sink of gravitational potential energy isgenerated in the models.

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498 Ocean, Energy Flows in

1.2 Angular MomentumConservation Law

In a rotating system, the linear momentum is notconserved; instead the angular momentum conserva-tion is more relevant (i.e., the rate of change of theangular momentum of the oceanic general circulationmust be balanced by torques). The angular momen-tum conservation law has been used extensively in thestudy of the atmospheric circulation. The AntarcticCircumpolar Current is the corresponding part in theoceans where the angular momentum conservationlaw dictates the balance.

1.3 Potential Vorticity Conservation Law

The potential vorticity equation can be obtained bycross-differentiation of the horizontal momentumequations and subtracting the results; it has beenextensively used in oceanographic studies. Accordingto the theory, total potential vorticity is conserved inthe interior of a stratified fluid, and the only source ofpotential vorticity must be on the outer surfaces ofthe stratified fluid.

1.4 Energy Conservation Law

Motions in the oceans must be associated withfriction; thus, to maintain circulation in the ocean,mechanical energy source is required to balance theloss of mechanical energy. Energy source anddissipation are the most important means of con-trolling the oceanic circulation system. However,

over the past years the mechanical energy balance ofthe oceanic general circulation has been overlooked,and there has been very little discussion about such afundamental issue. In fact, energy balance equationsfor the oceanic general circulation in most previouslypublished books or papers are incomplete becauseone of the most important terms in the mechanicalenergy balance, energy required for vertical mixing ina stratified environment, is not included. Therefore,there is no complete statement about mechanicalenergy balance for the oceanic general circulation. Inaddition, most numerical models do not conservetotal energy, especially in the finite difference schemein time stepping. Thus, energetics diagnosed fromthese models are unreliable.

2. ENERGETICS OF THEOCEANIC CIRCULATION

Energy in the ocean can be classified into four majorforms: the gravitational potential energy, kineticenergy, internal energy, and chemical potential, asshown in Fig. 1. Although the chemical potential canbe considered as part of the internal energy, it is listedas a separate item in the diagram.

There are four sources (sinks) of gravitationalpotential energy generated by external forcing. Amajor source is the tidal force, which is due to thetemporal variation of the gravitational forces of themoon and the sun. Although tidal motions have beenstudied separately from the oceanic general circula-tion in the past, it is now recognized that a strong

/

AtmosphericSolar heating/coolinginsolation

Freshwaterflux

pTv

Internalenergy

Dilutionheat Chemical

potential

Small-scalemixing

20%

FIGURE 1 Energetics diagram for the ocean circulation.

80%

Atmospheric FreshwaterWindTidal stressforces loading flux

LGravitational

Kineticpotential

energyenergy

connection exists between the tidal motions and theoceanic general circulation.

In addition, changes of the sea level atmosphericpressure (called the atmospheric loading) can generategravitational potential energy. The total amount of thisenergy flux remains unclear. Furthermore, freshwaterflux across the air-sea interface can generate gravita-tional potential energy. This turns out to be a smallsink of energy, and the global integrated amount ofenergy flux is about -0.007TW (1TW = 1012Watts).The reason for this loss of gravitational potentialenergy is that evaporation (precipitation) prevails atsubtropics (high latitudes) where sea level is high (low)due to warm (cold) temperature. Wind stress is one ofthe most important sources of mechanical energy forthe ocean. In fact, wind stress generates surface waves,thus providing a source of mechanical energy, which isequally partitioned into the gravitational potentialenergy and kinetic energy. The other source of kineticenergy is the energy input from the wind stress to thesurface geostrophic currents and the ageostrophiccurrents or the Ekman drift.

The external sources of internal energy includethree terms: the solar radiation, heat exchange to theatmosphere, and geothermal heat flux. Heat ex-change to the atmosphere includes latent heat flux,long wave radiation, and sensible heat flux. Geother-mal heat flux through the sea floor is much smallerthan the air-sea heat fluxes, but it is one of theimportant factors controlling the deep circulation inthe abyssal ocean.

The source of the chemical potential is associatedwith the salinity, which is generated by freshwaterflux through the air-sea interface in forms ofevaporation and precipitation. The general role ofchemical potential in the oceanic circulation remainsunclear. One of the major roles played by the chemicalpotential is driving the molecular mixing of salt.

2.1 Energy Conversion

Energy in any given form can be converted into otherforms through specific processes, as highlighted inFig. 1. For example, gravitational potential energyand kinetic energy can be transferred to each otherthrough the vertical velocity conversion term. Inaddition, kinetic energy can be converted intogravitational potential energy through small scalemixing by internal waves and turbulence. On theother hand, gravitational potential energy can beconverted into kinetic energy of meso-scale eddiesthrough baroclinic instability. This may be one of themajor pathways of energy flow in the ocean.

Ocean, Energy Flows in 499

2.2 Conversion from Kinetic Energy toGravitational Potential Energy

In a turbulent ocean, the conversion from kinetic topotential energy is represented by pwg, where theoverbar indicates the ensemble mean" This exchangecan be separated into several terms:

pwg = pwg + p'w'g + (p'w' + p'w + pw').

The first term on the right-hand side represents thekinetic to potential energy conversion associatedwith the ensemble mean density and velocity fields.The second term on the right-hand side representsthe contribution due to turbulent mixing. In astratified fluid, upward motion is usually correlatedwith positive density anomaly, so turbulentwixing ina stratified ocean increases the gravitational potentialenergy of the state, and thus requires a source ofkinetic energy. The rest of the terms on the right-hand side represent the kinetic to potential energyconversion due to the time-dependent component ofthe gravitational force, such as the tidal forces.

In the stratified oceans, the vertical eddy mixingrate K can be related to the energy dissipation ratethrough

'-,

KN2 = as N2 = _JLape, Po az'

where N2 is the buoyancy frequency, S is energydissipation rate, and IX~ 0.2 is an empirical coeffi-cient. Therefore, the decline in turbulent kineticenergy does not entirely become "wasted" heat. Infact, a small percentage of the turbulent kineticenergy "dissipation," represented by the empiricalcoefficient a, is actually transformed to large-scalepotential energy. The energy required to sustainmixing is one of the most important dynamic factorscontrolling the meridional overturning rate.

2.3 Conversion of Internal Energy toMechanical Energy

Internal energy can be converted to kinetic energythrough the compression term. Since sea water isnearly incompressible, this conversion rate is ratherlow. In addition, it is very important to note thatenergy transformation is not unconditional. Instead,the conversion between internal energy and mechan-ical energy is subject to the second law of thermo-dynamics-that is, mechanical energy can beconverted entirely into internal energy; however,internal energy can be converted into mechanicalenergy only partially, with the upper bound setby the


Carnot efficiency. As will be discussed later, however,the ocean is not a heat engine; therefore, theequivalent thermal-mechanical energy conversionefficiency is negative.

3. HEAT FLUX IN THE OCEANS

Oceans play an important role in the earth's climatesystem in many ways. In fact, most of the solar radia-tion penetrates the atmosphere and is first absorbed bythe ocean and the land and then sent back to theatmosphere in forms of latent heat, long waveradiation, and sensible heat. To a large degree, theseprocesses are controlled by the oceanic circulation. Inthe quasi-steady state, all heat flux absorbed by theocean must be released back into the atmosphere. Thespatial distribution of air-sea heat flux is one of thecritical components of the earth's climate system.

3.1 Heat Flux through the Upper Surfaceof the Ocean

The dominating form of energy flux in the oceans isthe heat flux. Solar radiation on Earth can penetratethe atmosphere, with only a small fraction beingabsorbed by the greenhouse gases, such as watervapor and CO2, Since oceans cover about 70% of theearth, most of the solar radiation is directly absorbedby the oceans (total amount of 52.4PW).

At low latitudes, solar radiation absorbed by theocean exceeds the heat flux from the ocean into theatmosphere, including the latent heat flux, long waveradiation, and the sensible heat flux. Thus, the oceanat low latitudes gains net heat through the uppersurface, and this extra heat is transported polewardand released at middle and high latitudes. The mostimportant areas of the ocean-to-atmosphere heatrelease include the Gulf Stream, Kuroshio, and theNorthern North Atlantic.

3.2 Poleward Heat Fluxes in the

Climate System

Heat fluxes in the current climate system consist ofthree components: the atmospheric sensible heat flux,the oceanic sensible heat flux, and the latent heat fluxassociated with the hydrological cycle in the atmo-sphere-ocean coupled system (Fig. 2). The sum ofthese three fluxes is the total poleward heat fluxdiagnosed from satellite measurements. The oceanplays the role of heat storage and heat redistributor.The most important part for climate study is the total

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FIGURE 2 Northward heat flux in PW: RT indicates the heat

flux required for radiation balance as diagnosed from satellitedata; AT indicates the atmospheric sensible heat flux; OT indicatesthe oceanic sensible heat flux; and LT indicates the latent heat fluxassociated with the hydrological cycle.

amount of poleward heat flux associated with theoceanic current, which is about 2Pw. Note that thelatent heat flux, which has been traditionally asso-ciated with the moisture flux in the atmosphere, canbe considered as an atmosphere-ocean coupled mode.

Although the atmospheric sensible heat flux is thelargest component in both hemispheres, it is notmuch larger than the other components. Thus, thetotal oceanic contribution to the poleward heat fluxmay consist roughly of 50% of the total heat flux.

The poleward sensible heat flux in the ocean canbe separated into two major components: the fluxassociated with the meridional overturning cell andthe flux associated with the horizontal gyration. Eachcomponent can be further divided into the contribu-tion by the mean Eulerian flow and eddies. Forexample, poleward heat flux in the North Atlanticreaches its maximum around 25°N, where both themean meridional overturning and horizontal wind-driven gyre contribute. In comparison, however, thecontribution by eddies is relatively small. In theNorth Pacific, the mean meridional overturning cellinduces an equatorward heat flux; however, the sumof heat fluxes is still poleward because it is associatedwith the domination of the wind-driven gyre.

II

3.3 Total Heat Flux through the Oceans

The oceanic to atmospheric heat flux consists of threecomponents: the latent heat flux, 31.1PW; the longwave radiation, 17.8PW; and the sensible heat flux,3.5PW (Fig. 3). Although air-sea interface heat flux is

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Short waves

52.4PW

Poleward heat flux -- 2PW


Sensible heat3.5PW

j(

Wind work Chemical

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~3.5TW

energy to the circulation in the oceans. The atmos-phere can be considered as a heat engine, which isdriven by differential heating, with an efficiency of0.8% (the corresponding Carnot efficiency is about33%). In this sense although the oceans are subject todifferential heating similar to the atmosphere, they arenot at all a heat engine. As will be discussed here, thedriving force for the oceanic circulation is the mecha-nical energy in the forms of wind stress and tides. Incomparison, differential heating is only a preconditionfor the thermohaline circulation, and not the drivingforce of the oceanic general circulation. Thus, theocean is not a heat engine; instead, it is a machinedriven by external mechanical energy that transportsthermal energy, freshwater, CO2, and other tracers.

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FIGURE 3 A diagram of external sources of energy for the ocean circulation.

of major importance to climate study, it does notdirectly drive the oceanic general circulation. Instead,air-sea heat flux is controlled by the oceanic circula-tion or, more accurately, controlled by the atmos-phere-ocean-Iand coupled system. From the energeticpoint of view, the oceanic circulation is governed bymany laws of conservation, in particular the energyconservation law. The thermohaline boundary condi-tions at the sea surface are preconditions for thethermohaline circulation only, while the ocean circu-lation is primarily controlled by the sources and sinksof mechanical energy, with the total air-sea heat fluxas the by product of the circulation.

In Fig. 3, energy fluxes into the ocean in otherforms are also included because this additional energyinput eventually turns into internal energy and isreleased in to the atmosphere in forms of heat flux.The amount of geothermal heat flux is about 32Tw,which is eventually lost in to the atmosphere throughthe air-sea heat exchange. Furthermore, there are threeother fluxes: the tidal dissipation, 3.5TW; the chemicalpotential generated through evaporation and precipi-tation; and the wind work, 64Tw. Thus, the totaloutgoing heat flux is the sum of the incoming heatflux, 52.4Pw, plus four additional energy sources: 64(wind) + 32 (geothermal) + 3.5 (tides) + 3.5TW (che-mical potential) = 103Tw.

4. THE OCEAN IS NOTA HEAT ENGINE

4.1 Is the Ocean a Heat Engine?

The atmosphere and oceanswork together as a heatengine, if we neglect the small contribution of tidal

4.2 Sandstrom's Theorem

Sandstrom theorem states: A closed steady circula-tion can be maintained in the ocean only if theheating source is situated at a level lower thanthe cooling source. Sandstrom's theorem can bedemonstrated by laboratory experiments, as shownin Fig. 4. In the first experiment, the heating sourceis put at a level higher than the cooling source. Thereis no detectable circulation, and a stable stratifica-tion can be observed between the heating andcooling levels. Theoretically, there is still a circula-tion driven by the molecular mixing, but it is sosluggish that there is practically none. In the secondexperiment, the heating source is put at a level lowerthan the cooling source. A vigorous circulation canbe observed between the levels of heating andcooling, just as we put a pot of water over thekitchen range.


A

Heat source higher than cold source: no circulation.

B

Cold source higher than heat source:there is a circulation.

FIGURE 4 Laboratory experiments demonstrating the Sand-strom theorem.

Sandstrom's theorem applies to both. the atmo-sphere and oceans. The atmosphere is heated frombelow and cooled from above; thus, it is a heatengine. On the other hand, the ocean is heated andcooled from the sea surface. Since heating andcooling take place at the same level, there is nocirculation driven by the thermal forcing (Fig. SA).Under such a condition, thermal forcing can create avery thin thermocline, on the order of meters on thesurface of the oceans. Below such a thin thermo-cline, temperature is virtually constant, equal to thecoldest temperature set up by the deepwater forma-tion at high latitudes. Since there is no densitydifference at depth, there is only a very sluggishcirculation. However, the effective depth of heat-ing is moved downward by wind and tidal mixing.The large horizontal density gradient thus createddrives a strong circulation in the world oceans(Fig.SB).

A

- - u _u u - - - u u - u u - u -- - n_-

- - u u - - - u - u u - u u - u - - - n - - - - - - - - - - --

- - -- -- - - - -,- - -- -- - - - -- - -- -- - - - -- - - - -- - - ---

- - - u u - u -- - -- -- - n - - - n - - - n - - - n - - - - --

Circulation driven by molecular mixingis extremf,!ly weak.

B

f/ /~

Effective depth of heat source moved downward bytidal and wind mixing: circulation is very strong.

FIGURE 5 Application of the Sandstrom theorem to theworld's oceans.

The essential point is that to maintain a quasi-steady circulation in the ocean, external sources ofmechanical energy are required to balance the loss ofmechanical energy caused by friction associated withmotion. Although there is a tremendous amount ofthermal energy going through the ocean, it cannot beconverted into mechanical energy needed to sustainthe oceanic circulation, as dictated by the fundamentallaw of thermodynamics. Therefore, instead of utilizingthe huge amount of thermal energy going through theocean, the maintenance of the oceanic circulationdepends on the availability of external mechanicalenergy, with a flux rate of three to four orders of mag-nitude smaller than the thermal energy fluxes (Fig. 3).

5. MECHANICAL ENERGY FLOWSIN THE OCEAN

Mechanical energy sources and sinks for the oceansare illustrated in Fig. 6. Wind stress applies to the

-- - - - - u - u u - u u u - u u - u u u - u u - -

Warm I- - u u - u u - u u - u - - - u u - - - u -- - n n - -

- - u u u - u - - - -- - -- n - - - n n - - - n -- - -- u-

I Cold- - - u -- - -- - - - - - - - - - - - - - n n - - - -- - - - u u - --

{i)-

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. ~- -- ---------- ~ -----------------

- 'amoo

C ~ Near-inertialwaves

Convectiveadjustment Wind 0 Ekman transport

geostrophic current

//

Tidaldissipation

~ Bottom drag

~


Atmospheric loading

Ekman spiralSurface waves

pumping

~ ..

Cabbeling

FIGURE 6 Mechanical energy diagram for the ocean circulation.

surface of the ocean and drives both surface currentsand waves. The mechanical energy input from windstress into the ocean Wwindis defined by

W - / ) ~ - ~ U~ ~,~, -,---,wind-\(jij .u-!. a+!Ua+pwa,

where :rand fj a are the spatially averagedtangentialstress and surface velocity respectively, :r' and it'a arethe perturbations, and p' and w' a are perturbations ofthe surface pressure and velocity component normalto the surface. The perturbations are defined in termsof the scale of the surface wavelength.

The first term on the right-hand side is the windstress work of the quasi-steady current on thesurface, and quasi-steadiness is defined in compar-ison to the timescale of the typical surface waves. fj ahas two components: the geostrophic current and theEkman drift:

fj a = fj a,G+ fj a,Ekman.

5.1 Geostrophic Current

Energy input through the surface geostrophic currentcan be calculated as the scaler product of windstress and surface geostrophic velocity. The recentcalculation by Carl Wunsch puts the global totalas 1.3TW This energy is directly fed into the large-

scale current, so it can be efficiently turned intogravitational potential energy through the verticalvelocity conversion term.

5.2 Surface Drift

There is a frictional boundary layer (Ekman layer) onthe top of the ocean, in which the wind stress isbalanced by frictional force. The surface drift is calledthe Ekman drift. The exact amount of wind stress

energy input through the Ekman spiral is unclear, andthe preliminary estimate made by Wei Wang and RuiXin Huang is about 2.4 TW for the frequency higherthan 1/(2 days). In addition, there is a large amount ofenergy input through the near-inertial waves, which isdue to the resonance at a frequency of OJ= -f; that is,for inertial frequency of the clockwise (anticlockwise)wind stress in the Northern (Southern) Hemisphere.Recent calculations by Watanaba and Hibiya gave anestimate of O.7TW

5.3 Geopotential and Kinetic Energy ofthe Wind-Driven Circulation

The convergence of the Ekman flux gives rise to apumping velocity at the base of the Ekman layer WE,


which is responsible for pushing the warm water intothe subsurface ocean and thus forming the mainthermocline in the subtropical ocean. The mainthermocline is a relatively thin layer of water at thedepth of 500 to 800 m in the upper ocean where thevertical temperature gradient is maximum. Sincesalinity contrition to the density is relatively small inmost places of the oceans, the thermocline is alsoclose to the pycnocline where the vertical gradient ofdensity is maximum. Ekman pumping sets up thewind-driven circulation and the associated bow-shaped main thermocline in the world's oceans. Inthis process, gravitational potential energy is in-creased, which is a very efficient way of convertingkinetic energy into gravitational potential energy.Simple scaling analysis shows that the amount ofavailable gravitational potential energy associatedwith the main thermocline is about 1000 times largerthan the amount of kinetic energy associated with themean flow of the wind-driven circulation.

5.4 Loss of Gravitational Potential Energythrough Convective Adjustment

Another important process taking place in the mixedlayer is the convective adjustment due to cooling andsalinification. According to the Sandstrom theorem,if both heating and cooling apply to the same level(the sea surface), there is no gravitational potentialenergy being generated by the thermal forcing alone.However, heating and cooling in the mixed layer isnot a linear process. During the cooling process,water at the sea surface becomes heavier than waterat the depth, thus a gravitational unstable stratifica-tion appears. Due to this unstable stratification, arapid convective adjustment process takes place and

A

Center ofmass

Beforeadjustment - - -

Afteradjustment

"

GPE loss due to convective adjustment

density becomes nearly homogenized in the upperpart of the water column. During this process,gravitational potential energy of the mean state isconverted into kinetic energy for turbulence andinternal waves (Fig. 7A).

As a result, the effective center of cooling is not atthe sea surface; instead it is located halfway of thewell-mixed layer's depth. Because of this asymmetryassociated with cooling/salinification, surface buoy-ancy forcing gives rise to a sink of gravitationalpotential energy. The total amount of energy lossthrough this process remains unclear. A preliminaryestimate based on the monthly mean climatology byRui Xin Huang and Wei Wang for this sink term isabout 0.24 TWo However, calculation in which thediurnal cycle is resolved may give rise to. a muchlarger value.

5.5 Baroclinic Instability

The steep isopycnal surface in the oceans, such asthat along the meridional edges of the wind-drivengyre, is unstable due to baroclinic instability. Becauseof this, a large amount of gravitational potentialenergy of the mean state can be converted into theeddy kinetic/potential energy (Fig. 7B). It is estimatedthat the amount of eddy kinetic energy is about 100times larger than the kinetic energy of the time-meanflow. Despite great effort in carrying out fieldobservations and numerical simulation, there is noreliable estimate on the total amount of eddy kineticenergy in the world's oceans. However, satelliteobservations have provided global distribution ofboth the mean and eddy kinetic energy on the seasurface. The ratio of these two forms of kineticenergy is on the order of 100, consistent with

B

p

~""'"

"<~ p

"""""""'\.<~',"""""

.. "" """"-

FIGURE 7 Gravitational potential energy loss due to convective adjustment and baroclinic instability.

GPE loss due to baroclinic instability

theoretical prediction based on scaling. The rate ofenergy conversion over the world's oceans throughthe baroclinic instability remains unknown, and therecent estimate by Rui Xin Huang and Wei Wang isabout 1.1Tw. Since most eddy energy is dissipatedthrough small-scale processes, the conversation fromthe mean state to eddies is considered as a sink of thegravitational potential energy of the mean state.

5.6 Surface Waves

Another major source of energy caused by windstress is fed through the surface waves. Wind stressdrives surface waves in the oceans, and this energyinput can be treated as the form drag for theatmospheric boundary layer. The rate of energyinput through surface waves remains unclear; how-ever, the preliminary estimate by Wei Wang and RuiXin Huang is about 60Tw. Although this seems to bea large amount of energy, it is believed that most of itis transformed into long waves and propagates awayfrom the source area. It is likely that only a smallfraction of this energy is dissipated locally throughwave breaking and white capping, but a majorfraction of this incoming energy may be dissipated toremote places in forms of swell. These long waveshave a rather low dissipation rate, their energy islikely to dissipate cascading into other forms ofenergy or through wave breaking along the beachesin the world's oceans; however, the details of thisdissipation mechanism remain unclear.

5.7 Diapycnal and alongIsopycnal Mixing

Tracers, including temperature and salinity, aremixed in the oceans through internal wave breakingand turbulence. Mixing can be classified intodiapycnal mixing and along isopycnal mixing. Sincealong isopycnal mixing involves the least amount ofgravitational potential energy, it is the dominatingform of mixing on large scales.

On the other hand, in stratified fluid verticalmixing increases gravitational potential energy be-cause light fluid is pushed downward and heavy fluidis pushed upward. Although molecular diffusion canplay the role of mixing, the corresponding rate is toosmall and thus the result is irrelevant to the oceans.In the upper ocean, below the mixed layer, diapycnalmixing rate is on the order of 10-5 m2s-1, which ismuch larger than the mixing rate due to molecularmixing. In other places of the oceans, the mixing rate


can be much higher than this background rate. Thestrong diapycnal (or vertical) mixing in the oceans isdriven by strong internal wave and turbulence.

The energy sources supporting diapycnal mixingin the oceans include wind stress input through thesea surface and tidal dissipation, which will bediscussed in the next section. Turbulent mixingassociated with fast current, especially that asso-ciated with flow over sill and the down-slope flowafterward, can provide a strong source of energysupporting mixing. There is much observationalevidence indicating that mixing can be on the orderof 1O-3-10-1m2s-1. The mixing rate can be as largeas 0.1 m2s-1 within the Romanche Fracture Zone,where water drops more than 500 m within 100 kmof a downward flow. -

Internal lee waves generated by flow over topo-graphy, such as the Antarctic Circumpolar Current,are probably one of the most important contributors.

The total amount of energy supporting diapycnalmixing in the oceans remains unclear because mixingis highly nonuniform in space and time. According tothe theory of thermohaline circulation, the meridio-nal overturning rate is directly controlled by thestrength of the external mechanical energy availablefor supporting mixing in the oceans, includingmixing in the mixed layer and mixing in thesubsurface layers. Therefore, understanding thephysics related to the spatial and temporal distribu-tion of mixing is one of the most important researchfrontiers in physical oceanography.

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5.8 Tidal Dissipation

The primary source of mechanical energy supportingmixing likely comes from both the wind stressapplied to the ocean's surface and tidal dissipationin the deep ocean. The total amount of tidaldissipation in the world's oceans is 3.5TW (Fig. 8),which is calculated from accurate tracking of themoon's orbit. The spatial distribution of tidal energydissipation remains inaccurate. Based on satellitealtimeter data assimilation, Walter Munk and CarlWunsch estimated that 2.6TW is dissipated withinthe shallow seas of the world's oceans, and theremainder 0.9TW is believed to be distributed in thedeep ocean (Fig. 6). Tidal dissipation in the deepocean takes place primarily over rough topography,where barotropic tidal energy is converted intoenergy for internal tides and internal waves thatsustain the bottom-intensified diapycnal mixing onthe order of 10-3 m2s-1. The conversion of kineticenergy to gravitational potential energy through


3.2

Earthtides

0.2

Suriace tides

Marginal seas

2.6

Shallow bottom

boundary layer

Distributedpelagic turbulance

k =10-5m2ts

r

3.7 0.02 Atmospherictides

3.5

3.5

Ridges, seamounts, etc.0.9

Barotropic

Trapped

f0.7

Localized

turbulent patchesk=10-4m2ts

FIGURE 8 Tidal dissipationdiagram, unit in Tw. Modifiedfrom Munk and Wunsch (1998).

internal waves and turbulence is of rather lowefficiency, typically on the range of 20%; thus, theamount of gravitational potential energy generatedby tidal dissipation in the deep ocean is about0.18Tw.

Tidal dissipation has varied greatly over thegeological past, thus the energy supporting diapycnalmixing may vary as well. The reader is referred to thereview by Kagan and Sundermann.

5.9 Geothermal Heat

In addition, geothermal heat or hot plumes provide atotal heat flux of 32Tw. Although this is muchsmaller than the heat flux across the air-sea interface,it may be a significant component of the driving forcefor the abyssal circulation. Since the geothermalheating is applied at great depth, and the correspond-ing cooling takes place at the sea surface, geothermalheat can be more efficiently converted into gravita-tional potential energy. The rate of this conversion isabout O.OSTw, which is a small term compared toother major terms; nevertheless it is not negligible,

especially for the abyssal circulation and temperaturedistribution in the abyss.

5.10 Bottom Drag

Oceanic currents moving over rough bottom topo-graphy must overcome bottom or form drag, asshown in Fig. 6. The total amount of bottom drag forthe world's oceans circulation remains unclear;however, the preliminary estimate for the openoceans is about 0.4 Tw.

5.11 Atmospheric Loading

Finally, sea level atmospheric pressure varies withtime, and the sea surface moves in the verticaldirection in response. As a result, changes in sea levelatmospheric pressure can input mechanical energyinto the oceans. The total amount of energy due tothis source for the world's ocean circulation remainsunclear; however, the preliminary estimate for theopen oceans is about 0.04Tw. .

5.12 Miscellaneous

.

Many other mechanisms contribute to the mechan-ical energy balance in the oceans.

Cabbeling. Due to the nonlinearity of the equationof state, water density is increased during bothdiapycnal and isopycnal mixing. The newly formedwater with higher density sinks is called cabbeling, asshown in Fig. 6. As a result, gravitational potentialenergy is converted into energy for internal wavesand turbulence. The total amount of gravitationalpotential energy loss associated with cabbeling in theoceans remains unclear.

Double diffusion: Seawater contains salt, thus it isa two-component chemical mixture. On the level ofmolecular mixing, the heat diffusion is 100 timesfaster than the salt diffusion. The difference in heatand salt diffusion for laminar fluid and turbulentfluid environment is one of the most importantaspects of the thermohaline circulation in the oceans.

Double diffusion in the oceans primarily manifestsitself by two types: salt fingers and diffusive convec-tion. Salt fingers appear when warm and salty waterlie over cold and freshwater. The mechanism thatdrives the instability is illustrated in Fig. 9A, assum-ing a vertical pipe connects the cold and freshwater inthe lower part of the water column with the warmand salty water in the upper part of the watercolumn. The wall of the pipe is very thin, so it allowsa rather efficient heat flux into the pipe thus warmingup the cold water. At the same time, the low saltdiffusivity preserves the freshness of the ascendingwater parcel. Thus, the buoyancy difference drivesthe upward motion of water inside the pipe, and aself-propelled fountain can be built in the ocean.

The subtropical gyre interior is a salt-finger'sfavorite place, where strong solar insolation andexcessive evaporation leads to warm and salty waterabove the main thermocline. In this salt-fingerfavorite regime, warm and salty fingers move down-ward and cold and fresh plumes move upward. Sinceheat is 100 times more easily diffused between thesalt fingers and the environment, salt fingers losetheir buoyancy and continue their movement down-ward. In this way gravitational potential energyreleased is used to drive the mixing. According to thenew insite observations in the upper thermocline ofthe subtropical North Atlantic, the mixing rate forthe temperature (salinity) is on the order of4 x 10-5 m2s-1(S x 10-5 m2s-1), and the equivalentdensity mixing rate is negative. The total amount ofgravitational energy loss due to salt fingering in theworld's oceans remain unknown.

t Cold freshwater

Salt fountain

BCold fresh

water

/.,/ / \/ Heat

/ / / / diffusion

f

I

, Restoringforce

Warm saltywater

Oscillating parcel

FIGURE 9 Two possible cases for double diffusion in theoceans.

The other possible double diffusive process is thediffusive convection which takes place if cold andfreshwater overlay warm saltwater. The system isrelatively stable and allows an oscillatory instability(Fig.9b).

5.13 Attempt at Balancing theMechanical Energy in the Ocean

The balance of mechanical energy, including both thekinetic energy and gravitational potential energy, isshown in Fig. 10. It is clear that at this time we donot know even the lowest-order balance of mechan-ical energy. There is much kinetic energy input into

Ocean, EnergyFlows in 507

A r-Warmsalty

rwater

Heatdiffusion II

Pipe


Air-sea fluxesAtmospheric

loadingGeostrophiccurrents

1.3

Tidal dissipation KE3.5

currentsinternalwaves and turbulence

Directconversion

III

I CoastalI ..I mixing'??1.3+??

GPE

Freshwaterflux

mean state

0.007

0.05 Geothermal heat

FIGURE 10 Mechanical energy balance for the world's oceans, unit in Tw.

the ocean, but it is not clear how such energy isdistributed and eventually dissipated in the oceans.On the other hand, there are two major sinks ofgravitational potential energy, but it is not clear howenergy is transported and supplied to such energysinks. It is fair to say that most of the energy fluxeslisted in Fig. 10 are accurate to the factor of 2 only.More accurate energy pathways and estimatesrequire further study.

6. MAJOR CHALLENGEASSOCIATED WITH ENERGETICS,OCEANIC MODELING, ANDCLIMATE CHANGE

6.1 Scaling Laws Governing theMeridional Circulation

Scaling analysis shows that the meridional mass fluxand heat flux are linearly proportional to themechanical energy available for mixing. Thus, theamount of energy available for supporting mixing iswhat really controls the strength of circulation, somore energy available for mixing means strongercirculation.

Surfacewaves

0.04 Breakingand dissipation

60

KE and GPE

surface waves Beach process

Viscousdissipation

I'", Baroclinic,

1.1 instability

Convective

0.24 adjustment

?? ~Salt fingeringand cabbeling

6.2 Energetics and Numerical Simulationof Ocean Circulation

Since we do not well know the distribution ofmechanical energy available for mixing, many ocea-nic general circulation models of the current genera-tion are based on rather simple parameterization ofsubgrid mixing. A common practice in oceanicgeneral circulation modeling is to choose a diapycnalmixing rate and let the models run; the diapycnalmixing rate remains the same all the time, even underdifferent climatic conditions. In fact, no modelershave ever checked how much energy is required tosupport mixing and circulation and, most important,whether this amount of energy is really available.

An interesting and important question is how toparameterize mixing in climate-related models.Should we use the same mixing rate or same mixingenergy when the climate is drifting? Clearly, both afixed mixing rate and a fixed mixing energy representthe two extremes, and the reality is likely to bebetween these two assumptions.

It is speculated that when we have the newgeneration of the Oceanic General CirculationModel (OGCM), in which the mixing parameteriza-tion is more rational, climate variability induced bysomething like the CO2 doubling may be different

..

from whatever we have learned based on existingmodels.

7. CONCLUSION

In summary, energetics of oceanic circulation is ofcapital importance in understanding ocean circula-tion and climate. Energetics of the oceanic circula-tion is one the most important research frontiers.There are many unanswered fundamental questions,and at this time, we do not have the lowest-orderbalance. Most flux terms cited here should be treatedas preliminary estimates, which will certainly beimproved in the near future. Since circulation in theoceans is primarily controlled by energy available formixing, further study of energetics will bring aboutmajor breakthroughs in our understanding of theocean circulation and climate.

SEE ALSO THEFOLLOWING ARTICLES

Aquaculture and Energy Use. Conservation ofEnergy Concept, History of . Desalination andEnergy Use. Earth's Energy Balance. Fisheries and


Energy Use. Lithosphere, Energy Flows in .OceanThermal Energy

Further Reading

Bryden, H. L., and Imawaki, S. (2001). Ocean heat transport. In"Ocean Circulation and Climate" (G. Siedler, J. Church, andJ. Gould, Eds.), International Geophysical Series, pp. 455-474.Academic Press, New York.

Garrett, c., and St. Laurent, L. (2002). Aspects of ocean mixing.J. Oceanogr. Soc. Japan 58, 11-24.

Gill, A. E., Green, J. S. A., and Simmons, A. J. (1974). Energypartition in the large-scale ocean circulation and the productionof mid-ocean eddies. Deep-Sea Research 21, 499-528.

Huang, R. X. (1998). Mixing and available potential energy in aBoussinesq ocean. J. Phys. Oceanogr. 28, 669-678.

Huang, R. X. (1999). Mixing and energetics of the thermohalinecirculation. ]. Phys. Oceanogr. 29, 727-746. . .

Kagan, B. A., and Sundermann, J. (1996). Dissipation of tidalenergy, paleotides, and evolution of the earth-moon system.Adv. Geophysics 38, 179-266.

Munk, W. H., and Wunsch, C. (1998). The moon and mixing:Abyssal recipes II. Deep Sea Research I45, 1977-2010.

Trenberth, K. E., and Caron, J. M. (2001). Estimates of meridionalatmosphere and ocean heat transport.]. Climate 14, 3433-3443.

Wunsch, C. (1998). The work done by the wind on the oceanicgeneral circulation. J. Phys. Oceanogr. 28, 2331-2339.

Wunsch, C. (2001). Ocean observations and the climate forecastproblem. In "Meteorology at the Millennium" (R. Pearce, Ed.),Royal Meteorological Society, pp. 233-245. Academic Press,New York. .

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