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Ocean, Energy Flows in ~ RUI XIN HUANG ~ ~\..J~ ~ Y" Ocean, Energy Flows in ~ RUI XIN HUANG ~ "- Woods Hole Oceanographic Institution Woods Hole, Massachusetts, United States ;","" -- ~-_Ti'_,Ti'-,_- strength of the oceanic general circulation. In 1. Basic Conservation Laws for Ocean Circulation particular, energy input through wind stress is the 2. Energetics of the Oceanic Circulation most important source of mechanical energy in 3. Heat Flux in the Oceans driving the oceanic circulation. 4. The Ocean Is Not a Heat Engine 5. Mechanical Energy Flows in the Ocean 6. Major Challenge Associated with Energetics, Oceanic 1. BASIC CONSERVATION LAWS Modeling, and Climate Change FOR OCEAN CIRCULATION 7. Conclusion J' Oceanic circulation is a mechanical system, so it obeys many conservation laws as other mechanical Glossary systems do, such as the conservation of mass, angular Ekman layer A boundary layer within the top 20 to 30 m momentum, vorticity, and energy. It is well known of the ocean where the wind stress is balanced by that these laws should be obeyed when we study the Coriolis and frictional forces. oceanic circulation either observationally, theoreti- mixed layer A layer of water with properties that are cally, or numerically. However, this fundamental rule almost vertically homogenized by wind stirring and has not always been followed closely in previous convective overturning due to the unstable stratification studies of the oceanic circulation. As a result, our induced by cooling or salinification. knowledge of the energetics of the ocean circulation thermocline A thin layer of water at the depth range of remains preliminary. 300 to 800 m in the tropicallsubtropical basins, where the vertical temperature gradient is maximum. thermohaline circulation An overturning flow in the ocean 1.1 Mass Conservation Law driven by mechanical stirring/mixing, which transports mass, heat, freshwater, and other properties. In addi- This is one of the most important laws of nature. tion, the surface heat and freshwater fluxes are However, mass conservation has not been applied in necessary for setting up the flow. many existing numerical models. In fact, most wind-driven circulation A circulation in the upper kilo- models are based on the Boussinesq approximations, meter of the ocean, which is primarily controlled by which consist of three terms: mass conservation is wind stress. In addition, this circulation also depends on replaced by a volume conservation, in situ density in buoyancy forcing and mixing. the horizontal momentum equations is replaced by a constant reference density, and tracer prognostic equations are based on volume conservation instead Oceanic circulation plays an important role in the of mass conservation. For models based on the climate system because it transports heat and fresh- Boussinesq approximations, heating (cooling) can water fluxes meridionally. There is a huge heat flux induce an artificial loss (gain) of gravitational through the upper surface of the ocean, but the ocean potential energy. Furthermore, precipitation (eva- is not a heat engine; instead, the ocean is driven by poration) is often simulated in terms of the equiva- external mechanical energy, including wind stress lent virtual salt flux out of (into) the ocean; thus, an and tides. Although mechanical energy flux is 1000 artificial sink of gravitational potential energy is times smaller than the heat flux, it controls the generated in the models. Encyclopedia of Energy, Volume 4. iQ 2004 Elsevier Inc. All rights reserved. 497 498 Ocean, Energy Flows in 1.2 Angular Momentum over the past years the mechanical energy balance of Conservation Law the oceanic general circulation has been overlooked, and there has been very little discussion about such a In a rotating system, the linear momentum is not fundamental issue. In fact, energy balance equations conserved; instead the angular momentum conserva- for the oceanic general circulation in most previously tion is more relevant (i.e., the rate of change of the published books or papers are incomplete because angular momentum of the oceanic general circulation one of the most important terms in the mechanical must be balanced by torques). The angular momen- energy balance, energy required for vertical mixing in tum conservation law has been used extensively in the a stratified environment, is not included. Therefore, study of the atmospheric circulation. The Antarctic there is no complete statement about mechanical Circumpolar Current is the corresponding part in the energy balance for the oceanic general circulation. In oceans where the angular momentum conservation addition, most numerical models do not conserve law dictates the balance. total energy, especially in the finite difference scheme in time stepping. Thus, energetics diagnosed from these models are unreliable. 1.3 Potential Vorticity Conservation Law The potential vorticity equation can be obtained by cross-differentiation of the horizontal momentum 2. ENERGETICS OF THE equations and subtracting the results; it has been OCEANIC CIRCULATION extensively used in oceanographic studies. According to the theory, total potential vorticity is conserved in Energy in the ocean can be classified into four major / the interior of a stratified fluid, and the only source of forms: the gravitational potential energy, kinetic potential vorticity must be on the outer surfaces of energy, internal energy, and chemical potential, as the stratified fluid. shown in Fig. 1. Although the chemical potential can be considered as part of the internal energy, it is listed as a separate item in the diagram. 1.4 Energy Conservation Law There are four sources (sinks) of gravitational Motions in the oceans must be associated with potential energy generated by external forcing. A friction; thus, to maintain circulation in the ocean, major source is the tidal force, which is due to the mechanical energy source is required to balance the temporal variation of the gravitational forces of the loss of mechanical energy. Energy source and moon and the sun. Although tidal motions have been dissipation are the most important means of con- studied separately from the oceanic general circula- trolling the oceanic circulation system. However, tion in the past, it is now recognized that a strong Atmospheric Freshwater Tidal Wind Atmospheric Freshwater stress Solar heating/cooling flux forces loading flux insolation L Dilution Gravitational Kinetic Internal heat Chemical potential energy potential energy energy pTv Small- scale mixing 20% 80% FIGURE 1 Energetics diagram for the ocean circulation. Ocean, Energy Flows in 499 connection exists between the tidal motions and the 2.2 Conversion from Kinetic Energy to oceanic general circulation. Gravitational Potential Energy In addition, changes of the sea level atmospheric pressure (called the atmospheric loading) can generate In a turbulent ocean, the conversion from kinetic to gravitational potential energy. The total amount of this potential energy is represented by pwg, where the energy flux remains unclear. Furthermore, freshwater overbar indicates the ensemble mean" This exchange flux across the air-sea interface can generate gravita- can be separated into several terms: tional potential energy. This turns out to be a small pwg = pwg + p'w'g + (p'w' + p'w + pw'). sink of energy, and the global integrated amount of energy flux is about -0.007TW (1TW = 1012Watts). The first term on the right-hand side represents the The reason for this loss of gravitational potential kinetic to potential energy conversion associated energy is that evaporation (precipitation) prevails at with the ensemble mean density and velocity fields. subtropics (high latitudes) where sea level is high (low) The second term on the right-hand side represents due to warm (cold) temperature. Wind stress is one of the contribution due to turbulent mixing. In a the most important sources of mechanical energy for stratified fluid, upward motion is usually correlated the ocean. In fact, wind stress generates surface waves, with positive density anomaly, so turbulentwixing in thus providing a source of mechanical energy, which is a stratified ocean increases the gravitational potential equally partitioned into the gravitational potential energy of the state, and thus requires a source of energy and kinetic energy. The other source of kinetic kinetic energy. The rest of the terms on the right- energy is the energy input from the wind stress to the hand side represent the kinetic to potential energy surface geostrophic currents and the ageostrophic conversion due to the time-dependent component of currents or the Ekman drift. the gravitational force, such as the tidal forces. In the stratified oceans, the vertical eddy mixing The external sources of internal energy include '-, three terms: the solar radiation, heat exchange to the rate K can be related to the energy dissipation rate atmosphere, and geothermal heat flux. Heat ex- through change to the atmosphere includes latent heat flux, KN2 = as N2 = _JLape long wave radiation, and sensible heat flux. Geother- , Po az' mal heat flux through the sea floor is much smaller than the air-sea heat fluxes, but it is one of the where N2 is the buoyancy frequency, S is energy important factors controlling the deep circulation in dissipation rate, and IX~ 0.2 is an empirical coeffi- the abyssal ocean. cient. Therefore, the decline in turbulent kinetic The source of the chemical potential is associated energy does not entirely become "wasted" heat. In with the salinity,
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