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

Fig. 3.54 Annual mean entropy production rate due to freshwater mixing in the world's oceans (0.1 mW/K/m2).

The removal of entropy is implicitly part of air-sea heat exchange, including the incoming short-wave solar radiation of low entropy and the high-entropy fluxes associated with outgoing heat fluxes. Thus, this net entropy flux plays a vitally important role in maintaining the ocean circulation against the accumulation of entropy associated with salt diffusion in the ocean.

If the oceans were a heat engine, mechanical energy could be made from internal energy due to surface thermohaline forcing. However, the new paradigm of thermohaline circulation claims that all mechanical energy involved in thermohaline circulation comes from the external sources of wind and tides. Thus, the total mechanical energy dissipation rate is equal to the rate of input from the external sources of mechanical energy, and the conversion of energy from internal to mechanical is negligible. As a result, the total entropy production due to momentum dissipation in the world's oceans is where W = 67.5 TW is the total mechanical energy from wind energy input and tidal dissipation.

The most important items in the balance of entropy are shown in Figure 3.55. The incoming entropy includes two terms: that due to the incoming short-wave radiation from the Sun, and that due to the incoming geothermal heat flux. The short-wave radiation has a very high radiation temperature, so it is high-quality energy with a very low rate of entropy, Hsw = 14 TW/K. The geothermal heat flux is associated with relatively high temperature.

Entropy production due to mechanical energy dissipation

Balance of entropy for the world's oceans

Fig. 3.55 Entropy balance for the world's oceans (in 1012 W/K).

Fig. 3.55 Entropy balance for the world's oceans (in 1012 W/K).

Sometimes the geothermal plumes can have temperatures on the order of a few hundreds of degrees; however, the temperature may be much lower in general. The exact amount of entropy due to geothermal heat flux is much smaller than that associated with the air-sea heat flux, so it is omitted in Figure 3.55.

The outgoing entropy fluxes include the following contributions: Hh = 120 TW/K, Hiw = 97 TW/K, and Hsh = 16 TW/K. All the mechanical energy input due to wind and tides is eventually dissipated and exported in the form of dissipated heat, Hdiss = 0.24 TW/K. In addition, both the heat transport and freshwater mixing are associated with an internal source of entropy of 0.68 TW/K and 0.11 TW/K, respectively. The geothermal heat flux goes through the sea surface, Hgeo = 0.11 TW/K. The entropy produced through these sources must be removed from the system in order to maintain the orderly circulation and dissipation in the world's oceans. Although these fluxes should be included as parts of the outgoing entropy fluxes related to heat flux discussed above, we list them as small items standing alone.

Active and non-active negative entropy flux

As stated above, a major portion of the negative entropy flux through the air-sea interface may not have any direct impact on the circulation. For example, if the solar radiation is received by a rock, this energy may be transferred back to the atmosphere in the form of long-wave radiation. In a steady state, there should be a big negative entropy flux; however, such entropy flux does not produce any orderly motions in the rock at all. In fact, the rock is in a thermal equilibrium, with no internal dissipation, and the only effect of solar radiation on the rock is to maintain a relatively high state of thermal equilibrium with more energetic random thermal motions of molecules in the rock.

Therefore, in order to explore the dynamic role of negative entropy flux, we need to differentiate two kinds of negative entropy flux: the active negative entropy flux and the non-active negative entropy flux. The active negative entropy flux is the part of entropy flux which is directly related to the circulation, and the remaining part is called the non-active negative entropy flux.

Since the total entropy flux through the air-sea interface is approximately 588 mW/K/m2, the ratio of active to total entropy flux is 0.36% (Table 3.8); therefore, the major part of the negative entropy flux is non-active. More importantly, the oceanic general circulation is not driven by surface thermohaline forcing from the viewpoint of energy; instead the oceanic circulation is driven by the external sources of mechanical energy, as discussed in the previous section of this chapter.

All the mechanical energy input is eventually dissipated, implying an entropy production term exported as part of the negative entropy flux. All entropy produced by the system has to be exported to the environment in the form of negative entropy flux. However, it is not a simple dissipation process, since any imposition of external mechanical energy induces the oceanic general circulation and the related mixing of freshwater and heat. The oceanic general circulation thus gives rise to additional entropy flux. According to our definition, such fluxes are active. The existence of such additional active entropy flux means

3.8 Entropy balance in the oceans Table 3.8. Partition of active entropy flux (mW/K/m2)

Active entropy flux

Total Driving

Induced active entropy flux entropy mechanical _

flux energy Heat mixing Freshwater mixing Sum Sum

the production of entropy associated with mechanical energy input is amplified, with an amplification factor of 2.14/0.6 = 3.57.

Evaporation/precipitation idealized as a thermo-chemical engine

The salinity field in a steady state is time-invariant because salt advection has to be exactly balanced by salt diffusion. Conceptually, thus, we can treat salt as a stagnant grid fixed in space, through which pure water from precipitation moves around. As a parcel of water originating from precipitation moves through the ocean, its salinity and entropy gradually increase through mixing. This water parcel eventually comes back to the sea surface, where pure water is extracted (unmixed) from the ocean and the extra enthalpy and entropy are removed through evaporation.

To analyze the evaporation process, we add an imaginary thin layer of pure water on the top of the ocean, and separate evaporation into two steps. In the first step, pure water is extracted from seawater below this thin layer, and the entropy generated through mixing is removed. This can be achieved by the entropy removal process associated with solar insolation or, equivalently, by pushing the freshwater through the semi-permeable membrane placed at this imaginary interface. In the second step, pure water in this thin layer is transformed into water vapor, which is carried into the atmosphere by wind.

At the sea surface in subtropical oceans, solar radiation with low entropy and heat flux back to atmosphere with high entropy play the role of a conveyor that takes up the entropy produced in the ocean by freshwater mixing, and this entropy removal is equivalent to a specific amount of mechanical energy required for extracting pure water from seawater. The osmotic pressure of seawater of salinity 35 and temperature 20°C is equal to posm = 248 db. The global evaporation is approximately/fS aev dS = 4.0 x 1014m3/y. The energy required for sustaining the hydrological cycle is posmjjS aev dS = 31.6 TW. The equivalent work is W = Hf w,mixing ■ Ts ~ 32.3 TW; about 2% larger than that calculated from the osmotic pressure formula. This error may be due to errors in the seawater property routine.

In the first part of this chapter, it was claimed that the ocean is not a heat engine. However, the possible contribution due to chemical potential was not included at that stage of the discussion. As discussed above, to maintain the hydrological cycle in the world's oceans, 32 TW equivalent of mechanical energy must be actually available. This huge amount of


Semi-permeable membrane

Fig. 3.56 An imaginary thermo-chemical engine driven by the hydrological cycle (evaporation and precipitation) induced by solar insolation in the world's oceans. A deep well contains the freshwater collected from precipitation, with the water level approximately D = 246 m below sea level.


Semi-permeable membrane

Fig. 3.56 An imaginary thermo-chemical engine driven by the hydrological cycle (evaporation and precipitation) induced by solar insolation in the world's oceans. A deep well contains the freshwater collected from precipitation, with the water level approximately D = 246 m below sea level.

energy has been overlooked so far. It is readily seen that such a source of energy might be utilized and converted into mechanical energy, at least in the following conceptual model.

In this conceptual model, precipitation in the ocean is collected and horizontally transported to deep wells, where the level of freshwater is maintained at approximately 246 m below sea level (Fig. 3.56). Mechanical energy in the form of electricity can be extracted from the geopotential difference between the sea surface and this deep level. Freshwater in the deep well can move through the semi-permeable membrane, which allows the through-flow of pure water only. As discussed above, the total amount of energy output is 32 TW. Assuming the total thermal energy input carried by the solar insolation is approximately 65 PW, the efficiency of this thermo-chemical energy is approximately 0.05%. This is a very low efficiency indeed. Nevertheless, in contrast with the previous claim that the ocean is not a thermal engine, the ocean is a thermo-chemical engine from the maintenance of the hydrological cycle. In principle, such a thermo-chemical engine may work in the oceans, where a strong thermohaline circulation is set up by sources of external mechanical energy. It is not clear whether or how this system will work without other sources of external mechanical energy.

Appendix: Source/sink of GPE due to heating/cooling

In the ocean, thermal forcing applies to both the sea surface and seafloor; thus, GPE change due to such forcing is a vital component of the energetics. The rate of GPE generation related to such forcing is discussed in this Appendix.

The amount of GPE for a water column with unit horizontal area from the sea surface to a depth of h is

Case 1: For a water column on the upper surface

X0 = mghcen

where g is gravity, hcen is the center of mass relative to the reference level for GPE, and m = f°h p0(z)dz — ph is the total mass of the water column, with p0(z) as the density profile in the water column, and p the mean reference density. When this water column receives an amount of heat Q, its temperature increases

and water column height increases Sh — aQ/pcp, where a is the thermal expansion coefficient, and cp is the specific heat under constant pressure. Thus, after heating, the center of mass moves upward Sh/2 and the total GPE of this water column is

The net change of GPE is gaQ i-h Po(z)dz gahQ

2cp p 2cp

Assuming that the rate of heating and cooling is balanced, the total GPE source/sink due to surface heating/cooling is d x g ff jjq (aheathheat - ac00ihc001 )dxdy (3.A5)

dt 2cp

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Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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