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Thermodynamics of Ocean Currents

The preceding description of the effect of the wind, especially the discussion of the secondary effect of the wind in producing currents in stratified water, may leave the impression that the wind is all-important to the development of the ocean currents and that thermal processes can be entirely neglected. Such an impression would be very misleading, however. In discussing the secondary effect of the wind, it was repeatedly mentioned that the development of the currents caused by a redistribution of mass by wind transport would be checked partly by mechanical processes and partly by thermal processes. Surface waters that were transported to higher latitudes would be cooled, and thus a limit would be set to the differences in density that could be attained. Upwelling water would be heated when approaching the surface, and at a certain vertical velocity a stationary temperature distribution would be established at which the amount of heat absorbed in a unit volume would exactly balance the amounts lost by eddy conduction and by transport of heat through the volume by vertical motion. The establishment of a stationary temperature distribution within upwelling water would check the effect of upwelling on the horizontal distribution of density.

The above examples serve to emphasize the importance of the thermal processes in the development of the currents, but an exact discussion of the thermodynamics of the ocean is by no means possible. So far, the principles of thermodynamics have found very limited application to oceanographic problems, but this statement does not mean that the thermal processes are unimportant compared to the mechanical.

Thermal Circulation. The term “thermal circulation” will be understood to mean a circulation that is maintained by heating a system in certain regions and by cooling it in other regions. The character of the thermal circulation in the ocean and in the atmosphere has been discussed by V. Bjerknes and collaborators (1933). Their conclusions can be stated as follows: If within a thermal circulation heat shall be transformed into mechanical energy, the heating must take place under higher pressure and the cooling under lower pressure. Such a thermodynamic

machine will run at a constant speed if the mechanical energy that is produced by the thermal circulation equals the energy that is expended for overcoming the friction.

In the ocean, “higher pressure” can generally be replaced by “greater depth,” and “lower pressure” by “smaller depth.” Applied to the ocean the theorem can be formulated as follows: If within a thermal circulation heat shall be transformed into mechanical energy, the heating must take place at a greater depth than the cooling.

This theorem was demonstrated experimentally by Sandström previous to its formulation by Bjerknes. In one experiment, Sandström placed a “heater” at a certain level and a “cooler” at a lower level in a vessel filled with water of uniform temperature. The heater consisted of a system of tubes through which warm water could be circulated, and the cooler consisted of a similar system through which cold water could be circulated. When warm and cold water were circulated through the pipes, a system of vertical convection currents developed and continued until the water above the heater had been heated to the temperature of the circulating warm water, and the water below the cooler had been cooled to the temperature of the circulating cold water. When this state had been reached and a stable stratification had been established, with temperature decreasing downward, all motion ceased.

In a second experiment, Sandström placed the cooling system above the heating system. In this case the final state showed a circulation with ascending motion above the heating unit and descending motion below the cooling unit. Thus, a stationary circulation was developed, because the heating took place at greater depth than the cooling.

From these experiments and from Bjerknes' theorem, it is immediately evident that in the oceans conditions are very unfavorable for the development of thermal circulations. Heating and cooling take place mainly at the same level—namely, at the sea surface, where heat is received by radiation from the sun during the day when the sun is high in the sky, or lost by long-wave radiation into space at night or when the sun is so low that the loss is greater than the gain and heat is received or lost by contact with air.

Because heating and cooling take place at the surface, one might expect that no thermal circulation can develop in the sea, but this is not true. Consider a vessel filled with water. Assume that heating at the surface takes place at the left-hand end, and that towards the right-hand end the heating decreases, becoming zero at the middle of the vessel. Beyond the middle, cooling takes place, and reaches its maximum at the other end. Under these conditions the heated water to the left will have a smaller density than the cooled water to the right, and will therefore spread to the right. Owing to the continuity of the system, water must rise near the left end of the vessel and sink near the right

end, thus establishing a clockwise circulation which at the surface flows from the area where heating takes place to the area where cooling takes place. When stationary conditions have been established, the temperature of the water to the left must be somewhat higher than the temperature of the water to the right, owing to conduction from above.

This circulation is quite in agreement with Bjerknes' theorem, because at the surface the water that flows from left to right is being cooled, since it flows from a region where heating dominates into a region where cooling is in excess. During the return flow, which takes place at some depth below the surface, the water is, on the other hand, being warmed by conduction, because it flows from a region of lower temperature to a region of higher temperature. Thus the circulation is such that the heating takes place at a greater depth than the cooling. This circulation, however, cannot become very intensive, particularly because the heating within the return flow must take place by the slow processes of conduction.

If the oceanic circulation is examined in detail, many instances are found in which the vertical circulation caused by the wind is such that the thermal machine runs in reverse, meaning that mechanical energy is transformed into heat, thus checking the further development of the wind circulation. When upwelling takes place, the surface flow will be directed from a region of low temperature to a region of high temperature, and the subsurface flow will be directed from high to low temperature. The thermal machine that is involved will consume energy and thus counteract a too-rapid wind circulation. In the Antarctic the thermal circulation will be directed at the surface from north to south and will counteract the wind circulation, which will be directed from south to north. On the other hand, systems are found within which the thermal effect tends to increase the wind effect and within which the increase of the circulation must be checked by dissipation of kinetic energy.

The Thermohaline Circulation. So far, only thermal circulations have been considered, but it must be borne in mind that the density of the water depends on both its temperature and its salinity, and that in the surface layers the salinity is subject to changes due to evaporation, condensation, precipitation, and addition of fresh water from rivers. In the open ocean the changes in density are determined by the excess or deficit of evaporation over precipitation. These changes in density may be in the same direction as those caused by heating and cooling, or they may be in opposite directions. When examining the circulation that arises because of the external factors influencing the density of the surface waters, one must take changes of both temperature and salinity into account, and must consider not the thermal but the thermohaline circulation. Bjerknes' theorem is then better formulated as follows:

If a thermohaline circulation shall produce energy, the expansion must take place at a greater depth than the contraction. In this form, the theorem can be used to determine whether within any given circulation energy is gained or lost because of thermohaline changes.

If thermal and haline circulations are separated, it is found that in some instances they work together and that in others they counteract each other. The greatest heating takes place in the equatorial region, where, owing to excess precipitation, the density is also decreased by reduction of the salinity. In the latitudes of the subtropical anticyclones the heating is less, and, in addition, the density of the water is increased by excess evaporation. Between the Equator and the latitudes of the subtropical anticyclones, conditions are therefore favorable for the development of a strong thermohaline circulation. North and south of these latitudes the haline circulation will, however, counteract the thermal, because the density is decreased by excess precipitation but increased by cooling. A weak thermohaline circulation might be expected there.

In the absence of a wind system, one might expect at the surface a slow thermohaline circulation directed from the Equator to the poles and directed at some subsurface depth in the opposite direction. This circulation would be modified by the rotation of the earth and by the form of the ocean basins, but nothing can be said as to the character of the system of currents that would develop under such conditions. It is probable, however, that the existing current system bears no similarity to the one that would result from such a thermohaline circulation, but is mainly dependent upon the character of the prevailing winds and upon the extent to which the circulation maintained by the wind is checked by the thermal conditions. In other words, the wind system tends to bring about a distribution of density that is inconsistent with the effect of heating and cooling, and the actual distribution approaches a balance between the two factors. These two factors—the wind and the process of heating and cooling—are variable, however, in time and space, for which reason a stationary distribution of density with accompanying stationary currents does not exist. Only when average conditions over a long time and a large area are considered can they be regarded as stationary.

Vertical Convection Currents. The thermohaline circulation is of small direct importance to the horizontal current, but is responsible mainly for the development of vertical convection currents. Wherever the density of the surface water is increased so much by cooling or evaporation that it becomes greater than the density of the underlying strata, the surface water must sink and must be replaced by water from some subsurface depth. The vertical currents that arise in this manner are called vertical convection currents. They are irregular in character and

should not be called “currents” if this term is defined as motion of a considerable body of water in a definite direction.

The depth to which vertical convection currents penetrate depends upon the stratification of the water. A mass of surface water, the density of which has been increased by cooling or evaporation, sinks until it meets water of equal density. If mixing with neighboring water masses takes place, it sinks to a lesser depth. When vertical convection currents have been active for some time, an upper layer of homogeneous water is formed, the thickness of which depends upon the original stratification of the water, the intensity of the convection currents, and the time the process has lasted. Thus, an upper homogeneous layer can be formed in two different ways: either by the mechanical stirring due to wind, or by the effect of the thermohaline vertical convection currents.

The vertical convection currents are, as a rule, of greater importance in higher latitudes. In latitudes where an excess of evaporation is found, the heating of the surface is often so great that the decrease of the surface density by heating more than balances the increase by evaporation. In these circumstances the surface salinity will be greater than the salinity at a short distance below the surface. The formation of deep and bottom water by vertical convection currents is dealt with elsewhere (p. 138).

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