DURING the past 15 years it has been learned that under certain conditions a motionless body of salt water whose density increases with depth can, without external stirring or heating, become unstable and generate vertical mixing. Such instabilities probably arise in the ocean, and investigators are beginning to look for them and to understand the mechanisms that cause them. The instabilities are known by such names as salt fountains, salt fingers and oscillatory instabilities. Seelye Martin of the department of oceanography of the University of Washington discusses these phenomena and describes several experiments for demonstrating them with simple homemade apparatus.

"The density of ocean water," Martin writes, "depends primarily on two properties: salt content and temperature. As the water becomes saltier its density increases; as it becomes colder its density also increases. In most regions of the ocean the density increases with depth. Exceptions are regions of strong, transient convection, such as parts of the Red Sea and the Mediterranean (where evaporation makes the upper layer of the ocean saltier and thus denser than the underlying layers) and parts of the polar oceans (where salt that is rejected by the growth of sea ice increases the density of the surface layer).

"Because the density depends on both salinity and temperature, cases exist where the total density increases with depth but where the density contribution from either salinity or temperature alone decreases with depth. Therefore two entirely different instabilities may arise. The first (called salt fingers and related to the salt fountain) appears when the density contribution from salinity decreases with depth. Salt fingers consist of thin streams of falling columns of brine separated from one another by rising columns of less salty water.

"The second kind of instability (called an oscillatory instability) appears when the density contribution from temperature decreases with depth. The instability consists of growing oscillations in the transition between the saltier and the less salty zones of water. Both forms of instability are important in understanding the behavior of the ocean because of their contributions to the vertical mixing of salt, heat, nutrients and pollutants.

"An example of a completely stable ocean is found in the Pacific Ocean above 45 degrees north latitude. In this region the temperature decreases and the salinity increases with depth. The density contribution from both conditions increases. The graphs accompanying these remarks [right] depict the relations among temperature, salinity and density for this case.

"A comparable example of an unstable condition is found when the density contribution from temperature increases and the one from salinity decreases with depth. This density profile occurs over large portions of the subtropical Atlantic, Pacific and Indian oceans and is particularly strong in the Sargasso Sea near Bermuda. The effect of this density profile on vertical mixing was first described in 1956 by Henry Stommel, Arnold Arons and Duncan Blanchard in a paper titled 'An Oceanographic Curiosity: the Perpetual Salt Fountain.' The authors proposed the following hypothetical experiment: Submerge a long piece of copper tubing, say 1,000 meters long with an inside diameter of two centimeters, in the Sargasso Sea and set the top of the pipe just above the surface of the water [see illustration at left]. Connect a pump to the pipe and pump water out of the tube for a period of time. Stop pumping and remove the pump. A fountain of water will continue to flow from the pipe forever!

"The perpetual flow is explained by the fact that the pump draws into the pipe cold water that is less salty than the water surrounding the pipe. The copper walls of the pipe allow heat transfer but not salt transfer, so that the water inside the pipe becomes warmer while retaining its low salinity. Therefore the column of water contained in the pipe is lighter in weight than an equivalent column of water outside the pipe. The difference in weight between the two columns creates a pressure difference that forces the less salty water up the pipe. If the top of the pipe does not extend too far above the ocean surface, the less salty water will spill over, so that more low-salinity water will enter the bottom and travel up the pipe, warming as it rises, until it in turn reaches the surface and spills over. This pumping will continue indefinitely, or until the salt of the Sargasso Sea is uniformly mixed.

"The reverse situation also yields perpetual flow. Suppose the top of the pipe is submerged slightly below the ocean surface and warm saline water is pumped down the pipe. As the salty water descends it will cool from heat conduction and become heavier than the surrounding water. When the pump is removed, the sinking will continue until the Sargasso Sea is again well mixed.

"Would these astonishing experiments actually work? Last February, Stommel, Louis Howard and Dave Nergaard made the first attempt to install a salt fountain in the deep ocean. Stommel described the experiment as follows: 'We took 1,000 meters of Tygon hose (5/8 inch in inside diameter) to a location near Martinique. We had a lot of trouble with tangling and collapsing of the tube; it was cheap but far too flexible. We got a fountain about 60 centimeters high but were not absolutely certain whether or not waves acting on the surface float were more important in pumping water up than the density difference that undoubtedly did exist inside the tube. We ought to try again with a stiffer hose and a spar buoy to isolate things from wave action. It might be rather premature to say that we actually got a salt fountain, although I think we did.'

"The salt fountain was the first clue to the presence of a natural instability. The next step came in 1960, when Melvin Stern, an oceanographer then at the Woods Hole Oceanographic Institution, pointed out that a related instability, salt fingers, would appear under the same conditions that maintain the operation of the perpetual salt fountain.

"A kind of natural copper pipe exists in the ocean because in saline solutions heat diffuses about 100 times faster than salt. If a layer of warm, salty water is placed over a layer of cold, not-so-salty water, miniature salt fountains or salt fingers form; naturally at the interface [see illustration at right]. What happens is that heat diffuses across the interface much faster than salt. The lower part of the warm, salty layer cools. The upper part of the cold, not-so-salty layer warms. Immediately a denser fluid overlies a less dense fluid. The most efficient way for these layers to overturn is for tiny fingers of fluid, with diameters of the order of one centimeter in the ocean and one millimeter in the laboratory, to alternately sink and rise at the interface. (The much weaker density differences in the ocean compared with the ones that can be created in the laboratory cause the change of scale in the size of laboratory and ocean fingers.)

"Another approach to understanding how salt fingers develop is to assume that a wavy disturbance deforms the initially flat interface [see illustration at left]. Blobs of cold, not-so-salty water move up into the warm, salty water and vice versa. Because of the difference in diffusivities the higher blobs gain only heat, so that they become lighter and continue to rise. Simultaneously the lower blobs lose heat, become heavier and fall. Four fingers of rising water surround each finger of falling water and vice versa. On a miniature scale salt fingers act as efficient heat exchangers.

"Because of heat losses through the side walls of uninsulated containers in the laboratory, experimenters encounter difficulties in generating salt fingers with heat and salt. To avoid this problem the British physicist Stewart Turner makes salt fingers with sugar and salt. Sugar diffuses much more slowly than salt. In Turner's experiment salt plays the role of heat and sugar plays the role of salt. The possibilities for confusion are great, of course, but Turner avoids it in part by referring to salt as T stuff (temperature stuff) and sugar as S stuff (salt stuff). The amateur experimenter should remember, however, that the density of ocean water increases as its temperature decreases, so that a cold solution implies an excess of T stuff.

"Following Turner's scheme salt fingers can be generated in the laboratory or the kitchen by filling the bottom half of a container with a solution containing more salt than sugar, so that the bottom layer has more T stuff than S stuff. The top half of the container is filled with a solution containing more sugar than salt, so that the top layer has less T stuff than S stuff. Salt fingers should develop at the interface.

"A more detailed recipe for salt fingers follows: Make a solution of two and a half level teaspoons of salt and one teaspoon of sugar in one measuring cup of water. In a second measuring cup mix a solution of two teaspoons of sugar and one teaspoon of salt in water. Stir both solutions thoroughly. (Incidentally, most brands of table salt contain either sodium silicoaluminate or magnesium chloride to prevent the salt from getting lumpy. Unfortunately the additives also make the salt solutions cloudy. Try to obtain salt without these additives.)

"Pour the solution that contains the most salt into a glass container, preferably one with vertical walls. Cut from writing paper a disk with a diameter equal to the inside diameter of the glass container. Tie a thread to the disk and carefully place the disk in the jar over the lower solution [see illustration, right]. It does not matter if the disk slips slightly below the surface.

"To make the salt fingers visible add dye to the upper solution. I used two dyes: a brilliant blue dye called methyl blue, which is available from chemical supply houses, and a red dye called 2 carmine, which is a drawing ink made by the Pelikan Company and is available from dealers in art and drafting supplies. Methyl blue, which comes in crystalline form, gave slightly better results. (The problem with kitchen dyes, such as food coloring and soy sauce, is that the diffusivities of these dyes are equal to or greater than the diffusivity of salt. In this demonstration the rate of growth of the salt fingers depends on the diffusion of salt. If the dyes diffuse at the same rate, the individual salt fingers become blurred.)

"Pour the second solution slowly onto the paper disk. When the fluid stops swirling, raise the disk gently above the interface. Disturb the interface as little as possible. For the salt fingers to be visible the initial interface between the dyed and the undyed fluid should be as distinct as possible. If the motion of the disk creates too much mixing, lift it less than an inch and let the paper remain in the container. Within an hour salt fingers will appear; they will remain visible for 12 to 24 hours.

"To see an individual salt finger, repeat the same experiment in a test tube with an inner diameter of about five millimeters. Seal one end with a cork. Mount the tube vertically. Using an eyedropper or a small pipette, pour the heavier fluid into the glass tube until the free surface rests near the midpoint of the tube. Next . pour the lighter solution gently into the tube. The walls of the tube will suppress the turbulent mixing. Within an hour several fingers will form. The details of an individual finger will be clearly visible [see illustration at left].

"A patient observer will see two different kinds of flow in the tube. The first kind is an ordered flow caused by the salt fingers. Above and below the salt fingers, however, lies a second region of random, near-turbulent plumes. The plumes appear because after the fingers fall or rise a certain distance their salinity becomes the same as the salinity of the surrounding fluid. At this point salt diffusion is unimportant. The ordering effect of the salt-finger mechanism ceases. The fingers become randomly falling plumes.

"Because of their small size salt fingers have not yet been observed in the ocean. On the other hand, salt fingers have proved to be an extremely general mixing phenomenon. Fingers can appear whenever two or more solutes stratify a fluid. For example, solar physicists speculate that an analogy to salt fingers may occur in the sun because of the variations in temperature and angular momentum with radius.

"Metallurgists are investigating another example: the cooling of molten metal castings that contain impurities. As the molten metal solidifies, the effects of the temperature and the impurities cause the casting to stratify. The investigators hope to show that a salt-finger analogy explains the distribution of impurities in the cold metal.

"The opposite density profile (where the contribution of temperature to density decreases with depth and the contribution from salinity increases) also yields an oscillatory instability. Profiles of this type are found in several places, including the hot-brine deeps of the Red Se [see "The Red Sea Hot Brines," by Egon T. Degens and David A. Ross; SCIENTIFIC AMERICAN, April, 1970]. There three large deeps (named Chain Deep, Atlantic II Deep and Discovery Deep after the oceanographic vessels from which the were discovered) are filled with a hot salty brine.

"The Atlantic II Deep is the largest of the three, being 14 by five kilometers in surface dimensions and about 100 meter deep. At the top of this deep the salinity and temperature have the characteristic Red Sea values of 41 grams of salt per liter of solution and 22 degrees Celsius 50 meters farther down the values are 257 grams per liter and 56 degrees C. The temperature and salinity profiles in the Chain Deep and the Discovery Deep are similar. Economics has stimulated interest in these deeps. Estimates of the gross value of the zinc, copper, lead, silver and gold contained in the top 10 meters of sediment in the Atlantic I Deep range as high as $2.5 billion, exclusive of recovery costs.

"A second example of similar stratification exists in Lake Vanda in Antarctica. Vanda is ice-covered. Relatively fresh water is found directly below the ice at a temperature of zero degrees C. Some 220 meters down the water temperature is 25 degrees C. and the salinity is about 150 grams per liter.

"Still another example is the solar ponds of Israel, which are used to convert heat from the sun into electricity. The ponds consist of large containers about a meter deep with black bottoms. The bottom half of the pond is filled with salt water, the top half with fresh. The black bottom absorbs solar radiation and heats the adjacent salty water. The density profile remains stable because of the salt. For this reason heat cannot escape to the atmosphere through the process of convective overturning. The hot, salty water is selectively withdrawn from the solar ponds and used to drive a generator, after which it is returned for reheating.

"To understand how the deeps and Lake Vanda were formed and to calculate the age of the brine contained in them the investigators must first understand how and with what speed hot, dense brine mixes with overlying, less salty, cold water. In the solar ponds the rate of mixing of hot brine with the overlying water decreases the efficiency of the heat trap. In practical terms the effect reduces the amount of electric power produced by a given pond. Insight into each of these systems can be gained by considering the mechanism of oscillatory instability.

"What happens when a layer of cold, not-so-salty water overlies warm, salty water? Suppose a fluid element on the interface is displaced slightly downward from its equilibrium position. In the ocean or the laboratory any small random disturbance can create the initial displacement. Because heat diffuses much faster than salt the displaced element will gain heat and buoyancy. It will rise above its original position into colder fluid and continue rising until the element loses its added heat and becomes colder and heavier. It will then sink again into warmer fluid, gain heat and initiate another cycle.

"If the salinity difference between the two fluids is not too great, the oscillation will continue to grow in amplitude until turbulence results. On the other hand, a large salinity difference will restrict the oscillations occur for every element of ly growing amplitude. In either case such oscillations occur for every element of the interface. A vigorous laminar, or turbulent, mixing results.

"To demonstrate instability of this kind Turner and Edward A. Spiegle of New York University designed the following simple kitchen experiment, which the Swedish oceanographer Pierre Welander and I built together while Welander was recently visiting the University of Washington. With the paper-disk technique a large glass container was filled half with saturated salt solution and half with fresh water. The container was placed in a frying pan with fresh water. We put the pan on the stove and boiled the water.

"Putting ice cubes on the surface of the water in a jar, we created a situation where water at the upper surface was near the freezing point and water at the bottom was near the boiling point. The resulting oscillations at the interface between the fresh water and the salt water were made visible in two ways. First, we put food coloring into the upper layer so that the turbulent billows were evident. Second, we improvised a glass float with a small, uncapped food-coloring jar about an inch in length. By winding copper wire around the open neck we weighted the bottle so that it floated neck down [see illustration at right]. Then, by adding to and removing from the bottle water as needed, we trimmed the bottle so that it floated at the saltwater-fresh-water interface. The trimming was surprisingly easy. When the bottle sank too deep, we recovered it with kitchen tongs.

"The trimmed bottle served as a nondiffusive element of salt water. The air in the bottle, which expanded and contracted with changes in temperature, responded as a fluid element would to changes in temperature. Once the bottle was properly trimmed it quickly developed an oscillation with a period of between 10 and 20 seconds and a peak-to-peak amplitude of about five centimeters.

"The amplitude of both the float displacement and the fluid oscillations depends on the density difference between the two fluids. We could increase the amplitude simply by stirring salt into the upper fluid. When the density difference is made great, the oscillations continue for hours. A small density difference quickly yields turbulent mixing of large amplitude. A sugar solution will produce an even longer-running oscillation because of its small diffusivity.

"Experiments of this kind demonstrate the effectiveness of both salt fingers and oscillatory instability in generating vertical mixing. A task for an inquiring mind is relating these intriguing mechanisms to an understanding of both the history of the ocean and the ocean circulation."

Bibliography

HOT BRINES AND RECENT HEAVY METAL DEPOSITS IN THE RED SEA: A GEOCHEMICAL AND GEOPHYSICAL ACCOUNT. Edited by Egon T. Degens and David A. Ross. Springer-Verlag New York Inc., 1969.

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