PLUMES OF SMOKE in the air can be both interesting and instructive to watch. Much can be learned from them about how the temperature of the atmosphere varies with height. Smoke plumes can assume a large variety of shapes, which are determined mainly by the variation in the temperature of the air between the ground and some point higher than the smokestack.

There are two basic types of smoke plume: the momentum jet, in which the upward thrust of the plume is due to its initial momentum, and the buoyant plume, which rises or falls according to the relation between its temperature and the air temperature. On a windless day both types of plume rise in a spreading vertical cone whose apex is near the top of the smokestack (provided, in the case of the buoyant plume, that the gas in the plume is hot enough). In the cones of both types of plume the velocity is highest at the central axis of the cone and tapers off toward the outside.

One difference can be noted between the two types of plume: a pure momentum jet has an apex angle of about 24 degrees and a pure buoyant jet has an apex angle of about 18 degrees. I can find no simple or straightforward explanation of this difference. The number apparently come from field observations of many plumes. By photographing a vertical plume on a windless day and then measuring the angle of the cone in the photograph you should b able to determine which kind of plume it is. If the angle is smaller than 18 degrees, vertical updrafts near the chimney stack must have forced the plume upward faster and thereby decreased the angle of its cone.

A plume is buoyant (and therefore rises) if it is warmer than the air at the same height, but other effects are involved. Since atmospheric pressure decreases with height, a parcel of gas in the plume must expand if it is initially forced upward. The energy for the expansion comes from the energy of the molecules in the parcel rather than from some heat source outside it. This internal energy is the kinetic energy of the molecules as they randomly move about.

The temperature of the gas is a measure of its internal energy: the higher the temperature, the greater the kinetic energy of the molecules. If some of the energy goes toward expanding the volume, the temperature of the gas must decrease. Such a temperature change, which involves no exchange of heat with the environment, is said to be adiabatic. Thus a rising parcel of gas in a smoke plume expands and adiabatically cools. Similarly, if the parcel of gas in a plume is initially forced downward, it contracts and adiabatically warms as the outside air works on it.

In rising gas the continuation of buoyancy depends on how fast the temperature of the ambient air changes with height. For example, if the rising plume gas is cooled but remains warmer than the ambient air, it continues to be buoyant and accelerates upward. On the other hand, if the rising plume gas becomes cooler than the ambient air, it ceases to rise and subsequently sinks. If the temperatures match, the plume rises at a constant velocity.

When the gas initially moves downward, it warms adiabatically but its temperature can be above, below or the same as the temperature of the surrounding air at the new height, depending on how the air temperature changes with height. If the gas is then warmer than the air temperature, its descent stops. If it is cooler, its descent continues at an accelerated rate. If the temperatures are the same, the descent continues at a constant velocity. Many of the plume characteristics you will observe depend on this interplay of buoyancy and the rates of cooling and warming and hence on how the temperature of the atmosphere changes with height.

Whether a parcel of gas in a smoke plume moves up or down, it changes temperature adiabatically at the rate of about one degree Celsius for each 100meter change in height. This rate is called the dry-adiabatic lapse rate, the word dry indicating that no condensation is involved. Depending on weather conditions and environmental sources of heat, the temperature profile of the atmosphere may decrease with height more or less rapidly or even at the same rate as the dry-adiabatic lapse rate. Each of these types of change is an example of a negative lapse rate for the air, because the air temperature in each case decreases with height. Occasionally, however, the air temperature increases with height, the condition termed a temperature inversion. Then the air has a positive lapse rate.

If the gas is wet, the lapse rate may change. The reason is that as the gas cools, its relative humidity increases; after 100 percent humidity is reached further cooling causes some of the water vapor to condense out as small drops. This change in state from vapor to liquid releases energy and prevents a rising parcel of gas from cooling as quickly as it would otherwise. In other words, part of the energy needed for expanding the gas now comes from the change in state of the water, and less energy is taken from the internal energy of the gas. The resulting rate at which a rising parcel of gas changes temperature with height is called the saturation-adiabatic lapse rate. When wet gases rise, they cool at the dry-adiabatic lapse rate until condensation begins, and thereafter they cool at the saturation-adiabatic lapse rate. This variation in cooling rates affects wet plumes of the kind emitted by power plants, since the plumes do not cool as rapidly while rising as a dry plume would.

It is possible for a plume to emerge as a momentum jet, diffuse somewhat and then behave primarily as a buoyant plume. Another type of plume that forms on calm days is strange to me. If the initial velocity of the emerging gases is small, which can happen when a home chimney has too large an opening at the top, the plume does not initially expand Ft in a cone. Instead it converges until the upward velocity increases enough for the plume to expand thereafter as a normal buoyant plume.

You can see a similar but inverted example of this convergence in your kitchen sink. The stream of water from the faucet falls, speeds up and becomes narrower. The narrowing is not due to air pressure, which remains the same throughout the fall. To make sense of it consider a cross section through the stream near the faucet and another one farther down. A certain amount of mass is passing through the upper cross section every second. The same amount must also be passing through the lower cross section every second, otherwise mass would be magically appearing or disappearing between the two levels. Since the speed through the lower section is higher, less cross sectional area is needed by the water in order for the same amount of mass to pass through the area every second. The stream is therefore narrower.

The hot gases leaving a stack at a low speed cannot initially expand the way a normal buoyant plume does because the typical cone shape requires a certain ratio between the velocity and the buoyancy. As a result the gases first rise as a stream, accelerating upward because of their buoyancy and contracting in width as the speed increases. Eventually they are moving fast enough to achieve the required ratio, and then the plume can expand in a cone. You might like to search for converging plumes on windless days above house chimneys or hot bonfires.

The prettiest buoyant plumes are seen during steady light winds that bend the plumes over. Whether they then rise, descend, spread up and down, remain thin or loop depends on how the air temperature varies with height and on the extent of the turbulence in the region. The illustration on page 168 displays a variety of plume characteristics, together with the approximate atmospheric temperature profile required for each characteristic. The dry-adiabatic lapse rate is also shown, but that line can be shifted to the left or the right. The line indicates the rate at which a parcel of plume gas changes temperature as it changes height. Before the line could represent the temperature of the gas as a function of height the gas temperature at some particular height (say the chimney top) would have to be known. The line could then be moved to the left or the right to give that temperature at that height.

If the air temperature decreases with height somewhat less rapidly than the dry-adiabatic lapse rate, the bent-over plume is limited in its rise and fall. An ascent would adiabatically cool the gas, with the result that the ascent would eventually halt. A descent would adiabatically warm the gas, bringing the descent to a halt. The temperature profile is close enough to the adiabatic lapse rate, however, for diffusion to gradually spread the plume and produce what is called coning.

When instead the temperature profile decreases much faster than the dry-adiabatic lapse rate (such a profile is called a superadiabatic lapse rate), heat from the chimney stack or the ground can generate thermal eddies large enough to catch the plume and make it loop up and down. This condition occurs on warm days when the ground quickly absorbs a lot of solar heat before the air circulation can remove it. Looping never occurs when there is a strong wind to cool the ground or when there is a layer of snow on it.

If the air-temperature profile has a positive lapse rate, that is, if it increases with height in an inversion, the plume is limited to a relatively thin streaming called fanning. When part of it attempts to rise, it adiabatically cools and becomes considerably cooler than the ambient air, so that the ascent quickly stops. Similarly, if part of the plume attempts to descend, it warms adiabatically, becomes warmer than the ambient air and quickly stops descending.

Lofting is what happens when a temperature inversion below the top of the stack limits downward movement. This type of temperature profile is usually found in the evening, when the ground and the lower part of the atmosphere have begun to cool as the sun disappears but the part of the atmosphere near the stack top is still relatively warm.

Fumigation is the term for what happens when positive and negative lapse rates exist simultaneously, with an inversion above the region where the lapse rate is negative. The inversion prevents the plume from diffusing upward, and the warming near the ground generates a turbulent mixing that brings the plume to ground level. This situation typically occurs in the morning as the ground and the lower air begin to warm.

A similar temperature profile, but one that has a less steep lapse rate near -the ground, creates a trapping of the plume between the inversion level and the ground. The plume diffuses to the ground without the aid of large-scale turbulent mixing from warm ground.

Plumes emitted in an otherwise coning or lofting situation might be hot enough to burst upward in thermals: blobs of hot air traveling upward in doughnut form with a strong upward motion in the center and a weaker downward motion on the outside. Such currents, found over well-heated ground or over factories, are used by glider pilots to gain lift.

The shape of the plume in each of these basic cases can be altered if the plume is initially released from the stack with a large momentum. For example, if the elevated inversion layer in fumigation or trapping is relatively shallow, a plume with enough momentum may be able to penetrate the layer instead of being confined below it. Some localities have frequent or persistent inversion layers, and chimneys there are often designed to give the escaping gas enough momentum to make the plume puncture the inversion before the plume levels ~ off. In this way the pollution at ground level is considerably reduced.

The shapes taken on by wet plumes may be somewhat different from those of dry ones because the adiabatic lapse rate is less steep once water begins to condense in the plume. Some plumes, such as those emanating from power plants, are visible because water condenses out almost immediately to produce a white stream. The mixing of the plume with the surrounding air quickly leads to evaporation, however, so that the visible part of the plume is short.

Sometimes the gas rising through a stack is washed with a spray of water to remove the pollutants. The plume then emerges with water already in the liquid state. When the water evaporates as the plume mixes with the air, the plume is cooled by the energy it loses to the evaporation. (When water evaporates from your skin as you stand in a breeze, you feel cool because your body heat provides the energy to change the water from liquid to vapor.) As a result this rapidly cooled plume will drop, probably reaching the ground near the stack.

If you watch and photograph plumes for an entire day, you will find them going through several changes as the ground warms and then cools off. In the early morning the ground and the lower atmosphere are cool and fanning or lofting plumes are likely. As the ground absorbs solar energy it and the lower level of air get warmer, which initiates turbulence. This warm and turbulent blanket gradually thickens and fumigation or trapping develops. Both effects bring the plume down to ground level. Later, as the upper air gets warm, the plumes may develop coning, thermaling or (if the ground heating is strong) looping. Late in the afternoon the intensity of the sunshine diminishes and the ground and the lower air begin to cool by radiation; then coning may develop in all the plumes. In the evening the lower part of the atmosphere develops an inversion because of the radiative cooling of the ground, and the plumes begin to fan or loft again.

You may be in a position to watch several stacks of different heights simultaneously. In Cleveland I can see at least a dozen such stacks in a shallow valley. By standing on the rim of the valley I can compare the kinds of behavior exhibited by the plumes. With an appropriate distribution of temperature the plumes emitted by the taller stacks can differ from the ones emitted by the shorter stacks because the two sets of plumes are in different parts of the atmospheric temperature profile. For example, tall stacks can emit into a region with a negative lapse rate and show lofting even as shorter stacks emit into an inversion and show fanning. With enough stack heights you can estimate where the change from a positive to a negative lapse rate comes. On days when there is an elevated shallow inversion you might see some plumes puncture the inversion while others are held below it.

Occasionally a plume clings to its smokestack. Sometimes the reason is that in the wind the stack sheds vortexes, which then force the plume initially downward along the stack. At other times a downwash results from the location of the stack with respect to buildings and hills. For example, if the stack is on the leeward side of a large obstacle, the wind is forced upward by the obstacle and then flows downward on the other side, thereby forcing the plume downward too. On the other hand, if the stack is on the windward side, the plume is likely to be lifted by the upward flow of the wind.

If the chimney opening is too large for the amount of gas it is discharging and the discharge is rather slow, you might find the chimney puffing. One moment it emits gas and smoke in the normal manner; the next moment the cold outside air flows into the chimney along the upwind side, temporarily cutting off the discharge. Eventually the hot gases build up and push their way out of the chimney again, producing another visible puff of smoke before the process is repeated.

If a stack discharges a buoyant plume that does not undergo much turbulent mixing, the plume almost immediately bifurcates. The velocity is greater in the center of the discharging plume than it is on the outside, forcing the plume to circulate in two roll vortexes with an upward motion in the middle of the bent- over plume and a downward motion on the outside. The resulting two roll vortexes split the plume. If you can get near a buoyant plume on a day with a steady nonturbulent wind, stand below the plume and look up into it. The rolling vortex motion is likely to be quite apparent as you watch the plume emerge and move downwind. You may even be able to see the sky between the two streams.

To make a serious study of plume behavior you should try to correlate the mixing of a plume downward to the ground with the way the plume is blowing and with the ground conditions below it. For example, a stack may emit a plume that fans for as long as it remains over ground that is relatively cool and has few obstacles to create large-scale turbulence. If the fanning plume passes over a body of water. the chances are that the water and the lower air will be warmer than the ground. The turbulence associated with the warmer water and air gives rise to fumigation, which brings the smoke down to the water level. I have seen stacks in Cleveland emit thin brown plumes that were blown out over Lake Erie, where fumigation set in and the brown material was mixed down to the water level.

Fumigation may also develop from fanning if the plume passes over artificial heat sources such as the inner city. There the heat mixes the air up to a level about three times the height of the average building. If you can find a plume that remains visible for a great distance, you might be able to see the transition from fanning to fumigation as the plume passes over either a natural or an artificial heat source.

The local terrain may affect plumes in other ways. A narrow valley may aid in holding a plume near the ground if a thermal inversion develops above the cool air trapped in the valley. Any plume created below the inversion would then be unable to penetrate the inversion layer and escape unless it had a high enough exit momentum to achieve the penetration while still behaving as a momentum jet.

Such trapping of noxious plumes in a valley has led to some disasters. An inversion developed over the Meuse valley of Belgium in December, 1930, holding in the valley the emissions of the steel mills and chemical plants. In three days 60 people died, most of them probably of respiratory failure, and thousands became seriously ill. It is hard to believe that the authorities, instead of halting the emissions, laid the tenfold increase in deaths to some strange and unknown disease, one biologist even contending that the cause was plague. Although some time later industrial pollution was blamed, apparently little was done about it. In September, 1972, the valley once again suffered a thermal inversion and a trapping of pollution, which again led to much illness (but no deaths).

The famous fogs that once characterized London resulted from the heavy use of coal, both in factories and in homes, which poured tons of sulfur dioxide into the air daily. As water condensed on the particles, thick brown fogs ("pea-soupers") were created. In December, 1952, as some 2,000 tons of sulfur dioxide were thrown into the air each day, a thermal inversion developed over cooler ground air and held all the factory and home plumes below the inversion. In the absence of wind to blow the material away the sulfur dioxide collected over the city for four days and nights, with the sky becoming first yellow, then brown and finally black. Some 4,000 people died as a direct result of the pollution and another 8,000 who died later were thought to have been afflicted by the respiratory problems brought about by the strong inversion.

If the day is too rainy for you to go outside to watch chimney plumes, you can stay indoors and examine the smoke rising from a cigarette. The stream is smooth and narrow near the burning tip; several centimeters higher it breaks up into swirls and the plume spreads out. To see the transition you need either a room with no air currents or a large vertical glass tube open at both ends. When the gases emerge from the burning tip, they experience a buoyant force because they are hotter than the room air. Because the initial velocity is relatively small, however, the hot gases rise in a smooth stream. After several centimeters, perhaps as many as 30, the upward acceleration from the buoyancy has increased the speed to the point where the stream becomes unstable and begins to break up into swirls.

Similar transitions from laminar to turbulent flow occur in water moving through pipes. If the water moves slowly (what "slowly" means depends on the radius of the pipe and the density and viscosity of the water), it moves smoothly. Each small parcel of water flows along a line parallel to the pipe wall. At a certain higher speed the flow becomes unstable. Swirls develop, and each small parcel of water follows an irregular route along the pipe. You can make this swirling apparent in a transparent pipe by using dye tracers. In a cigarette stream the smoke particles act as the tracers.

If the cigarette is unfiltered, you may notice a slow stream of smoke emerging from the unlighted end. After they have gone through the length of the cigarette, the gases carrying the smoke have cooled; they emerge at approximately the temperature of the room air and therefore have no buoyancy.

American Indians employed smoky bonfire thermals to communicate over considerable distances. In the book Natural Aerodynamics R. S. Scorer describes how aborigines in Australia sent up plumes as signs on a far larger scale. As several people lifted a bonfire with long poles, others threw on fresh brush. The lifting increased the airflow through the fire and thus the rate of burning, and the brush produced thick smoke. By means of a coordinated effort of the workers a smoking thermal was sent upward. When this procedure was followed in the morning or evening temperature inversion, the thermal would rise until its temperature matched that of the ambient air, at which point the smoke diffused horizontally to yield a pattern a huge mushroom. By carefully judging how hot to make the fire with lifting, the workers could control the height at which the spreading took place. If the occasion was a particularly significant one, the workers apparently were able to stack as many as fused six mushrooms over the bonfire.

Bibliography

NATURAL AERODYNAMICS. R. S. Scorer. Pergamon Press, 1958.

SOME RESTRICTIVE METEOROLOGICAL CONDITIONS TO BE CONSIDERED IN THE DESIGN OF STACKS. Eugene W. Bierly and E. Wendell Hewson in Journal of Applied Meteorology, Vol. 1, No. 3, pages 383-390; September, 1962.

GENERAL METEOROLOGY. Horace K. Byers. McGraw-Hill Book Company, 1959.

THE BEHAVIOUR OF CHIMNEY PLUMES. R S. Scorer in International Journal of Air Pollution, Vol. 1, No. 3, pages 198-220, January, 1959.

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