Why do plumes flatten?

Sometime the plumes from smokestacks just keep gong up until they disappear, but at other times they will stop and start spreading out once they have reached a specific height. Why?

One common explanation is that the plumes have reached a capping inversion and can’t go any higher. There is some truth in this, but it is a major oversimplification. Inversions aren’t something you reach, for one thing. Here in Fairbanks, and throughout the country at night, inversions often start at the ground. Further, they may extend for a considerable distance – up to a mile or more – vertically.

So just what is an inversion?

Under normal circumstances the air gets colder with height. One reason is that air cools as it rises. This is due to conservation of energy: the air is essentially swapping heat for potential energy. For dry air, the cooling rate is about 1°C per hundred meters, or 5.4°F per thousand feet. This is called the adiabatic lapse rate. When water is condensing, such as in a cloud, the air doesn’t cool quite as fast as it rises, because the condensing water adds heat to the air.

In an inversion layer, the air gets warmer with height. The rise can be only a degree or two occurring over a height of a few tens of feet, or it can be up to 20°C or more extending for a kilometer or two. But it is a layer of finite thickness, not just a flat plane at a specific height.

Here in Fairbanks, power plant plumes are generally visible because they contain water, which at low temperatures condenses. As a result it is very obvious when they reach a particular height and suddenly flatten out. But why?

They rise to start with because they are warmer than the surrounding air. They stop rising at the height where their temperature is the same as that of the air around them.

Part of this is because they cool as they rise. But if this were all that were involved, they would rise quite a long way. Suppose the plume temperature when it left the stack were 100°C – the boiling point of water. If it were simply cooling off at the adiabatic rate, it would take 10 kilometers just to reach the freezing point – and I guarantee that the air at 10 kilometers over Fairbanks in the winter never gets that warm.

So why do they flatten out and stop rising?

Because all the time they are rising, they are mixing with the surrounding air. This is actually visible in the photograph – the plume gets wider with height, due to the mixing in of cold environmental air. This works even for very small plumes. I have seen diesel trucks with stacks trailing a plume that flattens only a foot or two above the top of the stack, or stationary sources whose plumes flatten several hundred meters up. It’s a question of how fast the environmental air mixes with the plume as well as the initial plume temperature.

So if you see a plume flatten out, you can be pretty sure it is in an inversion, but not that there is a particular inversion at that particular height.

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