contrail – Bean Thinking

vortices in coffee — Vortices forming behind a tea spoon being dragged through coffee.

Drag a tea spoon through your cup of coffee (or tea). Start by dragging the spoon slowly, then faster. Initially, the coffee flows around the spoon smoothly then, as you speed up, small vortices appear at either side of the spoon. Pull the spoon out of the coffee, and the vortices continue to move together through the cup before bouncing off the sides. Such vortices form whenever there is a speed difference between two layers of fluid (gas or liquid), as there is around the spoon being dragged through coffee. It is this effect that is the second connection between the physics of coffee and contrails.

Of course it is not giant tea spoons in the air but aeroplanes. Behind each aeroplane is a series of vortices trailing behind the wings. These vortices do not (normally) cause the contrails, the reason that they form was discussed in Coffee & Contrails (I). However, the vortices do cause some interesting effects in the contrail that we can, occasionally, see.

wake vortex, contrail, coffee in the sky — In this contrail there is a set of protuberances at regular intervals along the lower edge.

As the plane moves through the air, the speed of the air going over the wing is greater than the speed of air under the wing. As well as leading to vortices forming behind the wing, this speed difference results in an air pressure difference (the air pressure under the wing is greater than the air pressure above the wing). The pressure difference (below and above the wing) pushes the plane upwards, or, perhaps more technically, ‘creates lift’ and enables the plane to fly. If you want a good demonstration of the fact that a higher air speed leads to a lower air pressure, get two pieces of flat A4 paper and hold them in front of you such that you are looking through the small gap between them. Now blow into the gap separating the two sheets; they will join together. The reason that they do this is that the air pressure for fast moving air (as you blow) is less than the air pressure for static air (around the paper) and so the difference in air pressure pushes the two sheets together.

Shadowy contrail — Look carefully for another interesting contrail optical effect. There are two contrails here, an obvious one cutting straight down the photo and a second contrail moving more horizontally across the photograph. The second contrail can be seen more clearly by its shadow.

On a clear day, if the air in the higher atmosphere is relatively humid, you will see lots of persistent contrails. These contrails last for a long time in the skies and can drift with the wind. Occasionally at the edge of such a contrail you will see regular protrusions from the contrail, almost as if waves are forming on the contrail and producing white horses in the sky (see picture above). Initially I had hoped that this was a manifestation of the Kelvin-Helmholtz instability however the actual explanation is still quite fascinating. It seems that these protrusions are the result of the “wake vortices“, the vortices that form behind a plane just as the coffee forms vortices behind your spoon. I find it quite impressive to realise that high in the sky, these contrails are showing us that the atmosphere behaves just as if it were a cup of coffee. A definite case for which a coffee is a telescope for viewing the world.

Please leave any comments in the comments box below. If you think of any other connections between the physics of coffee and contrails please share them either here or on my Facebook page.

contrail, sunset — A set of criss-crossing contrails taken in the evening.

If you gaze up at the sky on a clear day, you will often see a few contrails tracing their way across the blue. Formed as a result of water in the atmosphere condensing onto exhaust particles from aeroplanes, contrails are a regular feature of the skies in our modern life. There are at least two ways that I can think of, in which the physics of the contrail is connected to the physics of the coffee cup, so, there will be two Daily Grind articles about them. This first one, about the physics of how we see them, and a second post (scheduled for 10th June) about interesting effects that we can see in them.

Perhaps now would be a good point to go and make a cup of coffee before coming back to this post. Make sure that you notice how the steam clouds form above the kettle spout as the water boils. Do you see the steam at the spout itself, or just a few centimetres above it? With the cup next to you, notice the steam rising above it. Does the steam seem more obvious on some days than others? For example, the coffee always seems to me to steam more on cold damp days in winter than on warm-ish days in late spring. Both of these observations (about where and when we see the steam clouds) are mirrored in the contrails, it’s time to take a closer look at the coffee.

V60 from Leyas — The clouds above a coffee cup are a rough indicator of the relative humidity.

The difference in the day to day visibility of the steam above the coffee cup is an indicator of the relative humidity of the atmosphere. If we prepare our cup of coffee on a day when the relative humidity is already high, adding that extra bit of water vapour from the cup leads to clouds of steam above the mug, as the water condenses into droplets of liquid water and forms clouds. If our coffee was instead prepared on a day with low relative humidity, the water vapour above the coffee cup is less likely to condense into clouds. Contrails are formed high in the atmosphere when the relative humidity is quite high. Exhaust particles from the engines of the plane offer a surface onto which the water in the surrounding (humid) atmosphere can condense to form clouds. We know that it is mostly the atmospheric moisture that is forming the contrails (rather than water from the exhaust itself) because of research done by NASA. In research flights, the amount of water vapour leaving the aeroplane engine was 1.7 grammes per metre of travel while the mass of water in the contrail was estimated to be between 20.7 and 41.2 kilograms per metre. This means that contrails can give a clue as to the weather: on dry days, contrails will not form because the water in the atmosphere is likely to remain a gas and therefore invisible to us, it is only when the air is already quite humid that contrails are likely to form and persist.

glass of milk, sky, Mie scattering — A glass of (diluted) milk can provide clues as to the colours of the clouds in the sky as well as the sky itself

Then there is the question of why we see them at all. Contrails appear as white clouds trailing behind the plane. We see them as white because of an optical effect caused by the size of the condensed droplets of water (actually ice) in the contrail. Objects appear as having different colours either as a result of light absorption by chemicals in the object (leaves are green because of chlorophyll) or as a result of light scattering from the object. A water droplet is colourless and so the colour we see coming from the droplet must be purely a consequence of light scattering rather than a light absorption effect. Clouds appear white because the water droplets within the cloud are as large, or larger than, the wavelength of visible light (0.7 μm). Droplets this size will scatter all wavelengths of visible light and so appear white. If the droplets were much smaller than the wavelength of light they would scatter different wavelengths by different amounts. It is because the atmosphere is full of such tiny particles (and molecules) that blue light is scattered more than red light in the atmosphere and so the sky appears blue to us from our vantage point on the Earth’s surface. Milk is composed of large fat droplets (which will scatter a white light) and smaller molecules which will preferentially scatter blue light, just as the sky. This is why you can mimic the colours of the sky in a glass of milk. It is because the water droplets have formed a few cm above the kettle spout that you can see them scattering the light. For exactly the same reason, the contrails in the sky appear as white clouds.

Contrails can persist in the sky for anything from a few minutes to a few days. Just like clouds, contrails affect the way that light (and heat) is reflected from the Sun or back towards the Earth. However, unlike normal clouds they are entirely man-made, another factor that could have an unknown effect on our climate. A few years ago, a volcano eruption in Iceland caused the closure of UK airspace (as well as the airspace of much of Europe). I remember being in the queue to buy a cup of coffee in the physics department and hearing the excited conversation of two atmospheric physicists behind me. For the first time they were able to study some particular atmospheric effects without the influence of any contrails. In effect they could start to understand the influence of contrails by this unique opportunity of taking measurements during their absence. What was a major pain in the neck for so many travellers in 2010 meant a lot of extra (but presumably very interesting) work for them.

Coffee & Contrails (II) is about the structures you can sometimes see within the contrail. If you can think of any other connections between coffee and contrails (or coffee and clouds) why not let us know in the comments section below.