Coffee & Contrails (II)

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.

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