Kelvin Helmholtz instability

Dog and Hat, Dog & Hat, Hundred House, Quarterhouse coffee — Look what arrived! The package from Dog & Hat with the distinguished logo.

What would happen if, rather than five minutes taken noticing the surroundings of a café, you were to look closely at the coffee you brewed in the morning? Different roasters, different coffees, an opportunity to notice something new in each brew. And so it was that a couple of weeks ago a package arrived in the post from the coffee subscription site “Dog and Hat“. Together with a note (in answer to a question I had sent them) ‘Recycled box, paper, mail bag’, came two coffees. An Ethiopian honey processed coffee from Hundred House and a Mexican washed coffee from Coatepec via Quarter Horse coffee.

Each time I moved the bag from Hundred House, a lovely aroma was released. So I moved it around quite a lot. While brewing a V60 with it, the morning light poured through the window producing beautiful lensing effects through the bubbles on the coffee surface and reflections from the coffee itself. The brewed coffee had such a sweet, fruity aroma reminding me of cherries that gave way to plums on tasting. What I took as toffee seemed to be described on the tasting notes as “dates” or “molasses”. Close enough I think. A lovely coffee to enjoy slowly.

The Hundred House coffee bag. With that aroma, indeed how I wonder what you are.

Printed onto the bag was a star with extra lines coming out of it, suggestive of a twinkling star at night. Although each star is massive, they are all at such a great distance from us that they appear to us as point sources of light. And since all light gets refracted when it goes from one medium to another (think about the appearance of that paper straw in a glass of water) the star will appear to twinkle from our position on the Earth below our turbulent atmosphere. Although on a clear night we may not notice it directly, regions of relative hot and cool air in the atmosphere are constantly moving. Layers of air move over each other creating waves much like you see on the seashore and it is this turbulent environment that refracts the light from the stars in such a shimmering way. We can see a similar effect in tea (though not so easily in coffee*): When we pour hot tea into a cold cup, the convection in the cup leads to there being areas of hotter and cooler tea. The refractive index of water is temperature dependent and so the light incident on the tea gets refracted (bent) by different amounts depending on whether it encounters a cool region or a warm region. This leads to the lines of light that we see dancing on the bottom of the cup¹.

KH instability, Kelvin Helmholtz instability — Not a great example of a Kelvin Helmholtz instability but it gives the general idea. This one was quickly snapped from a moving car, I’m on the lookout for a better example.

Although atmospheric turbulence is inferred by the twinkling of stars, a beautiful visualisation of that turbulence can be seen in the form of the Kelvin-Helmholtz instability. Named after Lord Kelvin and Hermann von Helmholtz, this instability manifests as a string of waves on a cloud. It occurs when a fast moving layer of air flows over a slower moving one. The phenomenon is fleeting. If you are lucky enough to see it, the pattern manifests only for a very short time. They are definitely worth watching out for.

Depictions of atmospheric turbulence can also be seen in some paintings. It is said that Vincent van Gogh’s depiction of turbulence in his painting “Starry Night” is extraordinarily accurate. Certainly it is striking that the turbulence depicted by van Gogh does look like the turbulence in a coffee cup. However apparently it goes much deeper than this. In a numerical analysis of the turbulent patterns in a few van Gogh paintings, researchers showed that van Gogh’s depiction was very close to the mathematical (Kolmogorov) description of turbulent flow.

Coffee, Van Gogh — Van Gogh in a coffee cup. Reminiscent of his painting “Starry Night”, there are remarkable mathematical similarities between what van Gogh depicted and real turbulent events.

On their website, Hundred House discuss their aim of being a “collective space, where conversation, art and industry meet, over a cup of coffee”. Pouring a coffee, and watching the turbulence in the cup, perhaps pause a while to consider these points of connection and maybe add a bit of science to the mix. This week if you are in the Northern hemisphere, the Perseid meteor shower offers a particularly great time to reflect on turbulence in the atmosphere and the twinkling of the stars. If you locate the “W” of Cassiopeia (currently in the north east viewed from London) and watch, slightly underneath it towards Perseus, you should see a few meteors of the Perseid meteor shower (perhaps 60-70 per hour during the peak of 11th-13th August). While watching for the shooting stars, it is worth looking at those that twinkle. Which twinkle more, the stars of Cassiopeia or the stars toward the horizon? Why do you think this is?

Whether you watch the stars or just prepare your coffee, take the time. Enjoy your brew.

You can find out more about the coffee subscriptions at Dog and Hat coffee, here and more about Hundred House coffee, here. Do get in touch (email, Twitter, Facebook or comments) if you notice anything you want to share.

*We don’t see this so often in coffee because coffee, generally, absorbs more light than tea and so it is harder to see the bottom of the cup.

¹Another effect that can lead to these patterns in swimming pools and similar large bodies of water is caused by waves on the surface of the water. Where waves form on the surface of the pool, the curved surface acts as a lens focussing the light to the floor of the pond. As the waves move on the surface, the pattern on the pool floor will change similarly to that in the tea cup.

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.