vortex

Time standing still at VCR, Kuala Lumpur

VCR chalkboard

A trip down memory lane via a new cafe. VCR in Bangsar, KL

One of the first science-based talks I gave was about how VCR tapes worked. Depending on how you viewed it (and whether you had to listen), this was either an achievement given that I was at school and didn’t really understand magnetism nor magnetoresistive devices, or a thing to be suffered through (for much the same reasons). So when I learned that a new café called VCR had opened in Bangsar in Kuala Lumpur, it prompted a series of fond (and a few embarrassing) memories.

Moving on, it is clear that this second branch of VCR (the first is in Pudu, in the main part of KL), aims to provoke such memories of times past. From the name of the wifi to the pulleys behind the counter and the wooden screen at the back of the café, various details around the café pull your memory in different directions. However the coffee is very much in the present. With three types of coffee available to try as a pour over as well as the standard espresso based drinks, this café has a lot to offer. The coffee is roasted by VCR themselves in their Pudu branch. There is also an extensive food menu with an interesting Chawan mushi as well as an intricate avocado toast (topped with pomegranate seeds, toasted quinoa and feta).

coffee at VCR Bangsar

Coffee and pour over jug. But is the number 68 or 89?

The friendly baristas were happy to advise on which coffee to match with which brewing device (though there seemed a marked preference for V60s on the days I visited). In total I tried 4 pour-overs, one with the Kalita Wave and the others by V60. These coffees were all excellent but very different. A couple were fruity, one was sweet and full bodied, one reminded me a bit of the local fruit durian, not I hasten to add because of its taste, but because the aroma from the cup was so different from the flavour of the drink. It was a great privilege to be able to try these different coffees consecutively and to really experience the variety of flavours in coffee. Great care was taken while making the pour over before it was brought over to the table, together with a jug of water, it also seemed to me that the baristas kept a discreet eye on me afterwards to ensure I enjoyed the coffee. So it was a good experience to have had the opportunity both to enjoy one of those pour overs and to observe the people and the surroundings of VCR when I had to wait for 1 hour for someone with no phone and no book. If you get the opportunity to do this I would very much recommend it. Find a comfortable café, order a coffee and then sit, without distractions, and watch what your mind notices and where it wanders for an hour.

An obvious place for a mind to wander would be to the mechanism of tape recording (and why mini-disks are the superior recording medium for the elegance of the physics involved). However, in an hour a mind wanders far further than the name. Supporting the cakes (and a display case for the 2nd place award of the brewers cup), was a table with a concertina type decoration around its edge. Was this a nod to the Kalita Wave brewing device? This is a significant difference between the V60 and the Kalita Wave: the ridges (or wave pattern) on the filter of the latter. How does coffee flow past these ridges? Does this difference in flow dynamics make a difference to the taste of the coffee?

variables grind size, pour rate, pour vorticity

It seems that there would be a lot of physics to observe in the fluid flow in a Kalita Wave filter.

A few weeks previously a friend had made a (lovely) coffee with her Kalita Wave. It was interesting to note the different dose of coffee she used and the way the grinds built up in the ridges (compared with my ‘normal’ V60). Why do the grinds end up in the ridges? Why is there a layer of dust on the blades of a fan? Why do some corners of a building collect more dust or leaves than others? Are these questions related and does it change the flavour of the coffee in the Kalita?

In fact, there are many subtleties in understanding how fluids move around solid objects. One of these is that at the interface of the fluid with the solid, the fluid does not flow at all, there is a stationary layer. Known as a boundary layer or Prandtl boundary layer (after the person who first suggested their existence, Ludwig Prandtl), realising these layers existed revolutionised the field of aerodynamics. The problem had been how to model the drag experienced by a solid object in a fluid flow. Although perhaps only of academic interest in terms of the flow of coffee around a Kalita filter or a spoon, by the end of the nineteenth century and particularly, with the invention of airplanes, how to calculate fluid (i.e air) flow around a solid (i.e. wing) object became very important for practical reasons.

vortices, turbulence, coffee cup physics, coffee cup science

Another cool consequence of boundary layers:
Vortices created at the walls of a mug when the whole cup of coffee is placed on a rotating object (such as a record player).

Prandtl introduced the concept of a boundary layer in 1904. The idea allowed physicists to treat the main body of the moving fluid separately to the layer, very close to the solid, that was dominated by friction with the solid. This meant that the Navier-Stokes equations (that are used to describe fluid flow and ordinarily do not have an analytical solution) are simplified for this boundary layer and can be quantitatively solved. Although simple, by the 1920s Prandtl’s layer (and consequently the solvable equations) were being used to quantitatively predict the skin friction drag produced by airplanes and airships.

The boundary layer allows us to understand how vortices form behind cylinders or around the corners of buildings. I suspect a mix of the boundary layer, turbulence caused by the coffee going over many of the ridges and the brick like stacking/jamming of the coffee grains would combine to explain the difference in the grind shape around the Kalita Wave and the V60 filters. What this does to the flavour of the coffee and whether better brewing would involve more agitation, I will leave to Kalita Wave coffee lovers to investigate. And when you do, I would love to hear of your results, either here on Facebook or Twitter.

 

Coffee and the world

Welcome to the first post of 2018, Happy New Year! But before embracing 2018, perhaps let’s take a moment to remember those things that we discovered in 2017 that connect your coffee cup (or brewing device) with the physics of what occurs in the wider universe. Here are some of the highlights for me this year, if you want to share your highlight, please comment in the section below.

latte art, flat white art

A properly made latte. But what if you add hot espresso to the milk instead of the other way around?

1) Latte layering

In mid-December a study was published in Nature Communications that explored the complex, but elegant, physics involved in making lattes (ok, not quite by the technique that you would hopefully find in your neighbourhood café but keep with this…). When a hot, low density, liquid (espresso) was poured into a hot higher density liquid (milk) contained within a cold mug, the competition between the density gradients of the liquid (vertical) and the temperature gradient from the cup wall to the liquids (horizontal) produced multiple layers of varying coffee/milk concentration in the cup. Too late for a 2017 Daily Grind article, this looks to be too good an experiment to pass by, hopefully it will appear on the Daily Grind in early 2018.

 

science in a V60

Could this V60 mystery now be solved?

2) Bouncing drops

November 2017 saw research published about what happens when a cold droplet falls onto a hot liquid (think milk and coffee). The temperature difference causes currents to be established within the droplet (and in the main liquid) that in turn create air flows between the droplet and the liquid bath that prevent the droplet from merging with the bath. The research can explain why it is that you can sometimes see raindrops staying as spheres of water on the top of puddles. It may also explain a puzzling phenomenon that I have seen while brewing coffee in a V60.

 

Vortex rings get everywhere.

3) Vortex rings in coffee

June 2017 and it is again about adding milk to coffee (why do I drink coffee black?). When one liquid (such as milk) is dripped into another (such as coffee), it is very likely that you will observe the milk to form “vortex rings”. These rings are related to smoke rings and have, in the past, been proposed as an atomic model. This year however it was suggested that these vortex rings could form as a type of magnetic nanostructure. Mathematically impressive, beautiful, perhaps quite useful and mathematically similar to something you can find in your coffee.

 

bloom on a v60

How do craters form?

4) Crater shapes

April 2017. What happens while brewing a pour over? As you drip water onto a granular bed (or, in coffee terms, ground coffee in a V60 filter), each drop will create a crater. The size and shape of the crater will depend on the density of the granular bed (espresso puck or loose grounds in a filter) and the velocity of the falling drop. Fast frame photography revealed how the shape of the crater changed with time for different scenarios.

 

Coffee bag genuinely home compostable

How it started.
The Roasting House bag before it went into the worm composter.

5) A home experiment

Perhaps not quite in the theme of the other four stories but this is an experiment that you can do at home. Some have proposed compostable coffee cups as a more environmentally conscious alternative to ordinary, disposable, coffee cups. But how “compostable” are compostable cups and compostable packaging? Between May and September 2017, #howlongtocompost looked at how long it took the Natureflex packaging (used by the coffee roasting company Roasting House for their ground coffee) to compost in a worm composting bin. This one worked quite well. Within 17 weeks, it had been eaten by the worms. In comparison, the “completely compostable” take away coffee cup is still in the worm bin (although considerably degraded) 37 weeks after the start of the experiment. If you are interested, you can follow #willitcompost on twitter. Will it finally compost? I’ll leave you to place your bets but you may decide that a link to Brian’s coffee spot guide to re-usable cups will be helpful.

 

What will 2018 bring? Certainly there will be more composting experiments as I have a coffee bean bag from Amoret coffee, 3 different compostable cups and a compostable “glass” to try with the worms. But in terms of the science? We’ll have to wait. Meanwhile, if you have a coffee-science highlight from 2017, please do share it either here in the comments section, on Twitter or on Facebook. Happy New Year to you all.

 

 

 

 

 

On rings, knots, myths and coffee

vortices in coffee

Vortices behind a spoon dragged through coffee.

Dragging a spoon through coffee (or tea) has got to remain one of the easiest ways to see, and play with, vortices. Changing the way that you pull the spoon through the coffee, you can make the vortices travel at different speeds and watch as they bounce off the sides of the cup. This type of vortex can be seen whenever one object (such as the spoon) pulls through a fluid (such as the coffee). Examples could be the whirlwinds behind buses (and trains), the whirlpools around the pillars of bridges in rivers and the high winds around chimneys that has led some chimneys to collapse.

Yet there is another type of vortex that you can make, and play with, in coffee. A type of vortex that has been associated with the legends of sailors, supernovae and atomic theory. If you add milk to your coffee, you may have been making these vortices each time you prepare your brew and yet, perhaps you’ve never noticed them. They are the vortex rings. Unlike the vortices behind a spoon, to see these vortex rings we do not pull one object through another one. Instead we push one fluid (such as milk) through another fluid (the coffee).

It is said that there used to be a sailor’s legend: If it was slightly choppy out at sea, the waves could be calmed by a rain shower. One person who heard this legend and decided to investigate whether there was any substance to it was Osborne Reynolds (1842-1912). Loading a tank with water and then floating a layer of dyed water on top of that, he dripped water into the tank and watched as the coloured fluid curled up in on itself forming doughnut shapes that then sank through the tank. The dripping water was creating vortex rings as it entered the tank. You can replicate his experiment in your cup of coffee, though it is easier to see it in a glass of water, (see the video below for a how-to).

Reynolds reasoned that the vortices took energy out of the waves on the surface of the water and so in that way calmed the choppy waves. As with Benjamin Franklin’s oil on water experiment, it’s another instance where a sailor’s myth led to an experimental discovery.

chimney, coffeecupscience, everydayphysics, coffee cup science, vortex

In high winds, vortices around chimneys can cause them to collapse. The spiral around the chimney helps to reduce these problem vortices.

Another physicist was interested in these vortex rings for an entirely different reason. William Thomson, better known as Lord Kelvin, proposed an early model of atoms that explained certain aspects of the developing field of atomic spectroscopy. Different elements were known to absorb (or emit) light at different frequencies (or equivalently energies). These energies acted as a ‘fingerprint’ that could be used to identify the elements. Indeed, helium, which was until that point unknown on Earth, was discovered by measuring the light emission from the Sun (Helios) and noting an unusual set of emission frequencies. Kelvin proposed that the elements behaved this way as each element was formed of atoms which were actually vortex rings in the ether. Different elements were made by different arrangements of vortex ring, perhaps two tied together or even three interlocking rings. The simplest atom may be merely a ring, a different element may have atoms made of figure of eights or of linked vortex rings. For more about Kelvin’s vortex atom theory click here.

Kelvin’s atomic theory fell by the way side but not before it contributed to ideas on the mathematics (and physics) of knots. And lest it be thought that this is just an interesting bit of physics history, the idea has had a bit of a resurgence recently. It has been proposed that peculiar magnetic structures that can be found in some materials (and which show potential as data storage devices), may work through being knotted in the same sort of vortex rings that Kelvin proposed and that Reynolds saw.

And that you can find in a cup of coffee, if you just add milk.

 

Causing a stir

coronal hole, Sun

Where it all begins. The dark object is a Coronal hole on the Sun. Image credit and copyright NASA/AIA

What’s the difference between your cup of coffee and the solar wind (the fast stream of charged particles emanating from the Sun)? Perhaps this seems a strange question, we ought first to ask what connects your coffee with the solar wind. But, when we look at what connects them, you may be surprised to find the reason that they are different.

The solar wind is a flow of charged particles that streams past the Earth at roughly 400 km/s. To put this figure into some perspective, 400 km/s is 24, 000 km/min which means that the wind travels from the Earth to the Moon in 16 minutes. In comparison it took  Apollo 11 over 3 days between leaving Earth’s orbit and entering the Moon’s (over 4 days between launch and landing). The particles in the solar wind originate in the Sun’s Corona where temperatures get so hot that the gases have enough energy to escape the gravitational pull of the Sun itself. As these particles reach the Earth, they encounter the Earth’s magnetic field and, being rapidly slowed down by the Earth being in the way, a shock wave forms which is known as the Earth’s Bow Shock.

We must all have dragged a spoon through coffee and watched as the vortices form behind the spoon. It is a low-speed example of turbulent behaviour in the coffee. So it is perhaps not surprising that when the very hot and very fast solar wind hits the magnetic field region of the Earth, we find turbulence there too.

vortices in coffee

Vortices behind a spoon being dragged through coffee are an example of turbulence.

Now when we stir our coffee, we will see that there is one big rotation of fluid in the direction of the spoon but we may also notice smaller eddies in the drink. Some of these form from the fact that the coffee is rotating but the mug’s walls are staying motionless, friction forces the fast moving coffee to slow down at the walls. You can actually see this effect if, rather than stirring your coffee, you put it on a record player (or other rotating platform) as has been featured on Bean Thinking previously. Similarly, when you have a large vortex in the form of a smoke ring, it can decay into many smaller vortex “smoke rings” in what is known as a vortex cascade. This too is an effect that you can see in coffee (but rather than smoke rings you can make milk rings with a straw). Very often these milk rings will decay into many smaller rings in the same sort of vortex cascade as you get with the smoke, you can see a video of the effect here or at the bottom of this post. Big vortices decay into smaller vortices until they (to our eyes) disappear entirely.

vortices, turbulence, coffee cup physics, coffee cup science

Vortices created at the walls of a mug when the whole cup of coffee is placed on a rotating object (such as a record player). This is an image of water in a rotating mug with a drop of ink placed next to the mug’s wall.

The important thing is that this type of vortex cascade has also been observed in the solar wind. Rather than a giant spoon though, the solar wind stirs itself as the fast wind encounters the (relatively) slow Earth. We are used to stirring our coffee as a way of cooling it down, perhaps we blow on it gently to speed up the cooling process. But this is the difference between your coffee and the solar wind. When the solar wind is stirred up, it gets hotter. To examine how this occurs, scientists have been examining data from the Cluster set of satellites. Launched by the European Space Agency to study the magnetosphere of the Earth, Cluster has provided clues as to how the solar wind differs from a cup of coffee. Back in 2009, scientists analysed the data from Cluster looking at precisely how the turbulence produced as the solar wind meets the magnetosphere cascades into different sorts of eddies, different levels of turbulence. Comparing the data to theoretical models, they showed how the turbulence started off on large length scales (of the order 100 000 km), and decayed into smaller and smaller length scales until it reached 3km. At this point, all that energy, all that motion was dissipated as heat. Stirring the solar wind heated it up.

Why does stirring the solar wind heat it up whereas stirring your coffee cool it down? It’s to do with the environment of the coffee and the wind. On the Earth, the coffee will be surrounded by a cooler atmosphere. Stirring the coffee brings the hot liquid into contact with the cooler air and so the heat from the coffee can escape more efficiently into the atmosphere. They say in space, no one can hear you scream, which is another way of saying that there is no atmosphere through which sound waves can travel¹. No atmosphere means that there is no way of the heat generated by all that turbulence getting dissipated into a cooler air around it. So, as heat is energy, all that energy involved in stirring up the solar wind gets dissipated as heat in the wind which then has a higher temperature to that which we would naively expect.

So, next time you are waiting for your coffee to cool and stir it to hasten the process, take a moment to think about what is happening approximately 90 000 km above your head where the solar wind is being effectively stirred, and heated, by our planet’s magnetic field.

Seeing a vortex cascade in coffee:

 

¹The origin of the phrase however suggests that this was not quite the meaning that was intended, it was a promotional phrase used for the film Alien.

 

Stirring up some climate science

Everything is connected. At least, that is part of the premise of Bean Thinking, where the physics of a coffee cup is used to explore the physics of the wider world. So it was great to stumble upon a new connection that I had not previously appreciated¹.

vortices in coffee

Like the vortices behind a spoon dragged through coffee….

The connection is between climate science and that wonderful pastime of pulling a spoon through coffee and watching the vortices form behind it. Yet the research that revealed this connection was not looking for links between coffee and the atmosphere. Instead the researchers were interested in something seemingly (and hopefully) very far from a coffee cup: rogue waves.

Rogue waves are rare and extremely large waves that have been the subject of mariners tales for many years. Nonetheless, it is only relatively recently that they have become the subject of scientific research, partly because they are so rare and so outside our usual experience that they were thought to be the stuff of myth rather than of science. So it is only now that we are developing an understanding of how it can be that, in amongst a number of smaller waves, a massive wave of 20m height can suddenly appear, apparently out of nowhere. One of the groups looking at this problem investigated the effect of a particular sort of (known) instability on a series of waves in water. However, unlike other research groups, this particular study included the effect of the air above the water as well as the waves themselves.

Small waves seen from Lindisfarne

Rogue waves seem to come out of nowhere. A rogue wave can be 2 or 3 times the height of the other waves in the water at the time. How and why do they form?

Although this sounds a simple idea, modelling water waves in air is actually extremely complex. To do so, the authors of the study had to use a computer simulation of the air-water interface. It is not the sort of problem that can be solved analytically, instead the computer has to crunch through the numerical solutions. In order to start to see what was going on with the rogue waves, the authors had to simulate multiple waves of different amplitudes. Each simulation took weeks to perform. Given that this was only a few years ago (the study was published in 2013), you can start to see why people had previously been approximating water waves as waves in water (without worrying too much about the air interface).

Now here is where the link with coffee comes in. The group modelled waves as a function of steepness and found that, above a critical steepness, the wave breaking caused significant interaction between the air and the water layers. In addition to the bubbles that form when waves break, the movement of the air over the breaking wave formed into a vortex which, when it interacted with the back of the wave created an opposite vortex: a vortex dipole “much like the vortices that form behind a spoon dragged through a cup of coffee“.

Rayleigh Benard cells in clouds

The water droplets that form clouds are often ‘seeded’ by particles of salt or dust, such as the aerosols distributed by the vortices in this wave study. Image shows clouds above the Pacific. Image NASA image by Jeff Schmaltz, LANCE/EOSDIS Rapid Response

Just as with the vortices in the coffee cup, vortices were forming in the air behind the wave crest (which acted as the spoon) and travelled upwards through the atmosphere and away from the waves. As each wave broke, a train of vortex dipoles were produced that twirled off into the sky. Imagine a coffee bath and multiple spoons rather than a coffee cup. The authors suggested that these vortices could carry aerosols from the sea (salt, water droplets etc) into the atmosphere. Travelling within the vortices, these tiny particles could travel far further and far higher than we may have expected otherwise. Such aerosols can be critical for cloud formation and so the effect of these breaking waves could be important for climate modelling.

While an undergraduate, I had an opportunity to study a course in atmospheric physics. I remember the lecturer lamenting that while we (as a community, but not really as the students sitting in the lecture theatre at that time) understood atmospheric modelling quite well and that we understood how to model the oceans fairly well, we got problems when we tried to put the two sets of models together. It was clear that something wasn’t quite right. Years later, it seems that at least past of the reason for that is linked to those vortices that you see as you pull your spoon through your coffee cup.

Everything is connected indeed.

A summary of the study can be found here. The abstract (and link to the pdf) of the published paper can be found here. If you do not have access to the journal through a library, an early, but free, version of the paper is here – note though that this version may not include the amendments included after peer review.

 

¹A quote attributed to Jean-Baptiste Biot (1774-1862), is perhaps relevant here “Nothing is so easy to see than what has been found yesterday, and nothing more difficult than what will be found tomorrow.”

Seeing the trees for the wood at OJO Coffee, Bangsar, KL

coffees on display at OJO

OJO Coffee, Bangsar, Kuala Lumpur

It is very easy to sit for a long time watching the people and the surroundings at OJO Coffee in Bangsar, Kuala Lumpur. Initially I had thought that this medium-sized café with an impressive number of power points dotted around it was an independent. However similarities with CoffeaCoffee around the corner and a couple of other clues (CoffeaCoffee t-shirts) suggest that it is actually part of the CoffeaCoffee chain, something that was confirmed when I asked the barista. However, the standard of coffee in this chain should prompt some of the smaller independents to up their game a bit (and certainly all of the UK based chains). Not content with just serving the typical coffees of ‘latte’, ‘cappuccino’ etc. (which are made using their own blend), OJO’s additionally serves about 15 types of single origin coffee made with your choice of method (Hario V60, Aeropress or French press). For a while this summer I became a bit of a regular at OJO and so I would particularly recommend the Indonesian Sumatran prepared by V60, but with so many coffees to choose from (from the relatively local Indonesians to South American coffees from much further afield) there is plenty to try at this café.

wooden mosaic

The wall made of wood at OJO

The interior of OJOs is decorated with many types of wood. Different cuts of wood are made into a sort of wood mosaic on the wall while the tables are made using several types of wood so as to give a symbolism about the Sun that is a type of motif of the café. Much of the floor is wood too and so this got me thinking about the rainforests in this country. Malaysia has a rich variety of wildlife and forest, it is home to the Orangutan as well as many other species. Teak trees that can be used for more expensive furniture grow along the roadside. Much of this timber can be obtained sustainably and in a way that respects the rainforest and I am certainly not suggesting that the wood in OJOs was anything but sustainable. However, perhaps inevitably, there are many pressures on these invaluable forests. Some of these pressures have, in the recent past, resulted in significant deforestation. One such pressure is that of palm oil.

Palm oil is a massively useful commodity. It is now used in food products from margarine to biscuits to raisins (surprising but true, check the ingredients list of a packet of raisins) and non-food products such as soaps. It is literally everywhere. Both Malaysia and its neighbour, Indonesia, have profited enormously from growing and exporting palm oil. Unfortunately, at times the rainforest is cleared to make way for the palm oil plantations. As it is easier to burn felled trees to clear the land rather than to painstakingly pull the roots up by hand, the cleared forest is burned. But the ground is not any ordinary soil, the ground is often peat based which means that the fires on the surface penetrate deep below the ground and produce phenomenal amounts of smoke.

If at this point you were wondering where the ‘physics’ bit of this café-physics review is, I assure you it is coming. It is indeed linked to this environmental story and to OJOs, please keep with me.

Each year, parts of Malaysia, Singapore and Indonesia are enveloped by a haze produced by this burning peat land (It made the BBC in 2013 when it was particularly bad, but some haze is present for a few weeks every year). Haze has the appearance of thick fog but smells of smoke. At times, visibility can be reduced such that the tops of nearby tall buildings are obscured. Each time land needs clearing for new palm oil plantations, this smoke is produced. The haze can be reduced by local weather patterns but on many days, the haze is cleared by the torrential rains that can occur in this part of the world.

the haze is coming in

L-R: The haze comes in over part of KL in 2013 (series of 3 pictures)

It is commonly said that ‘rain clears the air’ but this is not completely true. It is not the raindrops themselves that somehow wash the air free of the dust of the haze, it is the vortices that form behind them*. Just as a spoon dragged through coffee produces vortices behind it, so a raindrop falling through the air forms vortices in its wake. The size of these vortices will depend on the size of the drop and the speed at which it falls through the air; a tea spoon and a dessert spoon pulled at different speeds through the coffee similarly produce different forms of vortex. So the amount of dust that is ‘sucked in’ and falls to the ground will depend on the type of rain that falls. Perhaps if you are in Malaysia, Singapore or Indonesia when this haze is present, you could make a study of which sort of rain clears the air most effectively. I have an idea but not the evidence to see if the idea is correct, it would be interesting to know what you think.

As I left OJO one afternoon, the rain had started to come down. The rain, or at least the vortices behind the raindrops, cleared some of the haze that had been around earlier. It is a temporary solution to a longstanding problem. A more long lasting solution may be to start (or continue) asking manufacturers of those biscuits you are eating: just how sustainable is the palm oil they are using?

OJO is at No 23, Jalan Telawi 3, KL

* JR Saylor and BK Jones, Physics of Fluids, 17, 031706 (2005)

 

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.

The destructive power behind a spoon

Have you ever sat waiting for someone in a coffee shop, slightly bored? Resisting the urge to check your email or Twitter on the phone (perhaps the battery is dead), you have been stirring your coffee and playing with the vortices that form behind the spoon. Have you wondered why they form? Or played with detaching a vortex from the spoon and getting it to ‘bounce’ off of the side of the cup?

chimney, coffeecupscience, everydayphysics, coffee cup science, vortex

The spiral around this chimney helps to prevent vortex formation in high winds

Such vortices form behind objects in a flow of liquid when either the speed of the liquid, or the size of the object, reaches a critical value. The research about how and why these vortices form is a huge field. From improvements to plane design, through understanding insect flight and even into how wind instruments such as flutes work, understanding these vortices is a challenging topic. It is also useful to know about the behaviour of these vortices when designing chimneys in order to prevent their collapse.

Chimneys are of course stationary, but when they are in high winds, vortices form around the chimney just like the vortices behind the spoon (rather than the spoon moving through the coffee, the wind moves past the chimney). At relatively low speeds, the wind forms small whirlwinds as we see behind the spoon in the coffee. At higher wind speeds, the vortices forming behind the chimney can start to detach and form a pattern known as a Karman vortex sheet. As each vortex detaches from the chimney it subjects the chimney to a small force. Under some conditions and around some objects, this can result in the rather beautiful sounds of the Aeolian harp. Under more extreme conditions, it can result in the collapse of chimneys. The Ferrybridge C cooling towers collapsed in 1965 in high winds as a result of the turbulence around the cooling towers. To minimise the chances of such vortex sheets forming, chimneys are now designed with a spiral pattern (pictured) around them. Far from being an aesthetic feature, this spiral channels the wind so that vortex sheets cannot form behind the chimney.

Something to think about next time you’re waiting for someone in a cafe.