turbulence

A Weight-y issue

Waves on the surface of of a coffee. But what do we know about gravity driven waves rather than surface tension driven ones?

Ever swung a bucket of coffee round in circles swooping down towards the floor and then over your head? Why would you, you may well ask? Well, the answer may surprise you. It’s all about turbulence.

We have probably all come across turbulence, perhaps by watching how milk is added to a black coffee or seeing the steam interact with the air as it evaporates off a hot mug of tea. But it turns out that there is a lot that we do not yet understand about turbulence and this is where the bucket of coffee comes in.

Waves on the surface of a coffee can be dominated by gravity or capillary effects. Capillary waves are short wavelength (higher frequency) waves that are forced into oscillation by the effects of the surface tension of the liquid pulling the surface of the coffee back into shape once its been distorted. Gravity waves are longer wavelength (lower frequency) waves where the disturbed surface of the coffee is pulled back into shape by gravitational effects rather than surface tension effects.

Benjamin Franklin famously stilled the (capillary) waves on one of Clapham Common’s ponds by adding just a teaspoon of oil to it.

The frequency at which there is a crossover from gravity dominated waves to capillary dominated waves is dependent on both the density and surface tension of the liquid as well as the strength of the gravitational acceleration experienced by the mug of coffee. (We’re getting to the bucket). On Earth, the gravitational acceleration is 9.8m/s, the ratio of a liquid’s density to surface tension is quite similar for many liquids and so the transition frequency between these two regimes is generally in the region of 10Hz.

What this means is that if you wanted to study the turbulence affecting one type of wave only you could measure at higher frequency (and so measure capillary waves) or measure the turbulence in a liquid in lower gravity eg. on the International Space Station (so that capillary waves dominate at lower frequencies too). But both of these types of measurement don’t give any insight into what’s happening to turbulent waves sustained by gravity, such as Rossby waves which travel the whole circumference of planets with atmospheres and affect the weather in different parts of the globe.

So how could you study turbulence in the gravity dominated surface waves of water? It goes back to the bucket mentioned earlier. By putting a freely moving bucket (the authors called it a ‘gondola’) at the end of the arm of a centrifuge of 8 m diameter, the authors of a recent paper created an effective gravitational force on a liquid of up to 20x the value of the Earth’s gravitational acceleration. It’s sort of like the bucket of coffee being whirled around in a circle apart from a lot bigger and capable of moving at up to 67 rpm! This meant that they could measure the effects of turbulence on gravity driven waves up to about 100Hz allowing them a large frequency range over which to compare their results to theoretical predictions.

Coffee, Van Gogh
Turbulence comes in many forms: What do you see in your coffee cup?

And when they did so, they proved one nagging problem for theoreticians studying turbulence: the size of the ‘container’ becomes important, something that models had previously neglected. For the 23cm wide bucket of distilled water used by the authors, this may be something that we can easily visualise but the research has consequences for how we understand the Rossby waves that circle our planet as well as the large wavelength waves in oceans. Slightly more connected with coffee (or at least doughnuts), the results are also important for understanding turbulence in plasma waves in tokamaks.

You may have better things to do over the holidays than swirl a bucket of coffee round and round while watching for the waves on top of it, but if you are stuck for something to do…

Hundred House: Wonder what they are?

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.

Hundred House coffee

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.

Drip coffee

The universe is in a cup of coffee. But how many connections to different bits of physics can you find in the time it takes you to prepare a V60? We explore some of those links below while considering brewing a pour-over, what more do you see in your brew?

1. The Coffee Grinder:

coffee at VCR Bangsar

Preparing a V60 pour over coffee. How many connections can you find?

The beans pile on top of each other in the hopper. As the beans are ground, the bean pile shrinks along slipping layers. Immediately reminiscent of avalanches and landslides, understanding how granular materials (rocks & coffee beans) flow over each other is important for geology and safety. Meanwhile, the grinding itself produces a mound of coffee of slightly varying grain size. Shaking it would produce the brazil nut effect, which you can see on you breakfast table but is also important to understand the dynamics of earthquakes.

Staying at the grinding stage, if you weigh your coffee according to a brew guide, it is interesting to note that the kilogram is the one remaining fundamental unit that is measured with reference to a physical object.

2. Rinsing the filter paper:

V60 chromatography chemistry kitchen

A few hours after brewing pour over, a dark rim of dissolved coffee can be seen at the top of the filter paper. Chromatography in action.

While rinsing the filter we see the process of chromatography starting. Now critical for analytical chemistry (such as establishing each of the components of a medicine), this technique started with watching solutes ascend a filter paper in a solvent.

Filtration also has its connections. The recent discovery of a Roman-era stone sarcophagus in the Borough area of London involved filtering the excavated soil found within the sarcophagus to ensure that nothing was lost during excavation. On the other hand, using the filtered product enabled a recent study to concentrate coffee dissolved in chloroform in order to detect small amounts of rogue robusta in coffee products sold as 100% arabica.

3. Bloom:

bloom on a v60

From coffee to the atmosphere. There’s physics in that filter coffee.

A drop falling on a granular bed (rain on sand, water on ground coffee) causes different shaped craters depending on the speed of the drop and the compactness of the granular bed. A lovely piece of physics and of relevance to impact craters and the pharmaceuticals industry. But it is the bloom that we watch for when starting to brew the coffee. That point where the grinds seem to expand and bubble with a fantastic release of aroma. It is thought that the earth’s early atmosphere (and the atmosphere around other worlds) could have been helped to form by similar processes of outgassing from rocks in the interior of the earth. The carbon cycle also involves the outgassing of carbon dioxide from mid-ocean ridges and the volcanoes on the earth.

As the water falls and the aroma rises, we’re reminded too of petrichor, the smell of rain. How we detect smell is a whole other section of physics. Petrichor is composed of aerosols released when the rain droplet hits the ground. Similar aerosols are produced when rain impacts seawater and produces a splash. These aerosols have been linked to cloud formation. Without aerosols we would have significantly fewer clouds.

4. Percolation:

A close up of some milk rings formed when dripping milk into water. Similar vortex rings will be produced every time you make a pour over coffee.

Percolation is (almost) everywhere. From the way that water filters through coffee grounds to make our coffee to the way electricity is conducted and even to how diseases are transmitted. A mathematically very interesting phenomenon with links to areas we’d never first consider such as modelling the movements of the stock exchange and understanding the beauty of a fractal such as a romanesco broccoli.

But then there’s more. The way water filters through coffee is similar to the way that rain flows through the soil or we obtain water through aquifers. Known as Darcy’s law, there are extensive links to geology.

Nor is it just geology and earth based science that is linked to this part of our coffee making. The drips falling into the pot of coffee are forming vortex rings behind them. Much like smoke rings, they can be found all around us, from volcanic eruptions, through to supernovae explosions and even in dolphin play.

5. In the mug:

Rayleigh Benard cells in clouds

Convection cells in the clouds. Found on a somewhat smaller scale in your coffee.
Image shows clouds above the Pacific. Image NASA image by Jeff Schmaltz, LANCE/EOSDIS Rapid Response

Yet it is when it gets to the mug that we can really spend time contemplating our coffee. The turbulence produced by the hot coffee in a cool mug prompts the question: why does stirring your coffee cool it down but stirring the solar wind heats it up?

The convection cells in the cooling coffee are seen in the clouds of “mackerel” skies and in the rock structure of other planets. The steam informs us of cloud formation while the condensation on the side of the cup is suggestive of the formation of dew and therefore, through a scientific observation over 200 years ago, to the greenhouse effect. The coffee cools according to the same physics as any other cooling body, including the universe itself. Which is one reason that Lord Kelvin could not believe that the earth was old enough for Darwin’s theory of evolution to have occurred. (Kelvin was working before it was known that the Sun was heated by nuclear fusion. Working on the basis of the physics he knew, he calculated how long the Sun would take to cool down for alternative mechanisms of heating the Sun. Eventually he concluded that the Sun was too young for the millions of years required for Darwin’s theory to be correct. It was the basis of a public spat between these two prominent scientists and a major challenge to Darwin’s theory at the time).

 

Of course there is much more. Many other links that take your coffee to the fundamental physics describing our world and our universe. Which ones have you pondered while you have dwelt on your brew?

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.

 

Reflections on physics and coffee

BeanThinking started as a way of slowing down and appreciating connections, often between a coffee and the physics of the wider world but also in terms of what can be noticed in any café. Perhaps, for this first post of 2017, it’s worth spending five minutes looking at your coffee while you drink it to see what you notice. Here are a few coffee connections that occurred to me recently:

reflections, surface tension

Reflections on a coffee.

Parallel lines and surface reflection: The parallel lines on the ceiling of a café were reflected in a long black. Surface tension effects on the coffee meant that the reflections were curved and not at all parallel. A piece of dust on the surface of the coffee was revealed in the reflection by the curved reflections of the ceiling. Astronomers can use similar effects (where images of a star appear in a different location to that expected) to infer the presence of dark objects between distant stars and their telescope. This gravitational lensing can be used to detect quasars or clusters of galaxies.

 

 

 

layering of coffee long black

Layers of coffee

Layering of crema as the coffee is consumed: The coffee stain effect and this layering of the crema suggests a connection between a coffee cup and geology. It used to be my habit to take a mug of tea with me when I taught small groups of undergraduates. In the course of one of these tutorials, a student (who had been observing similar layering in my tea mug) said, “You drink your tea faster when it is cooler than when it is hot”. Full marks for observation, but not sure what it said about his attention during my tutorials! Similar observations though can help geologists estimate the age of different fossils.

 

interference patterns on coffee

Bubbles in coffee

Bubble reflections: An old one but the interference patterns caused by bubbles on the surface of the coffee are full of fascinating physics. The fact that the bubbles are at the side of the cup and seem to be grouped into clusters of bubbles may also be connected with surface tension effects (although there is a piece of weather lore that connects the position of the bubbles to the weather. If anyone ever does any experiments to investigate this particular lore, I’d love to hear about them).

 

 

Coffee, Van Gogh

Art in a coffee cup

Van Gogh’s Starry Night: The effects of vortices and turbulence caused the crema of a black coffee to swirl into patterns reminiscent of this famous painting by Van Gogh. As a result of posting this image on Twitter, @imthursty sent me a link to this preprint of a paper submitted to the arxiv: the connections between Van Gogh’s work and turbulence. A great piece of coffee combining with art and science.

 

So many connections can be made between tea, coffee and science and the wider world, I’d love to see the connections that other people make. So, if you see some interesting physics, science or connections in your coffee cup, why not email me, or contact me via FB or Twitter.

 

On nuclear fusion and making tea

tea bag, tea cup, diffusion, turbulence

How not to prepare tea

Although largely a coffee drinker, occasionally I will order tea in a café. When I do so, one of my pet hates is being served a cup of hot water with an individually wrapped tea bag sitting on the saucer beside it. Quite apart from the unnecessary environmental cost of individually wrapping tea bags, there is the problem with the resultant cup of tea. Hot water poured onto tea (preferably in a pot) allows the tea to infuse by a mixture of turbulence, convection and diffusion as the hot water swirls around carrying the tea with it. A tea bag placed into hot water on the other hand relies on infusion by convection and diffusion only and so takes a lot longer to brew. Oddly enough, there is at this moment, a major scientific project being built in the south-west of France that has the opposite problem. The aim of the project is to generate electricity by nuclear fusion in extremely hot clouds of gas that are confined into the shape of a doughnut. To achieve this, they must reduce the turbulence within their doughnuts. Unlike the tea, nuclear fusion seems to require diffusion and convection to prevail over turbulence.

Supplying the growing energy demands of the planet is a major problem for us all. How can we simultaneously generate the electricity that we want while limiting our carbon dioxide emissions to levels that will cause minimal damage to our planet? Renewable energy is part of the solution, some have argued that nuclear fission could be another part of the solution (all of our current “nuclear” power plants run by nuclear fission). The “ITER” project in the Provence-Alpes-Côtes d’Azur region of France aims to demonstrate the feasibility of nuclear fusion to supply our energy needs instead.

Sun, heat, nuclear fusion

The Sun is powered by nuclear fusion. Could we generate electricity on Earth with a fusion generator? Image © NSO/AURA/NSF

Unlike nuclear fission which works by exploiting the decay of radioactive elements, nuclear fusion ‘fuses’ elements together to produce energy. Gazing up at the sky you can see thousands of nuclear fusion generators: Each star (including our Sun) produces light and heat, by nuclear fusion. First the stars fuse hydrogen into helium (as our Sun does now), then, as the star ages, the heavier elements combine until finally iron is formed in the core of the dying star. All the elements found on our planet and elsewhere in space have, ultimately been formed in the core of a star (or in reactions as the star dies in a final explosion). Every atom in us has been formed by such reactions in stars and so it is very true to say “from dust you came and to dust you will return”, the dust in question being star dust. If we can exploit it on Earth, nuclear fusion offers a method of providing energy with no long term radioactive by-products and limited carbon dioxide emissions. It is a possible, but very long term, route out of our quandary about energy generation.

doughnut tokamak

A photo to demonstrate “doughnut shaped” was probably unnecessary, but it did provide a good excuse for an unhealthy breakfast.

So why can’t we start using it immediately? A clue comes from the fact that the nuclear fusion reactors that we know of (stars) are very hot and relatively dense. It is not easy to smash two hydrogen atoms together such that they fuse, it requires them to have a lot of energy (ie. be very hot) and be quite close together. To build a nuclear fusion reactor requires us to heat a gas until it becomes a ‘plasma’ which means heating the gas to temperatures of around 150 million ºC. At this temperature we need to confine the plasma with very high magnetic fields so that it does not hit the walls of its container and it turns out that the best way to do this is to manipulate the plasma into a ring doughnut shape. This doughnut confinement, known as a ‘Tokamak’ has become the standard way of confining the plasma. At the moment, we cannot keep the plasmas hot enough for long enough (the current record is 6min30 sec confinement) for fusion to generate more energy than is required to form the plasma in the first place. One of the things limiting the lifetime of the plasma is the fact that the plasma cools down and one of the things that cools the plasma down is the turbulence in the plasma carrying the heat energy from the centre to the edge of the doughnut. Increasing the time it takes for the heat to escape from the centre of the doughnut to the outer edge is one of the challenges facing the ITER team. Just as with the pot of tea, were the cooling by diffusion and convection only, the plasma would take a lot longer to cool down. Understanding the turbulence inside the plasma is one of the challenges facing the team at ITER.

Our method of making tea can tell us a lot, not just about the problems for nuclear fusion generators, but also about diffusion and turbulence generally. It is worth pondering that brew a little more deeply next time you make your pot.