Video highlights from the third and final stop of the JFM China Symposia in Beijing. We were hosted by Tsinghua University with further speakers from Peking University, Xidian University, Beihang University and the Chinese Academy of Sciences.
Ke-Qing Xia describes how water in the ocean travels the entire globe over the course of 1000 years
Colm Caulfield explains how to the shape of a hanging chain is related to turbulence
Charles Meneveau discusses wind energy and its future as the current cheapest form of energy in the US
I’m in China this week documenting the JFM Symposia ‘from fundamentals to applied fluid mechanics’ in the three cities of Shenzhen, Hangzhou and Beijing. Check out the CUP website for daily blog entries as well as some of my favourite video highlights from the scientific talks in Hangzhou below.
Detlef Lohse describes how a good scientist must be patient like a good bird-watcher as demonstrated by his experiments with exploding ice droplets
Hang Ding discusses falling droplets and shows a video of one hitting a mosquito
Quan Zhou presents some amazing visuals of Rayleigh-Taylor turbulence
I’m in China this week documenting the JFM Symposia ‘from fundamentals to applied fluid mechanics’ in the three cities of Shenzhen, Hangzhou and Beijing. I’ll be writing daily blog entries on the CUP website as well as posting some of my favourite video highlights from the scientific talks, starting with the first symposium in Shenzhen.
Detlef Lohse explains the evaporation of a drop of Ouzo (a traditional Greek alcohol)
Colm Caulfield describes the two types of mixing present in the ocean (including a fantastic visualisation of KH instability)
Anderson Shum demonstrates how a fluid can behave as a ‘dancing ribbon’
I was interviewed by Autumn Neagle at Science Oxford about my toga-clad exploits in FameLab and the meaning of my maths-based tattoos… You can read the full article here.
What did you enjoy most about the FameLab experience?
“I’d been aware of FameLab for a few years, but I’d never entered because I thought that you had to talk about your own research – and with mine being lab-based I didn’t think it would translate very well to the live element of the show. But, once I found out that I could talk about anything within the subject of maths then it was a whole different ball game and I just had to give it a go. I think my favourite part was actually coming up with the talks themselves, just sitting down and brainstorming the ideas was such a fun process.”
What did you learn about yourself?
“The main takeaway for me was the importance of keeping to time. I knew beforehand that I was not the best at ‘following the rules’ and I think that both of my FameLab talks really demonstrated that as I never actually managed to get to the end of my talk! This was despite practicing several times beforehand and coming in sometimes up to 30 seconds short of the 3-minute limit – I think once I’m on stage I get carried away and just don’t want to come off!”
What about post-FameLab – how has taking part made a difference?
“Well, I certainly now appreciate the comfort and flexibility of wearing a toga that’s for sure! But on a more serious note, I think the experience of being on stage in front of a live audience really is invaluable when it comes to ‘performing maths’ – and I say ‘performing’ because that’s now how I see it. Before I would be giving a lecture or a talk about maths, but now it’s a full-on choreographed performance, and I think taking part in FameLab really helped me to understand that.
Any tips for future contestants?
“It has to be the time thing doesn’t it! I think everyone knows to practice beforehand to ensure they can get all of the material across in the 3-minutes, but for me that wasn’t enough. I’d suggest doing the actual performance in front of a group of friends or colleagues because – if they’re anything like me – then the adrenaline rush of being on stage changes even the best rehearsed routines and you can only get that from the live audience experience.”
What are you up to now/next?
“I’ve actually just received an award from the University of Oxford for my outreach work which is of course fantastic but also completely unexpected! I really do just love talking to people about maths and getting everyone to love it as much as I do, so the plan is very much to keep Tom Rocks Maths going and to hopefully expand into television… I have a few things in the pipeline so watch this space.”
Are all of your tattoos science inspired and if so what’s next?
“Now that I’ve reached the dizzy heights of 32 tattoos I can’t say that they are all based on science or maths, but it’s definitely still one of the dominant themes. So far I’ve got my favourite equation – Navier-Stokes, my favourite shapes – the Platonic Solids, and my favourite number – e. Next, I’m thinking of something related to the Normal Distribution – it’s such a powerful tool and the symmetry of the equation and the graph is beautiful – but I’ve yet to figure out exactly what that’s going to look like. If anyone has any suggestions though do let me know! @tomrocksmaths on social media – perhaps we can even turn it into a competition: pick Tom’s next tattoo, what do you think?”
In your YouTube video’s #EquationsStripped you reveal the maths behind some of the most important equations in maths, and I noticed that you describe the Navier-Stokes equations as your favourite – why is that and perhaps most importantly can you solve them?
“My favourite equations are the Navier-Stokes equations, which model the flow of every fluid on Earth… Can I solve them? Not a chance! They’re incredibly complicated, which is exactly why they’re a Millennium Problem with a million-dollar prize, and my idea with the video and live talk is to try to peel back the layers of complexity and explain what’s going on in as simple terms as possible.”
Does that mean that anyone can follow your video?
“The early parts yes absolutely, I purposefully start with the easier bits – the history, the applications, and then gradually get more involved with the physical setup of the problem and finally of course the maths of it all… And that’s pretty much where the idea to ‘strip back’ the equations came from – I thought to myself let’s begin simple and then slowly increase the difficulty until the equation is completely exposed. Being the ‘Naked Mathematician’ the next move was pretty obvious… as each layer of the equation is stripped back, I’m also stripping myself back until I’m just in my underwear – so almost completely exposed but not quite!”
Where did the whole idea of ‘stripping’ equations come from?
“I suppose I don’t really see it as ‘stripping’ per se, it’s there for comedic effect and really to show that maths is not the serious, boring, straight-laced subject that unfortunately most people think it is. Stripping for the videos is fine – it’s just me alone with my camera, but then earlier this year I was asked to give a live talk for the Oxford Invariants Society and they were very keen to emphasise that they wanted to see the Naked Mathematician in the flesh – quite literally!”
And how did it go?
“Well, barring some slightly awkward ‘costume changes’ between the layers of the equation – I went outside for the final reveal down to my underwear for example – it was good fun and definitely something I’d be keen to try out again… Perhaps maybe even an Equations Stripped Roadshow. I’m keen to try out anything that helps to improve the image that people have of maths.”
The fourth puzzle in the new feature from Tom Rocks Maths – check out the question below and send your answers to @tomrocksmaths on Twitter, Facebook,Instagram or via the contact form on my website. The answer to the last puzzle can be found here.
Viscosity is a property of a fluid on the molecular scale and is a measure of the strength of the internal friction between fluid particles. What this means in practice is that the thicker and stickier the fluid, the higher its viscosity.
Your task in this week’s puzzle is to order the six fluids below by their viscosity, lowest first. The answer will be posted in 2 weeks along with the next puzzle – good luck!
WARNING: answer below image so scroll slowly to avoid revealing it accidentally.
What do fish and aircraft have in common? Well, water and air are both fluids. And when fish move their tails and bodies from side to side, they push against the surrounding water and leave behind a mini whirlpool or vortex, which contains information about the drag forces experienced by the fish as it moved along. If you can wind back the events that produced the vortex you can work out how it formed in the first place and therefore how much drag the fish felt. This is what Florian Huhn, from the German Aerospace Centre, has managed to do. And because aeroplanes produce very similar vortices in the air, the same technique can be used to develop improved aircraft designs, as he explains…
Florian – We were looking especially at the swirls, at the vortices that the fish typically create. The water slides really close to the skin of the fish, then the water gets some rotation with it and the result of this rotation put into the water when the fish passes are the vortices. Once we have found these vortices behind the fish, what we do is we use the velocity data from the simulations to move this piece of fluid backward in time.
Tom – By tracking the vortex backwards in time Florian and his time are able to see where the fluid making up the vortex originally came from. Interestingly, they found that water from both sides of the fish flows along its body and merges together at the tail where the vortex is then formed. This not only gives us an insight into how fish swim but can also be applied to many other problems.
Florian – At the tip of the wing – take a typical airplane – and we have a huge vortex but its bad for the pilot because if you land at the airport of course there were other planes before you and they all left their wing-tip vortices in the air somewhere. And you don’t want to hit those with your plane because that really shakes the plane.
Tom – Are they what cause the delay between other planes landing?
Florian – I know that there are other causes away form the runway and all these things, but I know its one limiting factor.
Tom – Understanding how these vortices form, that would give us an idea about how to make them smaller or how to make them go away more quickly and therefore leading to potentially more efficient airports.
Florian – Yeah that would be a good thing if that was possible.
You can listen to the full interview for the Naked Scientists here.
If you’ve been following so far, we know why it’s useful to know where river water goes when it enters the ocean, why we can build a model of the situation in the lab, what the most important variables in the problem are and what the experimental setup looks like. I suppose you’re probably itching to know what actually happens when we open the floodgates and release the freshwater from the model river into the spinning saltwater tank that is our ocean. In which case, let me point you in the direction of the video below.
It probably doesn’t make much sense without some added explanation so here goes… This is a false colour image of an experiment viewed from above. The freshwater from the river is dyed red with food colouring which means that we can convert the colour intensity into a depth measurement. The more intense the red food colouring, i.e. the more of it there is, the deeper the current must be. The scale starts with black to represent no current (as is the case for the saltwater ocean), then increases with the current depth through red, yellow, green and finally blue for the deepest parts of the current.
If you look at the very beginning of the video you will see that as the river water is released from the source it travels forwards and then is immediately forced to turn to the right. This is due to the Coriolis force arising from the rotating tank (see article 3). As it turns back on itself it eventually collides with the tank wall where it then propagates as an anticlockwise boundary current. The anticlockwise direction is set by the direction of the rotation of the tank (also anticlockwise). The boundary current continues to travel around the edge of the tank, eventually filling the whole perimeter and returning back to the source by the end of the experiment.
As well as the propagating current, a second persistent feature can also be seen in the video: the outflow vortex. This is the large whirlpool-like feature that forms next to the source of freshwater. As the initial current turns to the right and back on itself to collide with the tank wall, the flow divides. One part moves anticlockwise and forms the boundary current that moves around the tank edge, whilst the other part continues in a clockwise direction and re-joins the initial jet of freshwater from the source. The result of this is to form a whirlpool next to the source which grows in size as the experiment progresses. Both features are labelled in the image below so that you can recognise them in the video.
Now that we’ve identified the two main features of the flow – the boundary current and the outflow vortex – the next step is to try to understand them in more detail. This is exactly what the first two sections of my thesis are about, beginning with the boundary current. For example, we might want to know how fast the current moves around the tank, how its depth changes as it does so and whether or not it has a constant width. For the outflow vortex, we are interested in similar properties, such as how deep the vortex is at its centre, what shape it forms at the surface and how it grows in size during an experiment. By looking at the experimental video you can begin to get a grasp on some of these questions, but to really understand them in detail you need two key ingredients: measurements and a mathematical theory.
In my thesis, I begin by discussing the mathematical models used to describe the flow and then compare this theory with the data collected from the experiments, with the hope that they will agree. The theory can only be correct if the measurements support it – which is pretty much my thesis in a nutshell. Do the predictions from the mathematical equations agree with the observations in the experiments? If we’re going to compare the two, we’d better start by forming some equations, which brings me nicely onto the next topic…
You can read the rest of the articles explaining my PhD thesis here.
Yes, you read that correctly. I really did spend a good chunk of the 4 years of my PhD spinning a giant fish tank. This isn’t just any old spinning fish tank though, as you may have guessed, it was specially designed to represent the real-world scenario of a river discharging into the ocean, but on a manageable scale in the lab. So what does such a setup look like? Well, below is a diagram of the tank, taken from my thesis (please excuse my crude drawing in Microsoft Word – it’s harder than you might think).
Let’s start with the tank itself. It’s made from acrylic (basically plastic) and is 1m x 1m with a depth of around 60cm, though it was only filled to 40cm with salt water. As you can see in the diagram, the tank is actually divided up into two sections by an internal barrier. The reason for this was to allow the source structure to be attached to the outside of the tank – I wasn’t allowed to drill holes into the actual tank despite all of my protests… It had to be attached in this way to allow the freshwater from the model river to flow into the main tank which contained the salt water in the model ocean.
The freshwater is stored in the reservoir (a plastic box) attached to the top of the metal structure surrounding the whole setup. This is to provide stability once the whole thing starts rotating, and also I assume to prevent things from flying off and hitting me. The river water flows out of the reservoir down a pipe and enters into the source structure. The amount of water released is controlled by a flow meter and an electronic switch. Once in the source structure, the water begins to accumulate until it resembles a flowing river and then it is released into the ocean (saltwater ambient). The water continues to flow throughout an experiment, much like a real river.
This all happens of course whilst the whole thing is spinning on a giant turntable. Turntable is an appropriate name because it basically just looks like a giant set of DJ decks (with only one disc a metre across). The speed is controlled by a computer and it can go pretty fast, trust me. Before the electronic switch was installed to start and stop the flow of freshwater from the reservoir, I used to have to climb up a ladder and flick the switch manually as it went spinning past. This was fine for the low speeds, but once things started speeding up I couldn’t flick the switch without knocking the entire structure which disturbed all of the measurements I had made. The only answer was to basically climb onto the structure myself and hang off the side whilst it went spinning round at high speed. If anyone ever saw me doing that I’m pretty sure I would have been thrown out of the lab, but hey when science calls ‘you gotta do what you gotta do’.
Now the source structure (shown in the diagram and picture above) was quite the piece of engineering… by which I mean an absolute nightmare to design. Most of the first year of my PhD was spent trying out different designs until finally we found one that gave a discharge that looked like an actual river. If the stream comes out too strong then it looks like a jet – think about squirting a hose in your garden. If it’s not strong enough then it’s just a point source – like a sponge slowly leaking out water. Neither of which represent a river. The trick was to feed the pipe carrying the freshwater into an l-shaped box filled with foam. The combination of the shape, plus the presence of the foam, meant that the box would become sufficiently filled with water before any of it exited into the ocean. It was key that the box filled up above the depth of the opening into the saltwater, so that the depth of the water when it left the source was known (and equal to the depth of the opening). We need to know this initial depth because the depth of the freshwater as it enters into the ocean is incredibly important in determining the properties of the current that forms, but that ladies and gentleman is another story for another day.
All of the articles explaining my PhD thesis can be found here.
How hairy are you? Whether you have hairs growing in all kinds of weird and wonderful places or prefer the smooth and supple look of a Greek statue, I can tell you now that you are hairier than you might think… Live interview with BBC Radio Cambridgeshire.
