The idea was to have one student slowly and steadily turn a balloon around its axis to mirror the Earth’s spin, and another one drawing on the balloon with a sharpie.
The context was a class where many students didn’t have any physics background, and we wanted to understand atmospheric circulation, and why trade winds don’t blow straight north-south (or south-north on the Southern Hemisphere). And I still think that this demonstration kind of works for this specific purpose.
The problem though: If you have a balloon and a sharpie, drawing one single trajectory and going “oh, I got it! So that is why the trade winds have a velocity component to the west!” (like I naively had imagined) is NOT what happens.
What happens instead is that students will draw tons of trajectories. And not only the ones that, even in this overly simplified system, show what I wanted them to see. Nope. They will also draw following a constant latitude, and then be confused as to why Coriolis force doesn’t seem to be acting. Or draw south-to-north on the Northern Hemisphere, and be confused why things are being deflected to the left. (And don’t get me wrong: this is good! They should start exploring. And they should be finding the limitations of demonstrations!)
Now. All of those issues that come up are things you can talk about and that can be explained. But I’m wondering whether this demo didn’t cause more harm than good, since the impression that might have stuck in the end is that Coriolis deflection only works under very specific circumstances, but most of the time it does not.
I’ve promised a long time ago to write a post on vorticity (Hallo Geli! :-)). So here it comes!
Vorticity is one of the concepts in oceanography that is often taught via its mathematical formulation, and which is therefore pretty difficult to grasp for those of us with less mathematical training. But it’s also a concept that you can have an intuitive grasp of, and I’ll try to show you how.
The easiest way to imagine what “vorticity” is, is to think of a little float in a flow. In a vorticity-free flow, that little float will always keep its orientation (see below). However if there is a shear in the flow, i.e. the flow field carries vorticity, it will start to turn.
Flow fields without vorticity (top) and with vorticity (bottom).
This even holds true for vortices: There are vorticity-free vortices as well as those that carry vorticity (as the name “vortex” would suggest).
Vorticity-laden and vorticity-free vortex. In the left plot, angular velocity of all particles is the same. In the right plot, angular velocity increases the closer you get to the center of the vortex.
If you think back to the discussion on a tank spinning up to reach solid body rotation, you might recognize that only the vortex with vorticity moves like a solid body. To me, a solid body is basically a fluid with so much friction in it, that molecules cannot change their position relative to each other. And that serves as my memory hook for one condition for the formation of vorticity – the flows must have viscous forces and friction in it.
This sounds very theoretical, but there are a lot of instances where you can spot vorticity in real life, for example twigs caught up twirling in eddies at the edge of streams are clearly moving in a vorticity-filled environment. Below, for example, the stream is clearly not vorticity-free.
In 2012, I happened to be at an ESWN workshop in Madison, WI, when, during one of the breaks, one of the participants mentioned that it might be possible to get into the historic Washburn Observatory to watch Venus’ transit. Of course I had to go!
We stood in a very long queue under overcast skies for a very long time. We slowly approached the observatory, all the while watching people ahead of us go in and leave disappointed – due to the clouds all they could see when inside were live streams from other observatories. Still, there was a lot of people still in front of us. We had dinner plans and we knew that we would have to be very lucky to make it in and out of the observatory and to the restaurant on time. Half our group left in order to not be late at dinner. The rest of us stayed, still hoping.
And then we were finally inside! The observatory itself was impressive enough, but then right when we were inside, the sun broke through the clouds. All the astronomers who had been there for hours and not seen anything got super excited, as did, of course, the rest of us. Having waited all that time, knowing that we would very likely not be able to see a thing, and then coming in the moment the skies were opening up? Unbelievable. I still get excited thinking about this 3 years later.
Projection of the transit of Venus, observed at the Washburn Observatory in Madison, WI, on June 6th, 2012
The projection on the screen shown above only shows a small area of the sun, zoomed in on Venus. You can imagine the size of the projected sun by looking at the curvature on the upper left: That’s the real rim of the Sun, the rest of the circle is just due to the telescope. Watch a (very shaky) movie to get an impression of what it looked like:
So why am I telling you about this today? Because on Friday, there’ll be a solar eclipse and you should totally make sure to watch it! It won’t be a total eclipse where I’m at, but still, I’m looking forward to it! :-)
That was quite a teaser on Wednesday, wasn’t it? I said I had the solution to any hydrodynamics problem you might want to illustrate. So here we go:
I recently had the privilege to be given a private demonstration of the “Elbe” flow solver, which is being developed at Hamburg University of Technology. Elbe allows for near real time simulation of non-linear flows, and can be run in an interactive mode.
Look at the Karman vortex street below (their movie, not mine!) – doesn’t it remind you of the vortex street on a plate?
Now. How can we use such an awesome tool in teaching?
There are a couple of scenarios I could imagine.
1) Re-create flow fields.
This is mainly to help students get “a feel” for how a flow reacts to obstacles.
Provide students with a picture of a current field and ask them to recreate it as closely as possible. This is not about creating the exact same field, but about recognizing characteristics of a flow field and what might have caused them. Examples could include a Karman vortex street or a Kelvin Helmholtz instability.
Possible sketches of A) Karman vortex street and B) Kelvin Helmholtz instabilities as examples for flow fields that students could be asked to recreate using Elbe.
In the above examples, students need to recognize, for example, that while a vortex street can be formed in a single-phase flow, a Kelvin Helmholtz instability typically forms on the boundary of layers of different densities in a shear flow (but could also form in a single continuous fluid), and recreate this in the model.
2) Visualize hydrodynamic concepts.
Here we would name a concept and ask students to set up a flow field that visualizes it. They might submit an annotated snapshot, for example. Possible examples are
– difference between stream lines, path lines and streak lines
– hydrodynamic paradox
– dead water
Hydrodynamic paradox. Moored ships are pulled towards each other because the flow is faster between them than upstream of them. (yes, the current in the picture is coming from the left, yet the ships are drawn as if the current was coming from the right. Shit happens.)
3) Test engineering applications.
Here we could imagine giving students different shapes and asking them to find their optimal position in a flow field, for example the pitch of a given wing profile to maximize lift, or the relative placement of a ship’s hull and a submerged ball for maximum canceling of waves.
4) Understanding of limitations of model and/or theory.
In some cases, students might be able to find optimal solutions from theory. In those cases it might be interesting to have them model those solutions and compare results with theoretical values. Can they come up with reasons why the modeled answers are likely different from the theoretical ones?
So far, so good. But how do we make sure that students don’t spend an insane amount of time fiddling with the nitty gritty details of the model, but focus on understanding hydrodynamics?
Combination of individual and group work
One idea might be to have students work individually on defining the important parameters (for example one- versus two-phase flow, obstacle at fixed position or moving, shape of obstacle) and then have them work in groups on putting those parameters into the model. If we were to grade this, we could give individual grades for individual answers to the first part, and then add a group grade in form of bonus points for a good model.
Model as a tool rather than the ultimate goal
Another idea would be to let them use the model as a tool rather than as the final application. As in students could be allowed to play with the model in order to, for example, figure out an approximate shape of an obstacle, and then they sketch their solution and annotate (e.g. “The longer X, the less turbulent region Y”). This would let them experience and explore hydrodynamics.
Whether or not a concept has been visualized well can be judged by the instructor, or it can become a learning activity in itself, for example as peer-review. Figuring out whether a visualization is correct or how it could be improved supports a deeper understanding of the concept as well as all kinds of interpersonal skills. In order to keep this interesting for students, several concepts could be visualized by different students and it can be made sure that the one students work on themselves is not the same as the one they will review later.
I am really excited to really start developing ideas on how to use this model in teaching. How would you use it?
I am usually very motivated to write posts for this blog, but for some reason today I’m not. I have interesting posts scheduled for next week, don’t you worry, but today was supposed to be a review of some literature on teaching and learning, and I just cannot be bothered. So instead you’ll get this:
Yep. I like playing with water!
As you’ll see in the movie below: All it takes to make a crappy mood go away are about two exploding water balloons and a camera that can do slow motion! :-)
Today, I am very excited to share with you a guest post by Dr Richard Kirby, who recently produced an amazingly beautiful film on plankton (linked at the very bottom of this post, a MUST SEE!)
Dr Richard Kirby – the Plankton Pundit @planktonpundit, tells us why it is important not to overlook the plankton:
Plankton are the ocean’s drifters. The plankton is an amazing diversity of life forms that get their collective name from the Greek word Planktos, which means wanderer or drifter, since what unites all these creatures is that none can swim against a flow of water; they all drift at the mercy of the ocean currents. The plankton are incredibly important. They bring life to our seas through the plankton food web and the marine food chain it supports, and they play a major role in the Earth’s carbon cycle to influence our climate and weather. While the majority of the plankton are microscopic and so hidden from view, they also include the largest invertebrates on Earth – the jellyfish.
The plankton live mainly at the sea’s sunlit surface. Here, the microscopic phytoplankton begin the plankton food web underpinning life in the sea. These plant-like cells photosynthesise, using the energy in sunlight to combine carbon dioxide with water to create sugar and oxygen. In this way the phytoplankton begin the marine food chain. The phytoplankton are grazed by the herbivorous zooplankton (animal plankton) that in turn are eaten by other carnivorous zooplankton to create the plankton food web that supports life in the sea. Without the plankton the oceans would be a barren wilderness, there would be no fish, sharks or whales, no crabs, mussels, starfish or worms on the seabed or upon the seashore (many bottom-dwelling creatures begin their life in the plankton). Without the marine food chain there would also be no seabirds in the sky, and no penguins or polar bears on the ice.
The plankton do much more than just support the marine food web, however. As mentioned above, the plankton also play a central role in the global carbon cycle. You can find out how they do this by watching Richard’s remarkable Ocean Drifters film (see below) that is narrated by Sir David Attenborough. This short film not only reveals the incredible beauty of the plankton and their amazing and intriguing adaptations to life at the surface of the sea, but it describes how these tiny creatures influence our climate to have a global impact far greater than their size would suggest. The film also importantly, reveals how we are currently influencing the plankton with ramifications for the marine food chain and the ecology of the seas.
To find out more, visit Richard’s website http://www.planktonpundit.org.
Dr Richard Kirby is also the leader of the global Secchi Disk project www.secchidisk.org, the world-wide citizen science project engaging sailors in a study of the phytoplankton.
For anyone interested: a couple of years ago we started working on a collection of translations of oceanography terms in English, Norwegian and German. If you find it useful, please feel free to use and share it!
This dictionary is definitely a work in progress. If you find typos, better translations, if you are missing terms – give me a shout and I am happy to fix it. If you think this is super useful and would like to help develop it further (or just add to it whenever you just looked up a new term anyway and want to write it down somewhere you won’t lose it): I’d love to have you on board! Let me know and I’ll give you editing permissions on the document.
Also if you are a meteorologist, paleontologist, climate scientist or someone from any other related discipline and want to expand the scope to include your speciality, or if you want to add a new language – you are very welcome to join us!
Thanks to Eli, Sindre and Kjetil for helping me getting this started!
An example of one topic at different levels of difficulty.
Designing exercises at just the right level of difficulty is a pretty difficult task. On the one hand, we would like students to do a lot of thinking themselves, and sometimes even choose the methods they use to solve the questions. On the other hand, we often want them to choose the right methods, and we want to give them enough guidance to be able to actually come to a good answer in the end.
For a project I am currently involved in, I recently drew up a sketch of how a specific task could be solved at different levels of difficulty.
The topic this exercise is on “spotting the key variables using Shainin’s variables search design”, and my sketch is based on Antony’s (1999) paper. In a nutshell, the idea is that paper helicopters (maple-seed style, see image below) have many variables that influence their flight time (for example wing length, body width, number of paper clips on them, …) and a specific method (“Shainin’s variables search design”) is used to determine which variables are the most important ones.
In the image below, you’ll find the original steps from the Antony (1999) paper in the left column. In the second column, these steps are recreated in a very closely-guided exercise. In the third column, the teaching scenario becomes less strict, (and even less strict if you omit the part in the brackets), and in the right column the whole task is designed as a problem-based scenario.
Flight time of a helicopter investigated at different levels of difficulty
Clearly, difficulty increases from left to right. Typically, though, motivation of students tasked with similar exercises also increases from left to right.
So which of these scenarios should we choose, and why?
Of course, there is not one clear answer. It depends on the learning outcomes (classified, for example, by Bloom or in the SOLO framework) you have decided on for your course.
If you choose one of the options further to the left, you are providing a good structure for students to work in. It is very clear what steps they are to take in which order, and what answer is expected of them. They will know whether they are fulfilling your expectations at all times.
The further towards the right you choose your approach, the more is expected from the students. Now they will need to decide themselves which methods to use, what steps to take, whether what they have done is enough to answer the question conclusively. Having the freedom to choose things is motivating for students, however only as long as the task is still solvable. You might need to provide more guidance occasionally or point out different ways they could take to come to the next step.
The reason I am writing this post is that I often see a disconnect between the standards instructors claim to have and the kind of exercises they let their students do*. If one of your learning outcomes is that students be able to select appropriate methods to solve a problem, then choosing the leftmost option is not giving your students the chance to develop that skill, because you are making all the choices for them. You could, of course, still include questions at each junction, firstly pointing out that there IS a junction (which might not be obvious to students who might be following the instructions cook-book style), and secondly asking for alternative choices to the one you made when designing the exercise, or for arguments for/against that choice. But what I see is that instructors have students do exercises similarly to the one in the left column, probably even have them write exams in that style, yet expect them to be able to write master’s theses where they are to choose methods themselves. This post is my attempt to explain why that probably won’t work.
* if you recognize the picture above because we recently talked about it during a consultation, and are now wondering whether I’m talking about you – no, I’m not! :-)
We (or I, at least) hardly ever see empty ships. For one, it doesn’t make a whole lot of sense economically to have ships driving around empty, but also the stability of ships is maximal at a certain position of the ship in the water. Therefore people will always try to drive a ship that is neither loaded too full or not enough. But don’t empty ships just look funny?
Ships in the port of Gothenburg
Especially when you see sister ships next to each other where one is full and the other is empty (below).