# Parabolic surface shape of a tank of water in solid body rotation

One of the first exercises Torge and I plan on doing with the students in our “dry theory to juicy reality” project is to bring a water-filled tank to solid body rotation and measure rotation, surface height at the center of the tank and the sides, as well as water depth before rotation, and then have them put those together according to theory.

Setup of the experiment as we did it using a glass vase my mom gave me as tank (diameter 24.5 cm). The non-rotating water depth was 9.2 cm. Once we rotated the tank with 10 rotations per 8.6 seconds, the maximum water level at the outside edge of the tank was approximately 10.8 cm, and the minimum 7.9 cm.

Seeing how difficult it is to “measure” the surface heights while the tank is rotating (we chose to draw circles on the outside of the tank at the heights where we thought the water levels were, in order to measure them later on a non-rotating tank), we were quite pleased with those results once we plugged them into the equations.

Calculating the resting water level as arithmetic mean between the rotating maximum value at the rim and the minimum value in the center, we are only off by 0.1 cm, so not too shabby!

And calculating the height difference between resting water level and rotating maximum level from the tangential velocity and radius of the tank, we are only off by 0.4 cm. So all in all, that’s working well!

Btw, below you see the resting water level and above the mark for the rotating maximum value. Quite impressive difference, isn’t it?

Anyway, looking at rotational surfaces and volumes and stuff this way is a lot more fun than doing it the dry theoretical way only! At least that’s what I think ;-)

# Rotating vs non-rotating turbulence — now with movie!

Lots of demonstrations being prepared for Torge’s and my “dry theory to juicy reality” project. Shown here today: rotating vs non-rotating turbulence. Because the only way to really appreciate how amazing rotating flows are is to compare them with non-rotating ones. And not everybody does have a clear idea what non-rotating flows would even look like.

So here we are dropping dye into a non-rotating tank. Top view shows it forming tons of small eddies and spreading to the sides.

Side view shows that most of the dye sank to the bottom of the tank and is spreading there, showing 3-dimensional turbulence.

Now, for comparison, the rotating case!

Top view shows one single, clean eddy.

And side view shows that the structure is coherent all the way from surface to bottom. Now doesn’t this look really fascinatingly different from the non-rotating case?

To show the difference even more clearly, check out the movie below. Speed of both movies is the same!

# Spinning dye curtain — when a tank full of water has not reached solid body rotation yet

With all the rotating tank experiments I’ve been showing lately, one thing that comes up over and over again is the issue of solid body rotation.

On our DIYnamics-inspired turntable for our “dry theory to juicy reality” project, Torge and I came up with a fun way to illustrate the importance of full body rotation in tank experiments, again inspired by the DIYnamics team, this time their youtube channel.

For the spinning dye curtain experiment, we start up the rotating table, and then pretty much immediately add in some dye. Below, you see what happens when you add in the dye too late (we waited for 2 minutes here before we added it): The water is so much in solid body rotation already, that we only form columns and 2D flow.

But if we add in the dye right away after starting up the tank, we form these spirals where the water further away from the center is spinning faster than the water right at the center, thus distorting the dye patches into long, thin filaments (Btw, I’ve shown something similar in my “eddies in a jar” experiment earlier, where instead of starting up a turntable I just stirred water in a cylindrical tank).

But as the tank continues to spin up, the eddies eventually stop spinning and the tank turns into solid body rotation. If new dye is added now, only columns form, but they stay intact as if they were, indeed, solid bodies.

But seeing the behaviour of a fluid change within half a minute or so is really impressive and something we definitely want to do in class, too!

# Baroclinic instabilities / Hadley cell circulation in a tank

The DIYnamics-inspired turntable that Torge and myself have been working on for our “dry theory to juicy reality” project is finally working well!

This is what the setup now looks like (how simple is that?!) and we had an exciting morning testing different experiments!

The one experiment that we have been using as test case in all our previous sessions is the Baroclinic Instability / Hadley cell circulation. There are sketches of the setup and the expected circulation in this blogpost, so just a quick reminder: We place a cold core in the center of our tank (here a glass with blue ice in it), spin the tank (at approximately 20rpm) into solid body rotation, and introduce dye (blue towards the center, red towards the outer edge of the tank).

And what happens then is just beautiful: We get 2D instabilities that transport cold (blue) water outwards and warmer (room-temperature, red) water towards the center of the tank.

We’ve run the experiment three times with different water levels (and once with Southern Hemisphere rotation just for fun) and it worked beautifully each time.

I find it always fascinating how there is hardly any mixing between the red and blue curtains (and there shouldn’t be any because rotating flows become 2D (as shown here)).

Just look at how the dye curtains form when we first add the blue dye…

And then a little later added some red dye…

And then let the field develop.

So I think we’ve got this experiment down and can run it with the students once the semester starts up again in October! :-)

# Combining rotation of a water tank with a temperature gradient: A Hadley cell circulation demo!

Yesterday, we combined a thermally-driven overturning circulation with the effects of rotation, and thus created a Hadley cell circulation. And while the tank was turning faster than we would have liked, we still managed to create a circulation that largely resembles the sketch below: An axially-symmetric overturning circulation (with cold water, indicated by blue arrows, moving down near the cooling in the middle and then outwards, and warmer water moving up along the outer rim and then towards the middle of the tank) which induces the thermal wind flow (sketched in green: Fast surface current in the direction of rotation but even faster than the tank is rotating, and slow bottom flow in the opposite direction).

But what would happen if we increased the tank’s rotation rate? It would make the induced azimuthal flow, the thermal wind, faster too, until it eventually becomes unstable and breaks down into eddies. And then, the experiment (first blogged about a long time ago) looks similar to this one: Lots and lots of eddies that are now rigid vertically and move as Taylor columns!

Heat exchange between the cold core and the warmer areas towards the rim of the tank now doesn’t happen via overturning any more, but looks something like sketched below: We now have radial currents bringing warm water towards the middle (red) and cold water away from it (blue), and the eddies that create those currents are coherent over the whole depth of the tank.

This is actually a really nice demonstration of the circulation in mid- and high latitudes where the weather is determined by baroclinic instabilities, i.e. weather systems just like the eddies we are showing here.

Btw, having two different experiments both represent the same Hadley cell circulation isn’t a contradiction in itself: On Earth, the Coriolis parameter changes with latitude, but in the tank, the Coriolis parameter is the same throughout the tank. So depending on what latitude we want to represent, we need to change the tank’s rotation rate.

Here is an (old) movie of the experiment, and I can’t wait for our own tanks to be ready to produce a new one!

# Combining a slowly rotating water tank with a temperature gradient: A thermal wind demonstration!

Setting up an overturning circulation in a tank is easy, and also interpreting the observations is fairly straightforward. Just by introducing cooling on one side of a rectangular tank a circulation is induced (at least for a short while until the tank fills up with a cold pool of water; see left plot of the image below).

But now imagine an axially symmetric setup where the cooling happens in the middle. What will happen to that overturning circulation if the tank is set into rotation (see right plot above)?

First, let’s check there is an overturning circulation. We can see that there is when we look at dye crystals that sank to the bottom of the tank: Dye streaks are moving outwards (and anti-clockwise) from where the crystals dropped on the ground, so at least that part of the overturning circulation is there for sure. If our tank were taken to represent the Hadley cell circulation in the atmosphere, this bottom flow would be the Trade winds.

Now, in addition to having water sink in the middle of the tank, spread radially outwards, and returning by rising near the outer edge of the tank and flowing back towards the middle, a secondary circulation is induced, and that’s the “thermal wind”. The thermal wind, introduced by the temperature gradient from cold water on the inside of the tank to warmer waters towards the rim, tilts columns that would otherwise stay vertically.

You see that in the image below: Dye dropped into the tank does not sink vertically, but gets swirled around the cold center in a helix shape, indicated in the picture below by the white arrows. In that picture, the swirls are tilted very strongly (a lot stronger than we’d ideally have them tilted). The reason for that is that we just couldn’t rotate the tank as slowly as it should have been, and the higher the rotation rate, the larger the tilt. Oh well…

So this is the current pattern that we observe: An overturning circulation (sketched with the red arrows representing warmer water and the blue arrows representing colder waters below), as well as the thermal wind circulation (indicated in green) with stronger currents near the surface (where the water is moving in the same direction as the rotating tank, but even faster!) and then a backward flow near the bottom. The velocities indicated here by the green arrows are what ultimately tilted our dye streaks in the image above.

The thermal wind component arises because as the overturning circulation moves water, that water carries with it its angular momentum, which is conserved. So water being brought from the rim of the tank towards the middle near the surface HAS to move faster than the tank itself the closer it gets to the middle. This flow would be the subtropical jets in the Hadley cell circulation if out tank were to represent the atmosphere.

Here is an old video of the experiment, first shown 5 years ago here. I’m looking forward to when Torge’s & my rotating tanks are ready so we can produce new videos and pictures, and hopefully being able to rotate the tank even more slowly than we do here (but that was the slowest possible rotation with the setup we had at that time). I promise you’ll see them here almost in realtime, so stay tuned! :-)

# Why do we need a rotating tank to study ocean and atmosphere dynamics? A demonstration

For our project “Ocean currents in a tank: From dry theory to juicy reality“, Torge, Joke and I are working on building affordable rotating tanks to use in Torge’s Bachelor class on ocean and atmosphere dynamics. When people ask what we need rotating tanks for, the standard answer is that rotation of the tank simulates rotation of the Earth. Which is of course true, but it is not really satisfying because it doesn’t really convey the profound effect that rotation has on the behaviour of the ocean and atmosphere, which is actually very easy to show in a quite dramatic way (at least I think it’s dramatic ;-)).

Imagine a cylindrical tank filled with fresh water. In its middle, we place a (bottom-less) cylinder filled with dyed, salty water. When we lift the cylinder out of the tank, the blue dye is released into the freshwater. And depending on whether the tank is rotating or not, the blue water behaves very differently.

The picture below shows top views and side views of a non-rotating and a rotating experiment, taken after similar amounts of time after the “release” of the blue water.

Let’s focus on the top view first. In the non-rotating experiment, a dipole of two counter-rotating eddies develops within seconds of the central dense column being released, spreading blue water pretty much all throughout the tank. In the rotating experiment, after a similar amount of time, the dipole looks different: Even though the same amount of dyed water was released, the two eddies are much smaller and much more well-defined.

In the side view, the difference becomes even more clear. In the non-rotating experiment, looking at the boundary between the blue and clear water, we see eddies moving water in all directions, so in combination with the top view, we know that turbulence is three-dimensional.

In the rotating experiment, however, the boundary between blue and clear water looks very different. There is a clear separation between a blue column of water and the clear water surrounding it. From the side view, we don’t see any turbulence. We know, however, from the top view that there is turbulence in the horizontal plane. In the rotating case, turbulence is two-dimensional.

And this is the dramatic difference between rotating and non-rotating fluids: rotating fluids are rigid in a way that non-rotating fluids are not. And this means that they behave in fundamentally different ways: rather than developing in 3 dimensions, they only develop in 2 dimensions. So in order to simulate the atmosphere and ocean of the rotating earth correctly, we need to also rotate our water tank.

P.S.: Images for this post were originally posted in this post (and in other posts linked therein) 5 years ago. Hoping we’ll have new images soon when our new tanks are up and running! :-)

# Demonstrating Ekman layers in a rotating tank: High pressure and low pressure systems!

Ekman spirals — current profiles that rotate their direction over depth, caused by friction and Coriolis force — are really neat to observe in a rotating tank. I just found out that they are apparently (according to Wikipedia) called “corkscrew currents” in German, and that’s what they look like, too. I tend to think of Ekman spirals more as an interesting by-product that we observe when stopping the tank after a successful experiment, but they totally deserve to be featured in their own experiments*.

Ekman layers form whenever fluid is moving relative to a boundary in a rotating system. In a rotating tank, that is easiest achieved by moving the boundary relative to the water, i.e. by increasing or decreasing the rotation rate of a tank and observing what happens before the water has adjusted to the new rotation and has reached solid body rotation. Spinning the tank up or down creates high and low pressure systems, respectively, similar to atmospheric weather system.

# Creating a low-pressure system: Slowing down the tank

In atmospheric low pressure systems, air moves towards the center of the low pressure system, where it rises, creating the low pressure right there. This situation can probably easiest be modelled by stirring a cup of tea that has some tea leaves still in it. As the surface deforms and water bunches up at the sides, an overturning circulation is set into motion. Water sinks along the side walls and flows towards the center of the cup near the bottom. From there it rises, but any tea leaves or other stuff floating around get stuck in the middle on the bottom because they are too heavy to rise with the current. So there you have your low pressure system!

You can observe the same thing with a rotating tank, except now we don’t stir. The tank is filled with water and spun up to solid body rotation on the rotating table. When the water is in solid body rotation, a few dye crystals are dropped in, leaving vertical streaks as they are sinking to the ground (left plot in the image below).

Then the tank is slowed down. The resulting friction between the water body and the tank creates a bottom Ekman spiral. The streaks of dye that were left when the dye crystals were dropped into the tank move with the water when the tank is slowed down. In the upper part of the tank, the dye stripes stay vertical. But at the bottom, within the Ekman layer, they get deformed as the bottom layer lifts up, and thus show us the depth over which the water column is influenced by bottom friction (see black double arrow in the right plot in the picture below). Again, we have created a low pressure system with a similar overturning circulation as we saw in the tea cup.

In the bottom right corner of the image above, we see a top view of the tank with the trajectory the dye is taking from the spot where it rested on the ground before the rotation of the tank changed.

Looking into the tank with a co-rotating camera, we can also observe the Ekman depth, i.e. the depth that is influenced by the bottom: We see a clear distinction between the region where the dye streaks from the falling crystals are still vertical and the bottom Ekman layer, where they are distorted, showing evidence of the friction with the bottom.

So this was what happens when water is spinning relativ to a slower tank (or a non-rotating cup) — the paraboloid surface is adjusting to one that is more even or completely flat. But then there is also the opposite case.

# Creating a high-pressure system: Spinning up the tank

If we take water that is at rest and start spinning the tank (or spin a moving tank faster suddenly), we create a high pressure system until we again reach solid body rotation.

Again, we dropped dye crystals when the water was in solid body rotation (or in solid body without rotation) before we start the spinup, as we see in the left plot below.

Now the sudden spinning of the boundaries relative to the body of water creates a high pressure system with the bottom flow outward from the center, which again we see in the deformation of the dye streaks. The Ekman depth is again the depth over which the dye streaks get bent, below the water column that isn’t influenced by friction where they still have their original vertical shape.

In the bottom right corner of the image above, we see a top view of the tank with the trajectory the dye is taking from the spot where it rested on the ground before the rotation of the tank changed.

Here is what this experiment looks like in a movie:

So here we have it. High pressure and low pressure systems in a tank!

*Which I actually did before, both in a rotating tank as well as on a Lazy Susan.

# Working on our own affordable rotating table for oceanographic experiments!

Inspired by the article “Affordable Rotating Fluid Demonstrations for Geoscience Education: the DIYnamics Project” by the Hill et al. (2018), Joke, Torge and I have been wanting to build an affordable rotating table for teaching for a while now. On Saturday, we met up again to work on the project.

This post is mainly to document for ourselves where we are at and what else needs to happen to get the experiments working.

New this time: New rotating tables, aka Lazy Susans. After the one I’ve had in my kitchen was slightly too off-center to run smoothly, we bought the ones recommended by the DIYnamics project. And they work a lot better! To center our tank on the rotating table and keep it safely in place, we used these nifty LEGO and LEGO Duplo contraptions, which worked perfectly.

We also used a LEGO contraption to get the wheel close enough to drive the rotating table. The yellow line below shows where the rim of the rotating table’s foot needs to sit.

And this is how the engine has to be placed to drive the rotating table.

First attempt: Yes! Very nice parabolic surface! Very cool to see time and time again!

Now first attempt at a Hadley cell experiment: A jar with blue ice is placed at the center of the tank. Difficulties here: Cooling sets in right away, before the rotating tank has reached solid body rotation. That might potentially mess up everything (we don’t know).

So. Next attempt: Use a jar (weighted down with stones so it doesn’t float up) until the tank has reached solid body rotation, then add blue ice water

Working better, even though the green dye is completely invisible…

We didn’t measure rotation, nor did we calculate what kind of regime we were expecting, so the best result we got was “The Heart” (see below) — possibly eddying regime with wavenumber 3?

Here is what we learned for next time:

• use better dye tracers and make sure their density isn’t too far off the water in the tank
• use white  LEGO bricks to hold the tank in place (so they don’t make you dizzy watching the tank)
• measure the rotation rate and calculate what kind of regime we expect to see — overturning or eddying, and at which wave number (or, even better, the other way round: decide what we want to see and calculate how to set the parameters in order to see it)
• use white cylinder in the middle so as to not distract from the circulation we want to see; weigh the cylinder down empty and fill it with ice water when the tank has reached solid body rotation
• give the circulation a little more time to develop between adding the cold water at the center and putting in dyes (at least 10 minutes)
• it might actually be worth reading the DIYnamics team’s instruction again, and to buy exactly what they recommend. That might save us a lot of time ;-)

But: As always this was fun! :-)

P.S.: Even though this is happening in a kitchen, I don’t think this deserves the hashtag #kitchenoceanography — the equipment we are using here is already too specialized to be available in “most” kitchens. Or what would you say?

# Supporting conceptual understanding of the Coriolis force through laboratory experiments

My friend Pierré and I started working on this article when both of us were still working at the Geophysical Institute in Bergen. It took forever to get published, mainly because both of us had moved on to different jobs with other foci, so maybe it’s not a big deal that it took me over a year to blog it? Anyway, I still think it is very important to introduce any kind of rotating experiments by first making sure people don’t harbour misconceptions about the Coriolis effect, and this is the best way we came up with to do so. But I am happy to hear any suggestions you might have on how to improve it :-)

# Supporting Conceptual Understanding of the Coriolis Force Through Laboratory Experiments

By Dr. Mirjam S. Glessmer and Pierré D. de Wet

Published in Current: The Journal of Marine Education, Volume 31, No 2, Winter 2018

Do intriguing phenomena sometimes capture your attention to the extent that you haveto figure out why they work differently than you expected? What if you could get your students hooked on your topic in a similar way?

Wanting to comprehend a central phenomenon is how learning works best, whether you are a student in a laboratory course or a researcher going through the scientific process. However, this is not how introductory classes are commonly taught. At university, explanations are often presented or developed quickly with a focus on mathematical derivations and manipulations of equations. Room is seldom given to move from isolated knowledge to understanding where this knowledge fits in the bigger picture formed of prior knowledge and experiences. Therefore, after attending lectures and even laboratories, students are frequently able to give standard explanations and manipulate equations to solve problems, but lack conceptual understanding (Kirschner & Meester, 1988): Students might be able to answer questions on the laws of reflection, yet not understand how a mirror works, i.e. why it swaps left-right but not upside-down (Bertamini et al., 2003).

Laboratory courses are well suited to address and mitigate this disconnect between theoretical knowledge and practical application. However, to meet this goal, they need to be designed to focus specifically on conceptual understanding rather than other, equally important, learning outcomes, like scientific observation as a skill or arguing from evidence (NGSS, 2013), calculations of error propagations, application of specific techniques, or verifying existing knowledge, i.e. illustrating the lecture (Kirschner & Meester, 1988).

Based on experience and empirical evidence, students have difficulties with the concept of frames of reference, and especially with fictitious forces that are the result of using a different frame of reference. We here present how a standard experiment on the Coriolis force can support conceptual understanding, and discuss the function of employing individual design elements to maximize conceptual understanding.

# HOW STUDENTS LEARN FROM LABORATORY EXPERIMENTS

In introductory-level college courses in most STEM disciplines, especially in physics-based ones like oceanography or meteorology and all marine sciences, laboratory courses featuring demonstrations and hands-on experiments are traditionally part of the curriculum.

Laboratory courses can serve many different and valuable learning outcomes: learning about the scientific process or understanding the nature of science, practicing experimental skills like observation, communicating about scientific content and arguing from evidence, and changing attitudes (e.g. Feisel & Rosa, 2005; NGSS, 2013; Kirschner & Meester, 1988; White, 1996). One learning outcome is often desired, yet for many years it is known that it is seldomly achieved: increasing conceptual understanding (Kirschner & Meester, 1988, Milner-Bolotin et al., 2007). Under general dispute is whether students actually learn from watching demonstrations and conducting lab experiments, and how learning can be best supported (Kirschner & Meester, 1988; Hart et al., 2000).

There are many reasons why students fail to learn from demonstrations (Roth et al., 1997). For example, in many cases separating the signal to be observed from the inevitably measured noise can be difficult, and inference from other demonstrations might hinder interpretation of a specific experiment. Sometimes students even “remember” witnessing outcomes of experiments that were not there (Milner-Bolotin et al., 2007). Even if students’ and instructors’ observations were the same, this does not guarantee congruent conceptual understanding and conceptual dissimilarity may persist unless specifically addressed. However, helping students overcome deeply rooted notions is not simply a matter of telling them which mistakes to avoid. Often, students are unaware of the discrepancy between the instructors’ words and their own thoughts, and hear statements by the instructor as confirmation of their own thoughts, even though they might in fact be conflicting (Milner-Bolotin et al., 2007).

Prior knowledge can sometimes stand in the way of understanding new scientific information when the framework in which the prior knowledge is organized does not seem to organically integrate the new knowledge (Vosniadou, 2013).The goal is, however, to integrate new knowledge with pre-existing conceptions, not build parallel structures that are activated in context of this class but dormant or inaccessible otherwise. Instruction is more successful when in addition to having students observe an experiment, they are also asked to predict the outcome before the experiment, and discuss their observations afterwards (Crouch et al., 2004). Similarly, Muller et al. (2007) find that even learning from watching science videos is improved if those videos present and discuss common misconceptions, rather than just presenting the material textbook-style. Dissatisfaction with existing conceptions and the awareness of a lack of an answer to a posed question are necessary for students to make major changes in their concepts (Kornell, 2009, Piaget, 1985; Posner et al., 1982). When instruction does not provide explanations that answer students’ problems of understanding the scientific point of view from the students’ perspective, it can lead to fragmentation and the formation of synthetic models (Vosniadou, 2013).

One operationalization of a teaching approach to support conceptual change is the elicit-confront-resolve approach (McDermott, 1991), which consists of three steps: Eliciting a lingering misconception by asking students to predict an experiment’s outcome and to explain their reasons for the prediction, confronting students with an unexpected observation which is conflicting with their prediction, and finally resolving the matter by having students come to a correct explanation of their observation.

The Coriolis force is essential in explaining formation and behavior of ocean currents and weather systems we observe on Earth. It thus forms an important part of any instruction on oceanography, meteorology or climate sciences. When describing objects moving on the rotating Earth, the most commonly used frame of reference would be fixed on the Earth, so that the motion of the object is described relative to the rotating Earth. The moving object seems to be under the influence of a deflecting force – the Coriolis force – when viewed from the co-rotating reference frame. Even though the movement of an object is independent of the frame of reference (the set of coordinate axes relative to which the position and movement of an object is described is arbitrary and usually made such as to simplify the descriptive equations of the object), this is not immediately apparent.

Temporal and spatial frames of reference have been described as thresholds to student understanding (Baillie et al., 2012, James, 1966; Steinberg et al., 1990). Ever since its first mathematical description in 1835 (Coriolis, 1835), this concept is most often taught as a matter of coordinate transformation, rather than focusing on its physical relevance (Persson, 1998). Most contemporary introductory books on oceanography present the Coriolis force in that form (cf. e.g. Cushman-Roisin, 1994; Gill, 1982; Pinet, 2009; Pond and Pickard, 1983; Talley et al., 2001; Tomczak and Godfrey, 2003; Trujillo and Thurman, 2013). The Coriolis force is therefore often perceived as “a ‘mysterious’ force resulting from a series of ‘formal manipulations’” (Persson, 2010). Its unintuitive and seemingly un-physical character makes it difficult to integrate into existing knowledge and understanding, and “even for those with considerable sophistication in physical concepts, one’s first introduction to the consequences of the Coriolis force often produces something analogous to intellectual trauma” (Knauss, 1978).

In many courses, helping students gain a deeper understanding of rotating systems and especially the Coriolis force, is approached by presenting demonstrations, typically of a ball being thrown on a merry-go-round, showing the movement simultaneously from a rotating and a non-rotating frame (Urbano & Houghton, 2006), either in the form of movies or simulations, or in the lab as demonstration, or as a hands-on experiment[i]. After conventional instruction that exposed students to discussions and simulations, students are able to do calculations related to the Coriolis force.

Nevertheless, when confronted with a real-life situation where they themselves are not part of the rotating system, students show difficulty in anticipating the movement of an object on a rotating body. In a traditional Coriolis experiment (Figure1), for example, a student launches a marble from a ramp on a rotating table (Figure 2A, B) and the motion of the marble is observed from two vantage points: where they are standing in the room, i.e. outside of the rotating system of the table; and on a screen that displays the table, as captured by a co-rotating camera mounted above it. When asked, before that experiment, what path the marble on the rotating surface will take, students report that they anticipate observing a deflection, its radius depending on the rotation’s direction and rate. After having observed the experiment, students report that they saw what they expected to see even though it never happened. Contextually triggered, knowledge elements are invalidly applied to seemingly similar circumstances and lead to incorrect conclusions (DiSessa & Sherin, 1988; Newcomer, 2010). This synthetic model of always expecting to see a deflection of an object moving on a rotating body, no matter which system of reference it is observed from, needs to be modified for students to productively work with the concept of the Coriolis force.

Figure 1: Details of the Coriolis experiment

Despite these difficulties in interpreting the observations and understanding the underlying concepts, rotating tables recently experienced a rise in popularity in undergraduate oceanography instruction (Mackin et al., 2012) as well as outreach to illustrate features of the oceanic and atmospheric circulation(see for example Marshall and Plumb, 2007). This makes it even more important to consider what students are intended to learn from such demonstrations or experiments, and how these learning outcomes can be achieved.

Figure 2A: View of the rotating table including the video camera on the scaffolding above the table. B: Sketch of the rotating table, the mounted (co-rotating) camera, and the marble on the table. C: Student tracing the curved trajectory of the marble on a transparency. On the screen, the experiment is shown as captured by the co-rotating camera, hence in the rotating frame of reference.

# A RE-DESIGNED HANDS-ON INTRODUCTION TO THE CORIOLIS FORCE

The traditional Coriolis experiment, featuring a body on a rotating table[ii], observed both from within and from outside the rotating system, can be easily modified to support conceptual understanding.

When students of oceanography are asked to do a “dry” experiment (in contrast to a “wet” one with water in a tank on the rotating table) on the Coriolis force, at first, this does not seem like a particularly interesting phenomenon to students because they believe they know all about it from the lecture already. The experiment quickly becomes intriguing when a cognitive dissonance arises and students’ expectations do not match their observations. We use an elicit-confront-resolve approach to help students observe and understand the seemingly conflicting observations made from inside versus outside of the rotating system (Figure 3). To aid in making sense of their observations in a way that leads to conceptual understanding the three steps elicit, confront, and resolve are described in detail below.

Figure 3: Positions of the ramp and the marble as observed from above in the non-rotating (top) and rotating (bottom) case. Time progresses from left to right. In the top plots, the positions are shown in inert space. From left to right, the current positions of the ramp and marble are added with gradually darkening colors. In the bottom plots, the ramp stays in the same position relative to the co-rotating observer, but the marble moves and the current position is always displayed with the darkest color.

## 2. What do you think will happen? Eliciting a (possibly) lingering misconception

Students have been taught in introductory lectures that any moving object in a counter-clockwise rotating system (i.e. in the Northern Hemisphere) will be deflected to the right. They are also aware that the extent to which the object is deflected depends on its velocity and the rotational speed of the reference frame. In our experience, due to this prior schooling, students expect to see a Coriolis deflection even when they observe a rotating system “from the outside”. When the conventional experiment is run without going through the additional steps described here, students often report having observed the (non-existent) deflection.

By activating this prior knowledge and discussing what students anticipate observing under different conditions before the actual experiment is conducted, the students’ insights are put to the test. This step is important since the goal is to integrate new knowledge with pre-existing conceptions, not build parallel structures that are activated in context of this class but dormant or inaccessible otherwise. Sketching different scenarios (Fan, 2015; Ainsworth et al., 2011) and trying to answer questions before observing experiments support the learning process since students are usually unaware of their premises and assumptions (Crouch et al., 2004). Those need to be explicated and documented (even just by saying them out loud) before they can be tested, and either be built on, or, if necessary, overcome.

We therefore ask students to observe and describe the path of a marble being radially launched from the perimeter of the circular, non-rotating table by a student standing at a marked position next to the table, the “launch position”. The marble is observed rolling towards and over the center point of the table, dropping off the table diametrically opposite from the position from which it was launched. So far nothing surprising. A second student – the catcher– is asked to stand at the position where the marble dropped off the table’s edge so as to catch the marble in the non-rotating case. The position is also marked on the floor with tape to document the observation.

Next, the experimental conditions of this thought experiment (Winter, 2015) are varied to reflect on how the result depends on them. The students are asked to predict the behavior of the marble once the table is put into slow rotation. At this point, students typically enquire about the direction of rotation and, when assured that “Northern Hemisphere” counter-clockwise rotation is being applied, their default prediction is that the marble will be deflected to the right. When asked whether the catcher should alter their position, the students commonly answer that the catcher should move some arbitrary angle, but typically less than 90 degrees, clockwise around the table.  The question of the influence of an increase in the rotational rate of the table on the catcher’s placement is now posed. “Still further clockwise”, is the usual answer. This then leads to the instructor’s asking whether a rotational speed exists at which the student launching the marble, will also be able to catch it themselves. Usually the students confirm that such a situation is indeed possible.

## 2. Did you observe what you expected to see? Confronting the misconception

After “eliciting” student conceptions, the “confront” step serves to show the students the discrepancy between what they expect to see, and what they actually observe. Starting with the simple, non-rotating case, the marble is launched again and the nominated catcher, positioned diametrically across from the launch position, seizes the marble as it falls off the table’s surface right in front of them. As theoretically discussed beforehand, the table is then put into rotation at incrementally increasing rates, with the marble being launched from the same position for each of the different rotational speeds.  It becomes clear that the catcher can – without any adjustments to their position – remain standing diametrically opposite to the student launching the marble – the point where the marble drops to the floor. Hence students realize that the movement of the marble relative to the non-rotating laboratory is unaffected by the table’s rotation rate.

This observation appears counterintuitive, since the camera, rotating with the system, shows the curved trajectories the students had expected; segments of circles with decreasing radii as the rotation rate increases. Furthermore, to add to the confusion, when observed from their positions around the rotating table, the path of the marble on the rotating table appears to show a deflection, too.  This is due to the observer’s eye being fooled by focusing on features of the table, e.g. marks on the table’s surface or the bars of the camera scaffold, relative to which the marble does, indeed, follow a curved trajectory. To overcome this optical illusion, the instructor may ask the students to crouch, diametrically across from the launcher, so that their line of sight is aligned with the table’s surface, i.e. at a zero-zenith angle of observation. From this vantage point, the marble is observed to indeed be moving in a straight line towards the observer, irrespective of the rotation rate of the table. Observing from different perspectives and with focus on different aspects (Is the marble coming directly towards me? Does it fall on the same spot as before? Did I need to alter my position in the room at all?) helps students gain confidence in their observations.

To solidify the concept, the table may again be set into rotation. The launcher and the catcher are now asked to pass the marble to one another by throwing it across the table without it physically making contact with the table’s surface. As expected, the marble moves in a straight line between the launcher and the catcher, whom are both observing from an inert frame of reference. However, when viewing the playback of the co-rotating camera, which represents the view from the rotating frame of reference, the trajectory is observed as curved[iii].

## 3. Do you understand what is going on? Resolving the misconception

Misconceptions that were brought to light during the “elicit” step, and whose discrepancy with observations was made clear during the “confront” step, are finally resolved in this step. While this sounds very easy, in practice it is anything but. For learning to take place, the instructor needs to aid students in reflecting upon and reassessing previous knowledge by pointing out and dispelling any remaining implicit assumptions, making it clear that the discrepant trajectories are undoubtedly the product of viewing the motion from different frames of reference. Despite the students’ observations and their participation in the experiment this does not happen instantaneously. Oftentimes further, detailed discussion is required. Frequently students have to re-run the experiment themselves in different roles (i.e. as launcheras well as catcher) and explicitly state what they are noticing before they trust their observations.

For this experiment to benefit the learning outcomes of the course, which go beyond understanding of a marble on a rotating table and deal with ocean and atmosphere dynamics, knowledge needs to be integrated into previous knowledge structures and transferred to other situations. This could happen by discussion of questions like, for example: How could the experiment be modified such that a straight trajectory is observed on the screen? What would we expect to observe if we added a round tank filled with water and paper bits floating on it to the table and started rotating it? How are our observations of these systems relevant and transferable to the real world? What are the boundaries of the experiment?

# IS IT WORTH THE EXTRA EFFORT? DISCUSSION

We taught an undergraduate laboratory course which included this experiment for several years. In the first year, we realized that the conventional approach was not effective. In the second year, we tried different instructional approaches and settled on the one presented here. We administered identical work sheets before and after the experiment. These work sheets were developed as instructional materials to ensure that every student individually went through the elicit-confront-resolve process. Answers on those worksheets show that all our students did indeed expect to see a deflection despite observing from an inert frame of reference: Students were instructed to consider both a stationary table and a table rotating at two different rates.  They were then asked to, for each of the scenarios, mark with an X the location where they thought the marble would contact the floor after dropping off the table’s surface.  Before instruction, all students predicted that the marble would hit the floor in different spots – diametrically across from the launch point for no rotation, and at increasing distances from that first point with increasing rotation rates of the table (Figure 4). This is the exact misconception we aimed to elicit with this question: students were applying correct knowledge (“in the Northern Hemisphere a moving body will be deflected to the right”) to situations where this knowledge was not applicable: when observing the rotating body and the moving object upon it from an inert frame of reference.

Figure 4A: Depiction of the typical wrong answer to the question: Where would a marble land on the floor after rolling across a table rotating at different rotation rates? B: Correct answer to the same question. C: Correct traces of marbles rolling across a rotating table.

In a second question, students were asked to imagine the marble leaving a dye mark on the table as it rolls across it, and to draw these traces left on the table. In this second question, students were thus required to infer that this would be analogous to regarding the motion of the marble as observed from the co-rotating frame of reference. Drawing this trajectory correctly before the experiment is run does not imply a correct conceptual understanding, since the transfer between rotating and non-rotating frames of references is not happening yet and students draw curved trajectories for all cases. However, after the experiment this question is useful especially in combination with the first one, as it requires a different answer than the first, and an answer that students just learned they should not default to.

The students’ laboratory reports supply additional support of the usefulness of this new approach.  These reports had to be submitted a week after doing the experiment and accompanying work sheets, which were collected by the instructors.  One of the prompts in the lab report explicitly addresses observing the motion from an inert frame of reference as well as the influence of the table’s rotational period on such motion. This question was answered correctly by all students. This is remarkable for three reasons: firstly, because in the previous year with conventional instruction, this question was answered incorrectly by the vast majority of students; secondly, from our experience, lab reports have a tendency to be eerily similar year after year which did not hold true for tis specific question; and lastly, because for this cohort, it is one of very few questions that all students answered correctly in their lab reports, which included seven experiments in addition to the Coriolis experiment. These observations lead us to believe that students do indeed harbor the misconception we suspected, and that the modified instructional approach has supported conceptual change.

# CONCLUSIONS

We present modifications to a “very simple” experiment and suggest running it before subjecting students to more advanced experiments that illustrate concepts like Taylor columns or weather systems. These more complex processes and experiments cannot be fully understood without first understanding the Coriolis force acting on the arguably simplest bodies. Supplying correct answers to standard questions alone, e.g. “deflection to the right on the northern hemisphere”, is not sufficient proof of understanding.

In the suggested instructional strategy, students are required to explicitly state their expectations about what the outcome of an experiment will be, even though their presuppositions are likely to be wrong. The verbalizing of their assumptions aids in making them aware of what they implicitly hold to be true. This is a prerequisite for further discussion and enables confrontation and resolution of potential misconceptions. Wesuggest using an elicit-confront-resolve approach even when the demonstration is not run on an actual rotating table, but virtually conducted instead, for example using Urbano & Houghton (2006)’s Coriolis force simulation. We claim that the approach is nevertheless beneficial to increasing conceptual understanding.

We would like to point out that gaining insight from any seemingly simple experiment, such as the one discussed in this article, might not be nearly as straightforward or obvious for the students as anticipated by the instructor. Using an intriguing phenomenon to be investigated experimentally, and slightly changing conditions to understand their influence on the result, is highly beneficial. Probing for conceptual understanding in new contexts, rather than the ability to calculate a correct answer, proved critical in understanding where the difficulties stemmed from, and only a detailed discussion with several students could reveal the scope of difficulties.

# ACKNOWLEDGEMENTS

The authors are grateful for the students’ consent to be featured in this article’s figures.

# RESOURCES

Movies of the experiment can be seen here:

Rotating case: https://vimeo.com/59891323

Non-rotating case: https://vimeo.com/59891020

Using an old disk player and a ruler in absence of a co-rotating camera: https://vimeo.com/104169112

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# Endnotes

[i]While tremendously helpful in visualizing an otherwise abstract phenomenon, using a common rotating table introduces difficulties when comparing the observed motion to the motion on Earth. This is, among other factors, due to the table’s flat surface (Durran and Domonkos, 1996), the alignment of the (also fictitious) centrifugal force with the direction of movement of the marble (Persson, 2010), and the fact that a component of axial rotation is introduced to the moving object when launched. Hence, the Coriolis force is not isolated. Regardless of the drawbacks associated with the use of a (flat) rotating table to illustrate the Coriolis effect, we see value in using it to make the concept of fictitious forces more intuitive, and it is widely used to this effect.

[ii]Despite their popularity in geophysical fluid dynamics instruction at many institutions, rotating tables might not be readily available everywhere. Good instructions for building a rotating table can, for example, be found on the “weather in a tank” website, where there is also the contact information to a supplier given: http://paoc.mit.edu/labguide/apparatus.html. A less expensive setup can be created from old disk players or even Lazy Susans, or found on playgrounds in form of merry-go-rounds. In many cases, setting the exact rotation rate is not as important as having a qualitative difference between “slow” and “fast” rotation, which is very easy to realize. In cases where a co-rotating camera is not available, by dipping the marble in either dye or chalk dust (or by simply running a pen in a straight line across the rotating surface), the trajectory in the rotating system can be visualized. The instructional approach described in this manuscript is easily adapted to such a setup.

[iii]We initially considered starting the lab session by throwing the marble diametrically across the rotating table.  Students would then see on-screen the curved trajectory of a marble, which had never made physical contact with the table rotating beneath it, and which was clearly moving in a straight line from thrower to catcher, leading to the realization that it is the frame of reference that is to blame for the marble’s curved trajectory. However, the speed of a flying marble makes it very difficult to observe its curved path on the screen in real time. Replaying the footage in slow motion helps in this regard.  Yet, replacing direct observation with recording and playback seemingly hampers acceptance of the occurrence as “real”. We therefore decided to only use this method to further illustrate the concept, not as a first step.

# Bios

Dr. Mirjam Sophia Glessmer, holds a Master of Higher Education and Ph.D. in physical oceanography. She works at the Leibniz Institute of Science and Mathematics Education in Kiel, Germany. Her research focus lies on informal learning and science communication in ocean and climate sciences.

Pierre de Wet is a Ph.D. student in Oceanography and Climatology at the University of Bergen, Norway, and holds a Master in Applied Mathematics from the University of Stellenbosch, South Africa. He is employed by Akvasafe AS, where he works with the analysis and modelling of physical environmental parameters used in the mooring analysis and accreditation of floating fish farms.