As someone living on the German Baltic Sea coast, I don’t spend a lot of time on the North Sea coast (except, actually, my week-long vacation after Easter with my godson and his family, and when my friend Frauke and I went to Sylt earlier this year, or when Frauke and I are going back to the North Sea next weekend. So maybe that’s actually not so little time on the North Sea coast compared to most other people?).
Anyway. I really like the North Sea, especially because I like the flat landscape where the highest points are dykes.
What I really dislike, though, is getting my feet muddy. But that’s pretty much the whole point of a North Sea vacation, according to my godson and his family.
On the other hand, though, having the opportunity to actively and directly influence water depth (or, as normal people would probably say, leaving footprints in the mud) makes for some pretty cool wave watching!
It’s a little hard to see, but if you look at the picture above, you see that the sun is coming from kinda behind my left shoulder, and the picture below is taken from a similar perspective (just telling you so you can interpret the footprints and resulting waves). So the left edges of the footprints are actually coming up and partly out of the water.
The wind is coming from the right, and you see the locally generated wind ripples and how they get defracted around the obstacles created by the foot prints!
Pretty cool, eh?
In the picture below, the wind is coming from the left and you see the muddy wakes of the fresh footprints! This I think is pretty awesome, especially because you at the same time see the refraction of waves around the obstacles.
What I also think is pretty cool are the little spaghetti piles of sand that the worms living in the mud leave behind.
And that, for each of the piles, there is a funnel somewhere close by, and a worm connecting the two inside the mud!
But then when the water is gone completely, it’s still pretty here, but also a liittle boring. Don’t you agree?
Ok, but it’s still pretty. But Wadden Sea and tides take the fun out of wave watching for quite substantial amounts of time every day, and I don’t approve of that ;-)
I took the selfie above mainly to send to my mom from my vacation in Dornumersiel on the German North Sea coast. But then when looking through the hundreds of pictures I took that day, I realized that not only was my hair parted on the wrong side because it was so windy (ha!), the wave fields to my right and left looked actually quite different, without the reason for that being immediately obvious. So let me show you a picture facing the other way.
Above, you see this wave breaker like structure, protruding into the sea. The wind is coming from the right side, thus the waves are a lot larger on the right side of the breaker where they are getting more and more energy from the wind as they come towards us, than the waves on the left, the lee side of the breaker, where they don’t get any new energy input and are just refracted around the breaker.
Looking the other way, towards the shore, the difference becomes even more clear (picture below) isn’t this fascinating?
I really like watching how waves interact with structures. Below, for example, we see that the wave crests are coming towards the wave breaker at an angle, and that they are reflected and traveling away from it, too. This contributes to making this side look a lot more choppy than the other side!
On the other side, the waves look smooth. I was still standing on the breaker when taking the picture below, and you see where the sea surface is still sheltered from the wind and where the fetch is long enough so the surface roughness increases and ripples and capillary waves form.
Since we are in the Wadden Sea, the shore has a very shallow slope going into the North Sea, so waves look super interesting when they are in the shallow water. Below you see many many almost-breaking wave crests behind each other, coming towards us. The water depth is clearly a lot less than a wave length, the waves are interacting with the bottom and thus have really long and uniform troughs and steep, short crests. (btw, for those of you wondering how I could say anything about water depth in my #friendlywaves post on Saturday: This is how. This is an example of waves in very shallow water, and you clearly see their shape being different, don’t you?).
I love looking at the details of where they hit the beach! All the sparkle, all the little Mach cones around the pebbles where the water is running off, all the small capillary waves!
Below, someone accidentally walked into my picture, but that’s actually a good thing, because it gives you a scale, and if you look at the little wave rings that were created when she put her foot into the water and it splashing forward a little. The wave rings actually have comparable sizes to all the other small stuff going on on the sea surface!
And what’s also pretty impressive: How the crests get refracted by changing water depth. Below it almost looks like parabolic shapes coming in from the right, right? The side of the parabola that is further away is actually the wave crest that is coming in from the open sea, and the rest, i.e. the actual curved part, is partly diffraction around the breaker and then refraction because of changing water depths. So cool!
Since I spent quite some time there, here is a picture later that day with a lot less water. Tides and all that… ;-)
And then another day with a different wind direction and less sun.
I think it looks really cool to see the fairly wide area to the right of the breaker, in its lee, where the surface is really smooth!
So far, so good. Gotta go now! Do you find this as fascinating as I do?
What I find super fascinating about the picture below is how clearly you see the ship’s feathery wake in the reflection of the street lamps on the bridge, as the ship is moving towards the left and you are looking out over it’s starboard side, more or less perpendicular to its direction of travel.
Towards the left of the picture, the street lamps reflect as straight lines towards you, as you would expect if the sea was calm and the surface more or less flat. (Why as a line rather than a single point source? Because, of course, the water isn’t completely calm, so in each wave there is an area that is positioned exactly such that the angle of the incoming light and the angle of the reflected, outgoing light (which have to always be the same) reflect the light from the lamp directly into the camera. As there are many waves that somewhere match that condition, we see light reflected in many spots even from a single lamp)
Towards the right, though, these lines of light get more and more deformed, bot as the lights get closer to us (so we notice the deformations more easily) and as there are waves caused by the ship.
Picture by Arnt Petter Både, used with permission
And isn’t it fascinating how the moon reflects as more of a smudge than a line? I think that is because its light is hitting the water at a steeper angle, so there would need to be much steeper waves further away if they were to reflect the light towards us.
Anyway, below there is another picture from the next night, I think. Here you very clearly see the ship’s feathery wake again, and here you can see how the slope of the waves is important for what gets reflected towards us and what doesn’t: Only where we have steep slopes (i.e. only at the wake) can we see reflections f the light from the land in the lower third of the picture. There is an area where the angles clearly don’t work between that and the clear reflections further towards the shore. Oh, and do you see the different surface roughnesses that make reflections seem clearer and less clear depending on whether the surface is flatter or rougher due to a local breeze?
Picture by Arnt Petter Både, used with permission
This is fun! Does anyone else have #friendlywaves for me? :-)
The other day, my friend and co-author Pierré sent me pictures he took during fieldwork in a Norwegian fjord. As I, sadly, wasn’t there, all I can do now is admire the pictures and wish I had been there. And, of course, do a #friendlywaves — an interpretation of a wave field that a friend sent me a picture of. Let’s see what he thinks about my interpretation!
So here we go. As you see, it’s a foggy day, and from the time he messaged me at, I know it was a foggy morning. The light seems to kinda be coming from a low angle which would support the morning (or evening) theory, but that’s always very hard to tell in the fog.
There are some waves on the sea surface, and below you see two distinct wave fields at a small angle to each other. What caused them?
I am guessing that the ones that look like sections of a circle are from some kind of point source, which would be located somewhere below and to the right of the picture’s lower right edge. Maybe something regularly dripping into the water, or a buoy being deployed. I think I’ve seen something like that when a CTD was coming up again and the wire was dripping as it went over a pulley. In any case, I am pretty sure the ship was on station as the picture was taken.
The second wave field, more or less parallel to the lower edge of the picture below, I would guess is the background field. Could be caused by anything, but nothing very close by: It’s not locally generated wind waves. If I had to guess it’s wind waves that have run for a little while. It might also be the ship gently rocking, radiating straight-ish wave fronts, but I doubt it.
As to what we can say about the spot the picture was taken in: There are no structures/shore lines really close by (otherwise we’d see reflections in the wave field), and the water depth is more than a meter or so — it’s definitely long compared to the wave length of the waves shown here as they can’t “feel” the ground (which we see from their shape — not shallow water waves).
Picture by Pierré de Wet, used with permission
The next picture, I am assuming, was sent to me to capture the mood. And to make me jealous. Yes, it worked ;-)
Picture by Pierré de Wet, used with permission
Below, we see that the ship is now moving. We are looking down and back and see the wake developing: The turbulent wake in the top left of the picture, one side of the feathery V-shaped wake on the right of the turbulent wake. The feathery waves are fairly steep, but that’s because of how they were generated, not because of any interference with the ground. The ground is still more than at least two or so wavelengths away (and it better had be, judging from the size of the ship).
There was hardly any wind when this picture was taken, the sea surface doesn’t show any locally created wind ripples.
Picture by Pierré de Wet, used with permission
I think it’s so fascinating to see the sharp line in the lower middle of the picture, separating the part of the sea surface that has been influenced by the ship from the one that hasn’t received any signal of the ship’s presence yet. If you think about the V-shaped wake as of the ship’s Mach cone, the outside of the V is where people would first hear the sonic boom after the ship has flown past!
The picture below is looking at a similar situation wake-wise. Now, though, there is a little wind: You can clearly see the enhanced surface roughness, and indeed individual capillary waves, in the bottom right corner.
Below is a third picture of the same situation. Now there are some small waves in the surface, however not locally produced, I think. Maybe they already sailed out of the spot (can you say breezy? It’s really not a windy spot) shown above?
Picture by Pierré de Wet, used with permission
What I find fascinating above is how clearly you see the one leg of the V-shaped feathery wake develop, and even in the foreground of the picture how you can see individual turbulence cells from where the bow wave broke as the ship sailed through the water.
What else do you observe? It’s not so easy to look at other people’s wave pictures and make sense of them! How did I do, Pierre?
So the main reason I got up early today and went for a run was because when I woke up and checked the weather forecast, it said that it would be raining and even snowing for the next hour. And since I wanted a really good reason to hang on my sofa and drink hot tea all day long, I though going for a run in that weather would certainly earn me that.
Yep, and then the weather was absolutely beautiful, and I got a lot of cool wave watching done!
Below, you see the straight wave crests from wind generated waves and then the half circles that radiate away from something sitting below the edge of the sea wall. Couldn’t see what it was since I couldn’t stop before I had run my 5k! ;-) But I am guessing it was a bird.
Next picture when I was done with my run already and — even better — had been inside the water, too! You see the wind wave field: High surface roughness in the top right where capillary waves are generated locally, larger, longer wavelength “normal” waves in the top right. And then the half circles radiating away from where the staircase goes into the water, which is interacting with the wave field.
Here is a different wave field from a different spot: Towards the left, you mainly see the wind waves. And to the right, you see that someone is scrubbing another one of the staircases leading into the water with a broom! That’s what made the waves coming in from the top right…
And last not least, I liked the cloud below.
And in that picture there is so much to see: different surface roughnesses where a breeze creates ripples and where there is no wind, reflection changing depending on the surface roughness, and, favourite topic of mine, total internal reflection!
Oh, forgot there was another picture coming. Wake of a bird plus total internal reflection plus the awesome play of light on the ground. What more could anyone want? :-)
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.
HOW STUDENTS TRADITIONALLY LEARN ABOUT THE CORIOLIS FORCE
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.
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.
The authors are grateful for the students’ consent to be featured in this article’s figures.
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[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.
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.
Showing double-diffusive mixing in tank experiments is a pain if you try to do it the proper way with carefully measured temperatures and salinities. It is, however, super simple, if you go for the quick and dirty route: Cream in tea! Even easier than the “forget the salt, just add food dye” salt fingering experiment I’ve been recommending until now.
The result of double-diffusive mixing of cream in tea is probably familiar to most (see above), but have you ever looked closely at the process?
Below, we pour cold cream into hot tea. The cream initially sinks to the bottom of the tea cup, but then quickly heats up and fingers start raising to the surface of the cup. They are visible as fingers because while the heat has quickly diffused into the cream, the actual mixing of substances takes longer and the opaque milk stays visible in the clear tea. Only when the fingers have risen to the surface the substances begin to mix due to shear and diffusion of substances. Hence the name “double diffusion”: First diffusion of heat, then of particles afterwards.
Pretty cool, isn’t it?
If you happened to stir the tea before pouring the cream, it looks even more awesome. Home-made galaxies :-)
And isn’t it fascinating how the blob of cream in the middle of the cup stays intact for quite some time?
So now you know the only reason why I am drinking black tea: So I can do salt fingering experiments with it! :-)
Walking along a beach, first, the waves looked like this: One wave breaking at a time.
That’s the situation you also see in the foreground of the picture below, while in the background, a little further down the beach, something else starts happening.
If we look closely at that situation (shown in the picture below), there are several waves breaking at the same time, one behind the other.
And it isn’t just coincidence, it keeps happening throughout hundreds of pictures I took that windy Sunday. Why is that?
I think (and this theory would be easy enough to test if the water was warmer or if I wasn’t such a sissy) that the slope of the beach is just different on either side of this little jetty or whatever it is. The shallower the slope, the earlier waves of the same wavelength can “feel” the sea floor, or the shorter waves have to be to “feel” the sea floor at the same distance from the water line.
So I think the slope on the left of the jetty is shallower than on the right, making the incoming wave field that is the same on either side (I’m assuming, but give me a good reason for why it shouldn’t be?) behave differently.
Funnily enough, the only reason I ended up on that beach was that I wanted to go watch a cruise ship go through the locks and into the Kiel canal with a friend. And, funnily enough, the ship decided to not go through the Kiel canal, as it did the week before. So we decided that we should go to the beach. Very good decision! :-)
But here is a “before” pic from when I was still thinking I would be writing a blog post about the ship going through the locks. Isn’t the seagull hilarious, posing like that?
You see them a lot here on Kiel fjord when it’s windy, and this is what they looked like last Saturday: Foam stripes than run parallel to the coast for as long as the coast is a sea wall (or at least something fairly straight). What’s going on there?
So I think there is just a surface convergence there, parallel to the coast, probably related to the typical wavelength. So the question should probably be: Why is there a convergence parallel to the coast independent of the wind direction? What do you think?
Occasionally working from home is awesome for many reasons, but mainly because I can use the time usually spent on commuting on … wait for it … wave watching. With my cup of coffee so I can warm up my fingers in between taking tons of pictures.
But I just love it. See below how the seagull is making waves where it is swimming, but is surrounded by a much larger circle, too, that it started when it landed on the water?
And especially gorgeous in the morning light: The reflections of sunlit structures on the water. The pier you see above gets distorted into something like this:
And if you look closely, you see the ring waves radiating from where the pylons disturb the water surface as waves go by.
I absolutely love to watch how the much longer waves can cause these ring waves with such a short wave length, and how they are deformed again by the waves that caused them. I can look at this for a long time without getting bored, it is so calming to me! Especially in the early morning light.
But anyway, time to start working. Have a great day everybody!