Category Archives: demonstration (difficult)

Please discuss: Experimental setup for Nansen’s “dead water”

During my last visit to Bergen in August, we set up a nice “dead water” experiment. However, there are nice experiments, and then there are awesome experiments, and since Elin wants to use this experiment in her teaching of the ocean and atmosphere dynamics class, we are going for the latter!

So I’ve done some reading and this is what I have come up with (and I am posting this before we’ve actually run the experiment as basis for discussion with Elin and anyone else who might be interested in discussing this. If you have any comments to share, please do! This is by no means final and I am really happy about any kind of input I am getting!)

Why we want to do an experiment

The ocean & atmosphere dynamics course is really theoretical. It would be nice to add something practical! At least for me it really helps to raise motivation to buckle down and think about the theory if I have observed something and I learn theory in order to understand or manipulate what I observed rather than just for the sake of learning theory.

What I want students to get out of the activity

Yay, learning outcomes! I know, people hate it when I start talking about those, but I really think they are the best starting point. So here we go:

  • Read (authentic) scientific literature, extract relevant information, apply it to an experiment and modify parameters accordingly
  • Get an intuitive understanding of the behaviour of internal waves
  • Explain qualitatively (and quantitatively?) how the speed of the boat and the phase velocity of internal waves relate to the drag on the boat

Why this experiment

  • Internal wave experiments get complex very very quickly. This is a two-layer system that should be comparatively easy to both control (Ha! I wish…) and interpret (Ha!! Yes. I know…).
  • This is a very nice historical example, too, going back to Nansen’s Fram expeditions. Nansen is a national hero in Norway, the Bjerknes Centre for Climate research which I am currently visiting is named after Bjerknes, who was involved in figuring this out. So lots of local references!

Setup of the experiment

Stratification

John Grue’s (2018) article “Calculating Fram’s Dead Water” uses the historical observations described by Nansen in “Farthest North” (1897) to quantify the conditions that led to Nansen’s observations: Nansen found a reduction of speed down to 1/5th of the expected speed, and Grue relates this to a density stratification, specifically a pycnocline depth. I’m using the Grue (2018) article as basis for our stratification in the tank, which we set up to best resemble the one the Fram experienced.

Layer depths

Grue describes a strong wave wake and force for a ratio of the ship’s draught (b0) to upper layer depth (h0) close to 1. For our model “Fram”, b0 is 5cm, which leads to an h0 of 5cm, too.

Grue used a ratio of h0/h1 of 1/18, which would lead to h1 of 90 cm. This is unfortunately not possible since our tank is only 50cm deep (of which the upper two cm cannot be used because of braces needed to stabilise the tank, and the water level needs to be another 3 or so cm lower because the ship will need to be able to pass below the braces. Hence our max h1 is approximately 40cm, leading to a ratio of h0/h1 of 1/8. No idea if this makes a difference? Something for students to discuss…

We could obviously also use a smaller model ship with half the drought and we’d be fine. Maybe we should do that just to figure out if it makes a difference.

Density stratification

To set up the density, we can manipulate both temperature and salinity of the water we are using.

For practical reasons, the temperature the water in our tank should be room temperature (so the tank can sit all set up, waiting for class, without equilibration with the room messing things up). Temperature in the teaching lab was T0=20.5°C when I checked this morning.

To minimize the amount of salt we need to use, we’ll use the freshest possible setup, with the upper layer having a salinity of S0=0g/l.

Grue describes a density difference between the layers of ρ0/ρ1 = 1/1.028. Using the density ρ0=0.998 g/l (calculated from T0 and S0 as above), this ratio leads to a density of ρ1=1.026g/l. For T1=T0=20.5°C, S0 thus needs to be 36g/l. (Phew! And seeing that I typically use 0 for “fresh” and 35 for “salty” anyway, this was a lot of thinking to come to pretty much the same result ;-))

How to move the boat

After just pulling it by hand in previous experiments (which was surprisingly difficult, because you need to pull veeery slowly, without jerking on the string), we’ve been thinking about different ways to move the boat.

First we thought we should program an Arduino to really slowly pull the ship through the tank, and use a dynamometer (you know, one of those spiral feathers that shows you how much force is applied by how far it stretches. Or the easy version, a rubber band) to figure out the drag of the ship.

But as I looked a little more into the experiment, and I found a really neat website by Mercier, Vasseur and Dauxois (2009) describing the experiment and the weight drop setup they used. They make the point that the dead water phenomenon is actually not about a constant speed evolution, it’s about applying a constant force and seeing how the boat reacts to that. Which I find convincing. That way we see the boat being slowed down and accelerating again, depending on its interactions with the internal waves it is creating which is a lot more interesting than seeing a feather or rubber band stretch and contract.

Mercier et al. have the boat strapped to a belt with constant tension on it, which they then force via a pulley system with a drop weight of a few milligrams (I think our friction might be higher then theirs was, so we might need a little more weight!).

Only problem here (and I am not quite sure how big a problem this really is): We can only pull the boat for a distance as long as the ceiling in the basement is high, and that’s definitely nowhere near the length of our 6m tank. That seems a waste, but maybe a shorter distance is still enough to see all we want to see (and at least we won’t have reflections from the ends of the tank interfering if we pick the stretch in the middle of the tank)? Or is there an easy way to use pulleys or something to have the weight seem to fall deeper? Any ideas, anyone?

10.10.2018 — Edited to include this idea I got on Twitter. This is so obvious yet I didn’t think of it. Thanks a lot, Ed, I will definitely try that! Also, is anyone still doubting the usefulness of social media?

11.10.2018 — Edited: Wow, as a sailor it’s really embarrassing that people have to point me to all kinds of different pulley systems to get this problem done! Only two issues I have now: 1) What I’ve been ignoring so far but can’t ignore any longer: The weight of the rope will increase with the length of the rope, hence the force won’t be constant but increasing, too. Since we are expecting to be working with weights of the order of a couple of paper clips, even a thin yarn might contribute substantially to the total force. Will definitely have to weigh the yarn to figure out how large that effect is! 2) Since we are expecting such tiny weights to be enough, all the blocks needed in a pulley system are already way too heavy, so we’ll have to figure out some light weight fix for that!

Mercier et al. also used a magnet at the back of the ship and one outside the tank to release the boat, which is a neat idea. But, as they point out, one could also just release the ship by hand, which is what I think we’ll opt for.

What we could ask students to do

Figure out the experimental setup

We could ask them to do basically what I did above — figure out, based on the Grue (2018) article, how to run a tank experiment that is as similar as possible to the situation Nansen described having experienced on the Fram.

Discuss layer depths

In the setup I described above, our ration of layer depths is 1/8 instead of the 1/18 assumed in the Grue (2018) article. Does that actually make a difference? Why would it? Do we think the differences are large enough to warrant running the experiment with the 1/18 ratio, even though that means changing the stratification and getting a new boat?

Check on how close we are to theory

For the density stratification as described above, the relationship

gives a phase velocity of the internal wave of c0=0.1m/s, meaning that it would take a wave crest 1min to cross our 6m long tank. We’ll see how that holds up when we do the experiment! And we could ask the students to do those calculations and compare them to the observations, too.

Compare dead water, deep water and shallow water cases

In their 2011 article, Mercier, Vasseur and Dauxois show the drag-speed relationships for dead water, deep water and shallow water (in Figure 1). The resistance will obviously be different for our setup since we’ll likely have a lot more friction, but qualitatively the curves should be similar. Might be fun to test! And also fun to interpret.

Even if we concentrate on the dead water case only (so we don’t have to empty and refill the tank), there is a lot to think about: Why is there a maximum in the resistance in the dead water case with both lower and higher speeds having a lower resistance? Probably related to how the ship interacts with the internal waves, but can we observe, for example, which Froude number that happens at, i.e. how fast the ship is moving relative to the phase velocity of the internal wave (which we both calculate and observe beforehand)?

Now it’s your turn!

What do you think? What’s your feedback on this? My plan is to go down to the lab tomorrow to figure out how to pull the boat with a drop weight. If you think that’s a really bad idea, now would be the time to tell me, and tell me what to do instead! :-)

Really, I welcome any feedback anyone might have for me! :-)

Fun notes that didn’t fit anywhere else

11.10.2018 — Edited: My former colleague Robinson pointed me to a research project he is involved in related to dredging the Elbe river (to make it possible for large container ships to reach the port of Hamburg) where they actually also look at how much ships are being slowed down, not by internal waves necessarily, but by the turbulence and turbidity they cause in the muddy river bed! That’s really cool! But the scaling is completely off from our experiment so their setup is unfortunately not transferable (they drag big objects with constant speed through the actual Elbe and measure the force that is needed).

Waves in a density stratification. One of the most beautiful tank experiments I’ve ever seen.

It’s pretty impressive when a mountain moves through a stratification and generates lee waves. But what I find even more impressive: The waves that travel behind the mountain when the mountain is long gone. See here:

This kind of stuff looks more like a numerical simulation than something actually happening in a tank, doesn’t it? I am pretty stoked that we managed to set up such a nice stratification! Those are the things that make me really really happy :-)

(The setup of this experiment is the same as in this post)

Dead water — the fancy experiment including Nansen himself

Now that we do have a really awesome 12-layer 6-color stratification, we obviously had to do the dead water experiment again. This time we chose to include a not-too-happy-looking Nansen on the ship, too!

I love this even more than the one we did yesterday!

“Coriolis fountain”

We’ve been thinking about Coriolis deflection a lot recently (see links at the end of this post). But this weekend, at Phaenomenta Flensburg, I came across a so-called “Coriolis fountain”. A fountain that you can put into spin and that then changes shape like so:

Uta, remember we talked about this a couple of years ago? Nice puzzle for anyone interested in fluid dynamics…

Watch the movie and be amazed :-)

Fictitious forces (3/5): Coriolis force — how we think it should be taught

So how do we teach about the Coriolis force? The following is a shortened version of an article that Pierre de Wet and I wrote when I was still in Bergen, check it out here.

The Coriolis demonstration

A demonstration observing a body on a rotating table from within and from outside the rotating system was run as part of the practical experimentation component of the “Introduction to Oceanography” semester course. Students were in the second year of their Bachelors in meteorology and oceanography at the Geophysical Institute of the University of Bergen, Norway. Similar experiments are run at many universities as part of their oceanography or geophysical fluid dynamics instruction.

Materials:

  • Rotating table with a co-rotating video camera (See Figure 1. For simpler and less expensive setups, please refer to “Possible modifications of the activity”)
  • Screen where images from the camera can be displayed
  • Solid metal spheres
  • Ramp to launch the spheres from
  • Tape to mark positions on the floor
folie1

Figure 1A: View of the rotating table. Note the video camera on the scaffolding above the table and the red x (marking the catcher’s position) on the floor in front of the table, diametrically across from where, that very instant, the ball is launched on a ramp. B: Sketch of the rotating table, the mounted (co-rotating) camera, the ramp and the ball on the table. C: Student tracing the curved trajectory of the metal ball on a transparency. On the screen, the experiment is shown as filmed by the co-rotating camera, hence in the rotating frame of reference.

 

Time needed:

About 45 minutes to one hour per student group. The groups should be sufficiently small so as to ensure active participation of every student. In our small lab space, five has proven to be the upper limit on the number of students per group.

Student task:

In the demonstration, a metal ball is launched from a ramp on a rotating table (Figure 1A,B). Students simultaneously observe the motion 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. They are subsequently asked to:

  • trace the trajectory seen on the screen on a transparency (Figure 1C),
  • measure the radius of this drawn trajectory; and
  • compare the trajectory’s radius to the theorized value.

The latter is calculated from the measured rotation rate of the table and the linear velocity of the ball, determined by launching the ball along a straight line on the floor.

Instructional approach

In years prior to 2012, the course had been run along the conventional lines of instruction in an undergraduate physics lab: the students read the instructions, conduct the experiment and write a report.

In 2012, we decided to include an elicit-confront-resolve approach to help students realize and understand the seemingly conflicting observations made from inside versus outside of the rotating system (Figure 2). The three steps we employed are described in detail below.

folie2

Figure 2: Positions of the ramp and the ball as observed from above in the non-rotating (top) and rotating (bottom) case. Time progresses from left to right. In the top plots, the position in inert space is shown. From left to right, the current position of the ramp and ball are added with gradually darkening colors. In the bottom plots, the ramp stays in the same position, but the ball moves and the current position is always displayed with the darkest color.

  1. Elicit the lingering misconception

1.a The general function of the “elicit” step

The goal of this first step is to make students aware of their beliefs of what will happen in a given situation, no matter what those beliefs might be. By discussing what students anticipate to observe under different physical conditions before the actual experiment is conducted, the students’ insights are put to the test. Sketching different scenarios (Fan (2015), Ainsworth et al. (2011)) and trying to answer questions before observing experiments are important steps in the learning process since students are usually unaware of their premises and assumptions. These need to be explicated and verbalized before they can be tested, and either be built on, or, if necessary, overcome. 

1.b What the “elicit” step means in the context of our experiment

Students have been taught in introductory lectures that in a counter-clockwise rotating system (i.e. in the Northern Hemisphere) a moving object 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.

A typical laboratory session would progress as follows: students are asked to observe the path of a ball being launched from the perimeter of the circular, not-yet rotating table by a student standing at a marked position next to the table, the “launch position”. The ball is observed to be rolling radially 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 ball dropped off the table’s edge so as to catch the ball in the non-rotating case. The position is also marked on the floor with insulation tape.

The students are now asked to predict the behavior of the ball 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 ball 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 ball, will also be able to catch it him/herself. Ordinarily the students confirm that such a situation is indeed possible.

 

  1. Confronting the misconception

2.a The general function of the “confront” step

For those cases in which the “elicit” step brought to light assumptions or beliefs that are different from the instructor’s, the “confront” step serves to show the students the discrepancy between what they stated to be true, and what they observe to be true.

2.b What the “confront” step means in the context of our experiment

The students’ predictions are subsequently put to the test by starting with the simple, non-rotating case: the ball is launched and the nominated catcher, positioned diametrically across from the launch position, seizes the ball as it falls off the table’s surface right in front of them. As in the discussion beforehand, the table is then put into rotation at incrementally increasing rates, with the ball being launched from the same position for each of the different rotational speeds. It becomes clear that the catcher need not adjust their position, but can remain standing diametrically opposite to the student launching the ball – the point where the ball drops to the floor. Hence students realize that the movement of the ball 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; circles with radii decreasing as the rotation rate is increased. Furthermore, to add to their confusion, when observed from their positions around the rotating table, the path of the ball 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. cross hairs drawn on the table’s surface or the bars of the camera scaffold, relative to which the ball does, indeed, follow a curved trajectory. To overcome this latter trickery of the mind, 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 ball is observed to indeed be moving in a straight line towards the observer, irrespective of the rate of rotation of the table.

To further cement the concept, the table may again be set into rotation. The launcher and the catcher are now asked to pass the ball to one another by throwing it across the table without it physically making contact with the table’s surface. As expected, the ball moves in a straight line between the launcher and the catcher, who 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.

  1. Resolving the misconception

3.a The general function of the “resolve” step

Misconceptions that were brought to light during the “elicit” step, and whose discrepancy with observations was made clear during the “confront” step, are finally corrected in the “resolve” step. While this sounds very easy, in practice it is anything but. The final step of the elicit-confront-resolve instructional approach thus presents the opportunity for the instructor to aid students in reflecting upon and reassessing previous knowledge, and for learning to take place.

3.b What the “resolve” step means in the context of our experiment

The instructor should by now be able to point out and dispel 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 is not a given, nor does it happen instantaneously. Oftentimes further, detailed discussion is required. Frequently students have to re-run the experiment themselves in different roles (i.e. as launcher as well as catcher) and explicitly state what they are noticing before they trust their observations.

Possible modifications of the activity:

We used the described activity to introduce the laboratory activity, after which the students had to carry out the exercise and write a report about it. Follow-up experiments that are often conducted usually include rotating water tanks to visualize the effect of the Coriolis force on the large-scale circulation of the ocean or atmosphere, for example on vortices, fronts, ocean gyres, Ekman layers, Rossby waves, the General circulation and many other phenomena (see for example Marshall and Plumb (2007)).

Despite their popularity in geophysical fluid dynamics instruction at the authors’ current and previous 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. In many cases, setting the exact rotation rate is not as important as having a qualitative difference between “fast” and “slow” rotation, which is very easy to realize. In cases where a co-rotating camera is not available, by dipping the ball 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 method described in this manuscript is easily adapted to such a setup.

Lastly we suggest using an elicit-confront-resolve approach even when the demonstration is not run on an actual rotating table. Even if the demonstration is only virtually conducted, for example using Urbano & Houghton (2006)’s Coriolis force simulation, the approach is beneficial to increasing conceptual understanding.

Pressure distribution on a wing

Another neat experiment in the collection I’ve recently been talking about is measuring pressure at different points on a wing profile. It’s not terribly surprising that – as long as the wing is oriented in the correct way in the flow – pressure is high below the wing and low above it. Kinda the whole point of having a wing profile. Yet, it’s nice to actually measure it.

Screen shot 2015-07-12 at 6.09.01 PM

Measuring pressure at different points on a wing profile

And yes – next time I set up that manometer I’m gonna make sure that it’s a little easier to get a good reading!

Pitot tube

Another one of those awesome hydrodynamics toys: A Pitot tube!

This is what it looks like:

IMG_1859

Pitot tube. The tip pointing downward in this picture would point right into the flow.

What you can’t see here is the little hole at the tip of the tube that is pointing downwards in the picture. What the Pitot tube measures is the pressure difference between that hole (the stagnation pressure since it’s the stagnation point) and the vents some 3.5 cm above (the static pressure), from which you can calculate the dynamic pressure, hence air speed of a plane (if the Pitot tube was mounted on said plane) or, in our case, the speed of air flow from a fan relative to a stationary Pitot tube.

Again, I’m sadly too lazy to calculate anything, but you can take the measurements from the movie below and do it yourself if you so desire! :-)

Playing with Venturi tubes II

On Monday I posted about playing with Venturi tubes. Guess what: We are going to play more today! Because today the Venturi tubes are connected to a “proper” manometer:

Screen shot 2015-07-12 at 5.19.03 PM

Venturi tube connected to manometer

Now, if I wasn’t so lazy this would be a great opportunity to get good readings of the pressure differences caused by different flow rates. However, I’ll just let the images speak for themselves. Enjoy!

 

Playing with Venturi tubes

A Venturi tube is one of the things one hears about in hydrodynamics class all the time, but one never gets to see them for real. And even though I just said on Friday that the thing that I found most fascinating in the aerodynamics collection I got to borrow recently was to see how the flow reversed downstream of a paddle I might have to take that back, because the hands-down most exciting thing was to play with a Venturi tube!

So what is all the fuss about? This is what a Venturi tube looks like:

IMG_1854

Venturi tube in the no-flow state

Basically, it is a tube, open at both ends, that gets thinner in the middle and wider again. All the rest you see in the picture is props: The mouth of the fan in the top right, and then three U-tubes filled with dyed water below the Venturi tube.

The Venturi tube is so famous because it nicely demonstrates the Venturi effect, namely the reduction in pressure that occurs when a flow is accelerated. In the case of the Venturi tube, the flow is accelerated in the thin section of the tube, where – for continuity reasons – it has to go faster than in the wider sections. So what happens when we turn on the fan?

IMG_1853

Venturi tube. Pressure decreases in the thin section of the tube, visible by the red water being “sucked up” in the middle U-tube

Yep! The levels in the three U-tubes change. And most importantly, the pressure for the middle U-tube drops, as demonstrated by the red water being “sucked up” on the side of the U-tube that is connected to the Venturi tube.

Watch the movie below to see this in action:

Flow direction reversing downstream of obstacle

One of the things that fascinated me most when playing with the huge fan we used to look at the flow downstream of a paddle was how the flow direction reverses.

Unfortunately (alas, it was to be expected) we didn’t really see this on the paper towel stream line test I did the other day.

But here is another way to visualize it: using a propeller!

IMG_1931

Propeller in air flow

Depending on the direction the air flows at the propeller, its direction changes. So as we move it towards and away from the paddle, when the flow direction changes, so does the direction of rotation of the propeller, too.

Watch!