Sea ice formation, brine release, or: What ice cubes can tell you about your freezer

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Many of my kitchen oceanography experiments use dyed ice cubes, usually because it makes it easier to track the melt water (for example when looking at how quickly ice cubes melt in freshwater vs salt water, or for forcing overturning circulations).

But the dyed ice cubes tell interesting stories all by themselves, too!

Salt water doesn’t freeze

“Salt water doesn’t freeze”? Then how do we get sea ice in the Arctic, for example?

When freshwater freezes, the water molecules arrange in a hexagonal crystal structure. If there is salt (or anything else) in the water, however, the ions don’t fit into the regular structure. Ice freezes from the water molecules, and all the disturbances like salt get pushed in the last remaining bits of liquid water, which therefore gets higher and higher concentrations of whatever was dissolved in it. As those little pockets with high concentrations of salt get cooled further, more and more water molecules will freeze to the surrounding freshwater ice, leading to even higher concentrations of salt in the remaining liquid water. So the freshwater is freezing, while rejecting the salt.

Of course if you cool for long enough, also the last bit of remaining water will freeze eventually, but that takes surprisingly long (as you can try by freezing salt water in some of the cups ice cube trays and freshwater in others, for comparison. Also the structures of freshwater vs saltwater ice look very different and are interesting to look at, see how here).

“Brine release”

When the ocean freezes, this rejection of high-salinity water leads to interesting phenomena: Even when you melt it again to include all the pockets of high salinity water, sea ice will have salinities way lower than the water it froze from. This is because of a process called brine release. Since you are cooling the ocean from above, sea ice also forms from the surface downwards. This means that it is easy for the salty water to be pushed, “released”, or “rejected”, downwards, into the liquid ocean below. That ocean will then of course get more salty right below the ice!

In the picture below you see something similar happening in the left pictures. Instead of salt, I have used blue food dye for visualization purposes. In the top left, you see an ice cube exactly as it looked when I took it out of the ice cube tray it froze in, and in the bottom left you see the same one after I let it melt a little bit so the surface got smoother and it got easier to look inside (a lot more difficult to hold on to, though!).

Do you see how the top part of the ice cube is pretty much clear, while the bottom part is blue? That’s because it froze top-to-bottom and the dye got pushed down during the initial freezing process!

Stuck in an ice cube tray

Something else that you see in the top left picture is the effect of the ice cube being stuck in the ice cube tray as it froze: Pores filled with blue dye that had nowhere to escape!

Had I taken out those ice cubes earlier, when they had just frozen half way through, we would have found a clear ice layer floating on a cold, blue ocean. Maybe I should do that next time!

Checking on the temperature distribution of your freezer

Something else fun we can observe from the right pictures: Here, the dye was concentrated towards the center of the ice cube rather than the bottom! How did that happen?

My theory is that those ice cubes were located in an area of the freezer that was cooling from all sides (more or less) equally, whereas the ones shown on the left must have been placed somewhere where cooling happened mainly from the top.

So if you ever want to know where the cooling in your freezer happens, just put lots of dyed little water containers everywhere and check from which side the dye gets rejected — that’s the cooling side! Actually, I might check that for the freezer below just for fun. Would you be interested in seeing that done?

Now it’s your turn!

Let’s look back at the ice cubes I froze yesterday in the picture above. I’ve now written about a lot of things I see when I look at them. What else do you see? Do you think it’s interesting to use with kids, for example? I’ve used those experiments with first year university students, too, I think there is plenty to observe and explain here!

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

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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).

This week I am taking over @IAmScicomm!

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You might think that I’d be busy enough with my visiting fellowship at the Bjerknes Centre for Climate Research in Bergen this month, and you would be right.

However, I’ve always* wanted to take over one of the rotating Twitter accounts (You know? Those accounts that tweet about certain topics, but are being run by a different person every week. People follow it for the topic and get to see a new person’s view on things every week. A very cool thing when you want to be exposed to a lot more people than you usually are and that are all interested in that topic!). And when I signed up for it in spring, October still seemed so far away that it seemed to be a good idea to do it then.

So this week, I am curating @IAmScicomm! Which I am super excited about, although it is also kinda scary. 18.6k followers is a little different from my usual couple of hundred… Anyway, this is what I am proposing to talk about:

Come join the discussion! :-)

Last week I already did a similar thing already for @geoscitweeps.”Only” 4.6k followers were slightly less scary, and I had the super cool surface drifters to tweet about. @geoscitweeps is another really interesting account you should be following!

*Yes, ALWAYS. It was actually pretty much on top of my list when I started my private #scicommcall, only at that time there were no vacant weeks available that suited my schedule, so I put it off. But now here we are!

Mystery picture! Can you solve this wave riddle?

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Today is a great day for a wave riddle! Below you see a picture I took on my walk home the other day.

Can you tell what caused those waves? (Solution underneath the picture!)

In the picture above, we are looking at the curb and the lid of a drain. There are two ring-shaped waves radiating outward from centres that seems to be sitting pretty much on the edge of the curb stone on both sides of the drain cover, and these are the waves we are trying to explain.

Now there are several possible explanations for ring-shaped waves:

Raindrops falling on the water

As we see from the absence of ring-shaped waves on the water surface (except for the two we are trying to explain), it wasn’t raining at the time this picture was taken, hence raindrops are not the explanation to our observed wave pattern.

Also, there are a lot of concentric rings radiating outwards from each of those two points. This doesn’t work well with a “rain drop” explanation. Raindrops do create more than one ring wave because a raindrop makes the water surface oscillate and sometimes secondary raindrops are thrown up into the air and then fall back into the same spot, creating a wave ring of their own. But still, raindrops typically do not create more than two or three rings. But as you see from the picture above, there are a lot more concentric waves!

Something other than rain dripping on the water

So if raindrops are out, since we can’t expect them all to be falling just in those two centres of the wave rings in order to create so many concentric rings, how about water dripping (or even pebbles falling, for that matter) from some defined place to create that structure?

This is actually a good explanation, except that we would expect to see some evidence of something falling. Yes, we might have just captured the picture right after the last drop or pebble or whatever else of a whole series of things dropped in the water, so we get the waves but don’t see what dropped in. But that’s pretty unlikely, isn’t it?

So on to the next explanation:

Something beneath the water surface poking at the surface from below

This is actually something we see a lot: If there are rocks or other obstacles on a shore and we have long waves washing over the obstacle, it will create wave concentric rings on the surface. This happens because when a wave trough goes over the obstacle, water is displaced in a different way than if there wasn’t an obstacle and the wave could just pass through undisturbed. And then, when a crest comes, the obstacle is in the way again, interrupting the orbital movements in the wave.

This might actually be the case in the picture above — except we don’t see any evidence of long waves on the puddle. So this explanation is out, too.

Water draining from the puddle

So now we’ve come to the last option that I can think of: Water draining from the puddle into the drain. And not only that: Water going around an obstacle and through two small-ish holes while draining underneath the drain cover! Those holes would be the centres of the wave rings. And the waves would be created by the little surges of water leaving whenever the water level was high enough, then a short pause as the reservoir filled up enough to overcome friction and surface tension, and then the next surge.

And after thinking through all this, I bent down to check, and indeed — the last solution is the correct one! Would you have guessed? :-)

Why are they so much slower than I thought? Observing the group velocity vs phase velocity of waves

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Have you ever seen a speedboat drive past, looked at its wake moving torwards you, then gotten distracted, and when you look back a little while later been surprised that the wake hasn’t moved as far towards you as you thought it would have during the time you looked away?

Well, I definitely have had that happen many times, and the other day I was sitting on the beach with a friend and we talked about why you initially perceive the waves moving a lot faster than they turn out to be moving in the end. While I didn’t film it then, I’ve been putting my time on the GEOF105 student cruise to good use to check out waves in addition to the cool research going on on the cruise, so now I have a movie showing a similar situation!

But let’s talk a little theory first.

Phase velocity

The phase velocity of a wave is the speed with which you see a wave crest moving.

Waves can be classified into long vs short waves, or deep- vs shallow water waves. But neither deep and shallow, nor long and short are absolute values: They refer to how long a wave is relative to the depth of the water in which it is moving. For short or deep water waves, the wavelength is short relative to the water depth (but can still be tens or even hundreds of meters long if the water is sufficiently deep!). For long or shallow water waves, the wave length is long compared to the water depth (for example Tsunamis are shallow water waves, even though the ocean is on average about 4 km deep).

For those long waves, or shallow water waves, the phase velocity is a function of the water depth, meaning that all shallow water waves all move at the same velocity.

However, what you typically see are deep water waves, and here things are a little more complicated. Since phase velocity depends on wave length, it is different for different waves. That means that there is interference between waves, even when they are travelling in the same direction. So what you end up seeing is the result of many different waves all mixed together.

If you watch the gif below (and if it isn’t moving just give it a little moment to fully load, it should then start), do you see how waves seem to be moving quite fast past the RV Harald Brattstrøm, but once you focus on individual wave crests, they seem to get lost, and the whole field moves more slowly than you initially thought?

That’s the effect caused by the interference of all those waves with slightly different wave lengths, and it’s called the group velocity.

Group velocity

The group velocity is the slower velocity with which you see a wave field propagate. It’s 1/2 of the phase velocity, and it is the velocity with which the signal of a wave field actually propagates. So even though you initially observed wave crests moving across the gif above fairly quickly, the signal of “wave field coming through!” only propagates with half the phase velocity.

Usually you learn about phase and group velocities in a theoretical way and are maybe shown some animations, but I thought it was pretty cool to be able to observe it “in situ!” :-)

At the end of the rainbow you’ll find … home-made surface drifters

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For Lars Henrik and Harald‘s GEOF105 class we are deploying home-made surface drifters on the student cruise. Today I had the opportunity to join the cruise again, and since the weather today made for beautiful pictures, I just have to share them here.

First, at the end of every rainbow, as we all know, you’ll find … home-made surface drifters!

Inga and Algot getting the drifters ready for deployment

Inga and Algot getting the drifters ready for deployment

The research ship we are on is the Hans Brattstrøm — cosy ship with a super nice and helpful crew!

We are sailing on RV Hans Brattstrøm

We are sailing on RV Hans Brattstrøm

The drifters themselves are equipped with a sea anchor made from a plastic bucket and four paint roller trays underneath a buoy, and then on top all kinds of equipment to make sure nobody runs over it: A safety flag, a lamp, a radar reflector. And, of course, the GPS sender!

Isn't it cool how those wave rings radiate from our drifter?

Isn’t it cool how those wave rings radiate from our drifter?

What we are using those surface drifters for? To determine the circulation in the fjord right outside Bergen. There are several things that might have an influence: Tides, wind, freshwater runoff from the land… And a tilted sea surface (although it is probably not as tilted as in the picture below…)

Drifter in front of RV Hans Brattstrøm in front of mountains covered in clouds

Drifter in front of RV Hans Brattstrøm in front of mountains covered in clouds

Another amazing day “at sea”, thanks for having me along, Lars Henrik!

Drifter in front of RV Hans Brattstrøm

Drifter in front of RV Hans Brattstrøm

Taking water samples

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A big part of any oceanographic research cruise: Taking water samples.

Here is a group of students practicing how to arm Niskin bottles that will go into the ocean open on both ends, and that will then, when the whole rosette is on its way up again, be closed one after another at depths that promise to be interesting in terms of water properties.

Arming those Niskin bottles is actually not as easy as it looks, there is a strong spring going through the bottle, connecting the lids. And it is actually pretty painful if you accidentally close the bottles while some part of your body is between the bottle and the lid. Ask me how I know…

When the bottles are all open, the rosette can be lifted off the deck and into the sea.

Usually, rosettes are equipped with instrumentation in addition to the Niskin bottles, usually a CTD, measuring conductivity (to calculate the salinity from), temperature, and depth (actually measuring pressure, which converts easily into depth). I contributed to a very nice movie about how CTDs work a couple of years ago, check it out!

And now the rosette is finally in the water.

Water samples in physical oceanography are mainly used to calibrate the sensors on the CTD, which give (pretty much) continuous measurements throughout the whole depth of the water column. And that’s also what we want to use our water samples for — we have a hand-held conductivity probe that is right now producing values that cannot be correct. How we are going to deal with that? We (and you!) will find out tomorrow! :-)

Home-made surface drifters

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A bicycle safety flag, a plastic bucket, four paint roller trays — what are those people doing there?! Until now this might almost count as kitchen oceanography!

Home-made surface drifters

But it’s only almost kitchen oceanography; at least my kitchen isn’t usually stocked with GPS trackers, which is what is mounted on this contraption. Let alone the research ship we used to deploy it. So this must surely count as real oceanography then!

Lars Henrik and students deploying a surface drifter to measure the surface current in a fjord

Lars Henrik and students deploying a surface drifter to measure the surface current in a fjord

Above, you see  Lars Henrik and his students deploying a surface drifter. The red buoy keeps it floating at the surface, the chain hanging below is heavy enough to make sure it stays upright. The bucket and four paint roller trays act as sea anchor so the whole thing moves with the water rather than being blown about by the wind. A safety flag, radar reflector and light make sure nobody accidentally sails over it, and the GPS sender lets the position be tracked.

For example like this:

Screen shot of the map and the drifter positions from my mobile phone

Screen shot of the map and the drifter positions from my mobile phone

Above, you see what it looked like when we had already deployed three of our four surface drifters (the red ones that are moving so slowly that the software tells us they aren’t moving at all), while the fourth one is still onboard the ship, moving to the position where it will be deployed (the green one moving at 3km/h).

Follow their positions on your mobile device!

Following surface drifters’ paths in real time is pretty awesome in itself, but what makes it even better is that the GPS positions can be accessed online from any device. Below, for example, you see the positions on my phone with the drifters behind it in the water (if you look really closely, that is. But they were there!).

My mobile phone with the drifters' positions and the drifters in the background

My mobile phone with the drifters’ positions and the drifters in the background

What you also see is that three of the drifters have huddled together after a couple of hours out in the fjord. Nobody really knows why yet, but that’s what we are here to find out!

Just from observing the wind and the movement of the drifters throughout the day, it seemed that the surface circulation in this fjord is dominated by the wind over the tides. But there will be a Master’s thesis written on the data we collected today (plus a lot more data and a regional ocean model!) so we’ll soon know how good my assumptions are and what really drives the surface currents here.

Three of the drifters huddling together due to currents that have yet to be understood

Three of the drifters huddling together due to currents that have yet to be understood

Come time to recover the drifters, the weather wasn’t quite as nice as earlier throughout the day. Just to give you an impression of the conditions under which the drifters were recovered:

Algot and Inga recovering a drifter

Algot and Inga recovering a drifter

Yep, if you look at the sea state, there is nothing to complain about, really, just a little water coming from the sky! But it was cold water… ;-)

And everything got recovered safely and made it back to port — ready to be deployed again tomorrow to gather more data and understand the fjord a little better. Exciting times! Thanks for letting me be part of this GEOF105 adventure, Lars Henrik!

The drifters coming home to the port of Bergen

The drifters coming home to the port of Bergen

Rainbows in regnbyen Bergen

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Yesterday when approaching Bergen airport, I saw something super cool: The lower half of a rainbow!

Even though I grabbed my phone and snapped a picture in record time, I didn’t manage to capture it. Bummer! But that doesn’t keep me from writing about it while showing you a “normal” rainbow I took a picture of a couple of minutes later.

Rainbow seen from a plane approaching Bergen airport

Rainbow seen from a plane approaching Bergen airport

Have you ever seen the lower half of a rainbow?

But can you imagine it? A u-shaped rainbow?

Have you ever seen anything like that before? It’s not something that we are used to seeing, at least not if we are looking a) at rainbows that are occurring on natural rain “curtains” and b) while we are on the ground. Let me explain…

Under perfect conditions, a rainbow is a full circle

Imagine you are a floating in space, looking at a curtain of rain drops. The sun is shining from behind you onto that curtain. What you then see on that rain curtain is a full rainbow circle, purple towards the middle and red towards the outside.

The size of the rainbow depends on how far away from the rain curtain you are. Imagine looking at the shadow that your head is making on the rain curtain. The line from your eyes to the shadow of your head will be our reference. Now imagine looking at any point on the rainbow. The line from your eyes to any point on the rainbow will be at a 40 to 42 degree angle to the reference line (40 degrees if you are looking at a purple point, 42 if you are looking at a red point, anything in between for the other colors).

Tweaking the size of the rainbow

Now imagine moving the rain curtain farther away. The angle between the reference line and the line to the rainbow stays the same, but the further away the rain curtain, the larger the rainbow. And vice versa: The closer the rain curtain, the smaller the rainbow!

So now imagine a nice curtain of droplets that you can walk towards and away from (sprinklers! garden hoses!) — the further you walk away, the larger the rainbow gets. And the closer you come, the more it shrinks again.

Standing on the ground, you only see the upper half

If you walk close enough to the rain curtain, you can actually see a full rainbow. But typically when we think of rainbows, we think of those occurring naturally, and then the rain curtains aren’t as neat and tidy as those from a sprinkler, and rainbows that we see are usually far far away, and thus really big. And that is why we aren’t used to seeing the lower half of a rainbow: Where the lower half would be there isn’t any rain curtain for it to appear on, because there is ground there! And the only way not to have the rainbow hit the ground is either have it close enough in front of us so it’s too small to even reach the ground, or to look at it from a plane that is high enough above the ground that even a large rainbow has enough space above the ground to fully appear on the rain curtain.

Next steps

So where do we go from here? I need to a) play with sprinklers and take pictures of rainbows! b) draw illustrations of the stuff I tried to describe above, and c) hope that I’ll be faster next time to finally get my u-shaped rainbow picture from a plane!

Thinking about the Doppler effect as of a boat sailing against the waves!

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I can’t believe I haven’t written about this on my blog before, thanks Markus Pössel for reminding me of this great way to understand the Doppler effect!

Doppler effect, or why ambulances change their sound as they race past you

Doppler shift is everywhere, but it’s maybe not obvious how to imagine what’s going on if you think of sound waves.

But look at the picture below. Can you imagine the sound of those waves lapping against the shore?

Now imagine taking a speed boat riding out on the water. Can you feel how you are bouncing over the wave crests, and notice how you are meeting them a lot more often than when you were standing on the beach, looking out on the water?

Or imagine being a surfer, riding that perfect wave. You are staying with the same wave crest for a really long time, while in front of you creat after crest breaks on the beach.

Yes, the Doppler effect is as easy as this! As you are moving with or against the waves, their frequency changes. Totally obvious when you think about waves on water, right? But the same happens with sound waves, and in their case, a changed frequency means that the sound appears to change pitch. If the ambulance is coming towards you, the sound gets higher and higher, and then as it races away, it gets lower again. So now you don’t even have to look when you hear an ambulance, you know whether it’s coming or going! (Just kidding! Please definitely look out, anyway, and don’t get run over!)