Tag Archives: refraction

Sunday #wavewatching. Shallow water waves, deep water waves, #wakewatching, reflections, refractions, and more.

This is the blogpost I wanted to write today before I got distracted by all the adventures on MS Stadt Kiel with sightseeing and swing dancing and all the good stuff that wasn’t wave watching. I had even uploaded all the pictures of this morning’s wave watching walk on my blog already, but then things just got too exciting… But here we go now!

Here we see a really nice example of shallow water waves: The wavelength is a lot longer than the water depth and the shape of the waves looks very different from the almost sinusoidal waves in deep water: The troughs are very long and the crests short and steep.

And here they show the influence of water depth on phase velocity: Where the water gets shallower and eventually the land falls dry, the waves get slowed down. This means the part of the wave crest that is still in deeper water is faster, overtaking the shallower part, and thus the waves get bent around, towards the shallower areas in the water.

For comparison here the shape of waves in deeper water. Do you see how they are much more sinus-shaped?

Above we also see fairly well how gusts of wind change the water’s surface roughness: where the water surface looks darker, it is covered in small capillary waves caused by gusts of wind.

Btw, if you were wondering where the longer wave length waves came from: They are the wake of a boat accompanying the training session of some race kayakers.

When those waves hit the sea wall, we see nice reflections and a checkerboard pattern!

Btw, I find it super eye opening how the structures that, to me, absolutely dominate the picture above are not picked up as dominant in my comic app (see below). Of course the structures of the power plant or sea wall are more prominent, but the criss cross of the reflected waves is hardly visible. Maybe that’s how little it is visible to most people even in the photos? On my Instagram poll on whether comic-y-fying pictures helps to show what I am talking about, 60% of the responses were that yes, comics make it easier to see what I mean. Not quite sure yet what I will do with that information moving forward…

Something else really curious today, btw: The way the sea floor looked! Usually there are lots of ripples here, mostly parallel to the sea wall. And today these weird patterns of darker (finer?) sediment. I think I need to observe the sea floor more consciously to figure out what’s going on there!

And now the race kayak and accompanying boat are coming back. I love how you see their wake and then that bird’s wake in the picture below!

And then, finally, some larger waves, again the wake of some ship that I didn’t pay attention to.

And sometimes, the reflections are just suuuuuper difficult to see when you don’t know what you are looking for. Do you see them in the picture below?

The wonders of a Wadden Sea. Or what someone addicted to #wavewatching thinks they are

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 ;-)

Influence of wind and water depth on a wave field (or: a beach vacation in Dornumersiel)

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?

Reflecting waves, reflected and refracted light, and a Fata Morgana

How much physics can you spot in a single picture?

What I see here:

  • Waves and their reflection on the sea wall (Do you see the two main fields? One coming in from the top right, and then the other one (technically the reflection of the first one) going out to the top left)
  • Total reflection of light: Looking at the water surface at steep angles, we can look into the water and see the sandy sea floor and some stuff growing on it. At small angles, all we see is the reflection of the sky (and see how the angle we look at the water surface at depends not only on the direction we are looking, but also the local orientation of the water surface that is deformed by waves!)
  • The way light is focussed on the sea floor by the incoming wave field, creating these bright lines parallel to the incoming wave crests, but nothing similar going on for the reflected wave field
  • The Fata Morgana might be a little difficult to see, but if you click on the picture below, or even more clearly in the one at the bottom of this post, they will enlarge and you can see the light house (on the horizon, between the bird and the ColorLine) seemingly balancing on a rock with a very slim base, when in reality the base of the lighthouse only gets wider towards the ground…

And then there is of course lots more physics to see:

  • A bird flying
  • A ship swimming
  • water vapour condensing into clouds and condensation trails
  • a breeze changing the texture of the water surface

What else do you see?

Guest post: Alice shows magic tricks and explains refraction of light in water

My friend Alice Langhans runs a super cool science communication Instagram (@edu_al_ice), where she posts about her experiences as PhD student in physics education research. And there is a lot more going on on that Instagram than just pretty (but oh so pretty!) pictures. I make sure to read all her posts, because there are always interesting, motivating, inspiring thoughts hidden behind that “read more” button. And now she’s even started a new series of physics experiments on #experimentalfriday, and I am super excited that she wrote this guest post for me!

But now look at the picture below, and then read about some magic! :-)

Alice writes:

Magic! One of the arrows changes its direction and here is why:

Click for large picture. Picture by Alice Langhans.

First, the arrows are unchanged and visible through the glass.

Click for large picture. Picture by Alice Langhans.

Adding water to the glass, the image of the arrow gets bigger and appears mirrored!

Click for large picture. Picture by Alice Langhans.

With even more water even the second arrow appears bigger and mirrored.

Click for large picture. Picture by Alice Langhans.

The waterglass I used is round and the refraction of light in water is different than in air, which makes the water glass act like a positive (converging) lens. This is why the image of the arrow appears bigger and mirrored.

Think of the arrow as many points, each of which is the source of a divergent bundle of light. The light coming from the point that is the arrowhead on the right, is refracted through the waterglass and reaches our eye to the left. The light from the left end of the arrow refracts in such a way that it now enters our eye on the right side.

Notice, how you can also see how the upper arrow appears even bigger? The glass is more wide at that height, magnifying properties of the water glass lens are therefore increased.


Isn’t that a super nice demo? I love it! Thank you for writing this guest post, Alice! :-)

P.S.: Alice has just been interviewed for a podcast. Curious what she’s talking about on there? Me too, but that’s why I follow her Instagram (@edu_al_ice) — to never miss out on all the cool stuff she’s up to! :-)

The first autumn storm and its impact on dye tracer and water level

Last night it rained a lot. So the first thing to do this morning was to check what that had done to my green lake!

The dye is now a lot more diluted, but overall it still looks surprisingly green seeing that there is a lot of rain water draining into the lake. To give you an idea of how much more water is going through now than when I last showed pictures of the green stream: Look at how clearly you see the inflow into the lake in the picture above! And remember the little waterfall in the picture below? There is a lot more flow now.

Another thing that has gotten a lot easier to see now is where the dye goes into the Kiel fjord. Because the flow rate is a lot higher, so the flow itself is clearly visible, independent of the tracer, but also because … well, there isn’t a lot of water left in Kiel fjord!

This is what it looks like this morning: That little stream is water from the lake going into the fjord. Usually there is about a meter more water here!

It looks actually pretty cool to see exactly what the sea floor looks like.

Even though there are no tides in the Baltic (well, hardly any), we do have some large changes in water levels sometimes. They are due to changes in wind or pressure; in this case there was a lot of wind last night that pushed a lot of water out of the Kiel fjord into the Baltic.

What typically happens now is that this water doesn’t stay away indefinitely, but once the winds stop, forms a “seiche”, a standing wave, with a period of a little more than a day.

Of course I am going to check if there is water back by tonight, and then gone again tomorrow morning! Assuming, of course, that the winds stay calm. Otherwise that would influence where the water goes, too.

What I found really interesting, too, is that I saw a lot of herons now that I’ve hardly ever seen in this part of Kiel fjord before. It makes sense — usually there is too much water so they have nowhere to stand — but it was still weird to see five at once, and more as I walked along the fjord.

And — at last! — it was possible to see from land what those two sticks in the water are warning about: The stone in the middle! I had never actually seen that before. Now I know! And now the water can come back; wave watching is more fun when the waves have slightly shorter periods than the seiche’s 27 hours… ;-)

…Update in the afternoon…

After more rain throughout the day, we now actually see a clear plume of the rain water going through the green lake, with a little mixing on the sides as the green water is entrained!

And some water is back in Kiel fjord. Phew. So there is wave watching to be done right away:

Below, we see a really nice example of waves changing their direction as they run into shallow water, since their phase velocity depends on water depth (more about that here).

Wave watching: Refraction and diffraction of waves

A little more wave watching, today with a focus on how waves change direction when they run into shallow water. Let’s look at this beautiful wave and see what happens when it reaches the shallow shore.

Above, you see the wake of the pilot ship, consisting of many wavelets that propagate as parallel wave crests towards the shore.

Below, you see that the wave is propagating at an angle to the shore (something around 45 degrees, maybe?). If you focus on the wave crest that is just offshore of that little obstacle in the water (curious enough, a piece of brick wall), you clearly observe that angle. But then looking at the next wave crest in-shore, it is almost parallel to the shore! Assuming that both crests come from the same wave field, so that the second one was in the same position as the other one only moments before (which I know it was because I observed it), something clearly happened between then and now.

Refraction of waves

Why do waves change direction as the water depth changes? As waves run from deep into shallow water, at some point they start to “feel” the bottom, which slows them down.

Or, more scientifically speaking, the dispersion relation for shallow water waves is a function of water depth: The shallower the water, the slower the waves. That means that if a wave crest is running on a slope with one side being in shallower water while the other one is still in deeper water, it will change direction towards the shallow water because the shallow side of the crest is slowed down while the deeper side keeps on moving faster, thus forcing the whole crest around a curve.

But in this picture series there is more to see: See how the wave crest gets deformed after it has passed that obstacle?

Diffraction of waves

This is a process called diffraction: The change of direction after a wave crest has passed either through a slit and then starts radiating from that slit as circle segments, or, in this case, an obstacle. The wave passing an obstacle is, in a way, the same as the wave passing through two wide slits which are very close to each other, only separated by the obstacle: The edges of the wave crest at the edges of the “slits” also start radiating out as circle segments!

One spot, so many things to observe!

And there are, of course, ships. What I wanted to show on this picture is a close-up of the turbulent wake of the ship, but it’s really difficult to see so I’ll let that pass for today.

And the picture below shows so much cool stuff: Waves radiating from that pylon. Ripples on the surface by a gust of wind. Wave crests getting a lot steeper as they run up on the slope. And, my main reason for posting: I really like how the wave is spilling as it breaks! :-)

Weekend wave-watching

Of course I did not only take pictures of lighthouses and instructional activities during the teacher training at Lotseninsel last week. I also took TONS of pictures of water! Some of which I’ll share with you now.

For example below you see where the Schlei flows into the Baltic Sea. This is actually a fairly narrow outlet, and you can see the strong current and the eddies that are formed where it flows into the Baltic Sea! It had been raining a lot previously, so there was a lot of water trying to get out of the Schlei!

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A similar pattern can be spotted at the outlet of the marina, but in this it’s mainly wind-driven.

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And very nice here: Long swell and short wind waves on top of it.

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Of course I also looked at wakes. This is a particularly nice one:

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Oh, and reflections. Isn’t it super pretty how the mast gets reflected with all these little twists and turns?

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And then we had some shielding from the wind, and waves only appearing after a certain fetch.

Btw, that’s the house we all — and all the teachers — stayed in.

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Here we see waves being dampened by some algae stuff, and being deflected downwind of those patches.

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Here is another view of the strong current going out of the Schlei and the distinct separation between the two water masses.

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And now the same thing in combination with the sailboat’s wake. So pretty!

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When we were on our way home, the wind had picked up substantially and we saw lots of foam stripes! Langmuir circulation, nowhere near the coast line.

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Here we get a last glimpse of the house we had stayed in… And more foam stripes!

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And some more ;-)

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And then in Maasholm, we see the waves arriving upwind of the pier and then the tiny ones in the sheltered area. You can see a gust of wind somewhere in the foreground to the right, where there are all those small ripples in a darker patch.

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It was a pretty windy day!

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And more foam stripes…

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And a wake!

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And another wake!

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And just a couple of pictures of water, because I love water.

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Refraction of waves towards the beach

As you see from my parents’ attire and the lack of leaves on the trees, these pictures are not brand new. But still interesting: Do you see how the waves are bent towards the coast as they run into shallower water?

And can you believe I still have to look up which one is refraction and which one is diffraction to make sure, despite having a PhD in oceanography? They really should consider retracting that. I am pretty sure I “was instructed” (avoiding to say “learned”, since I clearly didn’t) about this in a lab during first year physics. On the other hand, I know where to look it up. Does that count?

And maybe it’ll help if I write it down once more:

Diffraction is what happens to waves behind slits or obstacles.

Refraction is what happens when waves run into shallower/deeper water (or into a different medium if we are talking about light waves) due to dispersion.

Does anyone know a nice “Eselsbrücke”/mnemonic/way to remember?

Refraction of light in moving water — why stuff seems to be jumping around

I was waking along Kiel fjord one morning and noticed a stone “jump” on the ground as waves went over it (and actually, that observation was the motivation to dive into stuff from the last post, too).

I think the stone only looked so curious because the rest of the ground was uniformly sandy and hence didn’t seem to move.

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So seeing that jumping stone made me want to draw the optical path, which I’ve animated for you here:

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Funny. I think in physics class in school, I would absolutely have hated it had I gotten the task to draw all those different diagrams, and here I really enjoyed it. Maybe because of that jumping stone? Would the right motivation have helped me as a kid to get interested in this? I think it wasn’t that I was not interested in physics, but it would never have occurred to me to sit down on my own to sketch optical paths or anything like that. Now if I could figure out what changed for me, maybe we could use that to make other people interested in physics, too?