In the picture above, you can still see the ship on the left, and having seen the ship, I am sure you can recognise the turbulent wake in the picture below, too: It’s the lighter blue stripe towards the horizon with darker, rougher sea surface to either side.
And in the top picture, you see individual “feathers”, i.e. parts of the V-shaped wake with the ship at its tip, coming towards us, whereas in the bottom picture, a little later, the one part of the V has reached us and we see the “feathers” as the wave crests that are more or less perpendicular to the bottom of the picture.
I find it interesting how the perspective makes it seem as if the wavelength gets a lot longer towards us, but that’s really only the perspective. Also the closest two or so crests are really hard to see — can you spot them? The closest one you can see better on the right side of the picture where there is a sudden change from a darker to a lighter part coming across, and the second one you see more easily on the left side, again, with a quick change between darker and lighter. And the third one is fairly easily visible all across the picture.
Do you do wave watching when you are at the water?
(Disclaimer: The physics the title refers to are somewhere in the second half of the blog post when I am done rambling)
In case you are wondering why I am blogging so much all of a sudden: Sometimes I just love to spend a couple of hours on my sofa, drink something warm, and play with my blog (as I told you I would last Saturday, when I wrote all the stuff that got published recently [technically it’s still said Saturday morning as I am writing this, I am just scheduling all these posts to be published over the next couple of days. I usually select and upload the pictures I want to use on my blog the day I take them, and I always know what I want to write about them, too. In case you were wondering about my blogging process…]). Anyway, moving on.
The pictures for this post were taken a couple of weeks ago, when it was still feasible for me to be at Kiel fjord in the mornings when the sun was this low. Early bird and all, but these days the sunset is too early to just accidentally observe.
What really irritates me is how the condensation trails in the sky look like scratches on the picture. Even though I took the pictures on my phone and then watched them on the phone’s screen (so there is no way they could have gotten scratched somehow) I kept thinking they were scratches. But the pictures are still pretty…
But what the low sun made really easy to observe because of the sharp contrasts between lit and shaded sides of the structure, is how you can actually use the deformation of the structure in the reflection to determine the slope of the water’s surface.
As you know, you can only see the reflection of whatever is exactly in the pathway of the ray from your eye, reflected at the sea surface, and going out at the same angle it came in. Even if you were looking in the same direction all the time, if the slope of the surface changed, what you could see in the very same spot would change, too. Hence if you look at reflections on water, they move and get deformed as waves go past the spot you are looking at…
Above, looking at the white hand rail’s reflection, it becomes very obvious that the wave field is actually quite complex. There are waves that pull the hand rail’s reflection out to the right side, and those that move it up and down in the picture. I find it absolutely fascinating how some parts of the hand rail are visible several times in the reflection, how there are even bits of handrail that seem completely detached from the rest (see the little white dot inside a white loop somewhere in the bottom right?) and how the whole thing still seems so organic and smooth.
Below, you even see how you can see how each wave crest relates to a “spike” in the reflection.
When looking at waves in pictures, it is usually pretty difficult to see which parts of the pictures correspond to which side of the wave, the one facing us or away from us (unless, of course, the waves are breaking, or you see stuff like total internal reflection going on). But the reflections make it a little easier, I think.
And just because staring at the reflections made me feel a little dizzy, here is something to give your eyes a little rest: The view towards the Baltic Sea out of Kiel fjord.
Hope you are all having a nice day full of #wavewatching! :-)
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?
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?
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!
Berlin is full of interesting history to discover … for example that of ships that have gone past on the Spree! :-D
Let’s start with some easy wave watching. In the picture above, you see a ship and its wake (both parts: the turbulent one where the ship has gone, and the feathery wake that forms the V with the ship at its tip). And you can make out the wake of a ship that has already gone round that bend of the Spree: the turbulent part showing a different surface roughness, and reflected remains of the feathery V on the right shore of the Spree. So far, so good!
Below, you see two turbulent wakes: The one of the ship you still see, and then the one of a ship that went the other way, but already went out of the area captured in the picture.
Berlin Cathedral Church seen from across the Spree
And here is a series where you see the feathery wake reach the side of the Spree…
Bode museum and television tower Berlin
…get reflected there…
…and then meet the reflection of the other side of the V to form a checkerboard pattern! Would you have known what’s going on here if you hadn’t spotted the ship just about to leave the picture, or seen the previous images?
Below is another nice one. What happened here? A ship sat there, waiting, and then started moving again right before I took the picture! This is the beginning of a turbulent wake right here.
Reichstag, home of parlament
And below another nice wake plus reflection.
And here you see another feathery wake, plus the turbulent wake of the same ship on the other side of the Spree.
Reichstag, home of parlament
Similar picture as above, except in a different spot…
German Chanellery in Berlin seen across the Spree
Yes, that’s a pretty good representation of what sightseeing trips with me are like ;-)
On a recent evening stroll with a friend, the seal basin looked like this:
“Do you think there are any seals in there today?” she asked. “Why yes, of course, don’t you see the waves?” I replied. Because obviously in a basin sheltered by the wind and with no moving parts in it except possibly a seal or three, there is no other mechanism that I could imagine that would create such a wave field. Sometimes I wonder what everybody else is thinking about all the time that I am thinking about waves while they aren’t… Who’s missing out on the cooler thoughts, me or them?
Anyway, we got to do some proper seal watching and wave watching, respectively:
Pretty, isn’t it? the wake of a seal. Pay close attention, I might be testing you on this some time soon ;-)