Early morning Kiel fjord — today even featuring a hot-air balloon!
But, more interestingly, the wake of this police boat. I find it already pretty cool in the picture below: The fjord is calm and mirror-like, but inside the ship’s V-shaped wake the surface changes completely and the reflections look totally different (now only reflecting the sky back, not the cranes). And, of course, the V-shaped wake itself has quite a large amplitude, too.
A little while later, the wake has not only reached the sea wall, it is already being reflected back away from the wall. See the original wake at the bottom of the picture below, and the reflection further away, near the five bollards?
Looking slightly further right, we see the concave shape of the sea wall here, and how waves are being focussed similarly to how radio waves are focussed towards the receiver with parabolic antennas.
So as the reflected waves propagate out further and further, they little by little reach a focal point.
Which you see in the picture below: An area of higher waves in the middle of the water, seemingly for no reason.
And the area where waves interfere and amplitudes are so high moves a bit over time, but it’s a quite persistent pattern.
Had I just come across this pattern without seeing it develop, I don’t think I would have been able to explain what is going on here.
And see how, now that the wake has passed, the checkerboard pattern of interfering waves in the foreground is a lot more prominent again?
The waves that ducks (or ships, or anything else moving through water) make are called “wakes”. And wake watching is so much fun! A wake is pretty much the Mach cone in 2D — waves from the duck can’t propagate faster than the leading edge of the wake. When a wake passes by, that’s the moment you would hear the supersonic boom of an aircraft in the Mach cone analogy. That explains why the wake develops as a feathery V with the duck at its tip. Or several ducks at the tips at several Vs, as in the picture above. How awesome is that?
But wake watching is usually more complicated than just Vs with stuff at their tips. See for example below — two ducks with Vs, two row boats also with Vs, but with the additional eddies where their oars pushed through the water.
See how different the two pairs of wakes look?
Or here, we have wakes again, but they are now occurring on a lake surface that shows more different waves: The half circles that my feet tapping on the water made! And, if you look closely, you can spot algae growing in the lake in the foreground of the picture.
Isn’t it fascinating how you see the algae in the foreground, but the further you look towards the other shore of the lake, the more you see the reflection of the sky or the other shore instead?
That’s due to a phenomenon called “total internal reflection“: For light that hits the interface between two different materials (air and water in this case), there are angles at which it can cross the interface (at steep angles we can look from the air into the water and see the algae), and others where it can’t (at small angles, we cannot look into the water, light gets reflected at the lake’s surface and we see the opposite shore instead). This fascinates me time and time again!
Note how the duck in the image above doesn’t actually have a wake? That’s because it’s swimming too slowly for the wake to develop — it is just radiating ring waves in all directions.
Below, this is kind of a boarder line wake — we can see the V developing, but se also still see the ring waves in the spot where the duck first started swimming.
But of course, wakes are only straight Vs when the ship is driving in a straight line, too, otherwise it will get deformed like below.
I love #friendlywaves! Victor sent me the picture above. He took it in 2017 in Tampa, Florida, and I think it’s so fascinating! There is so much going on, let’s try to make sense of it!
First, the most obvious thing making waves here: The two boats. Clearly they are making waves, and they might explain a lot of what we see here. But on the other hand, they might not.
Below, you see the part of the wave field that is 100% due to these two ships: Their V-shaped wakes (in red) and the turbulent wake behind one of the ships (in yellow).
The very prominent wave pattern (marked in red in the image below) might be due to these two ships as was suggested to me, but if it is, then those ships changed course quite drastically before they created the waves I marked in the previous picture (and I can see no evidence of such a change of course, usually a turn would leave a trace similar to this one).
If the boats, as I assume they did, came out from underneath the bridge and sailed in a more or less straight line (and that seems to be the case judging from their wakes as indicated in the picture above), there is no way they could have made waves that travel in front of their V-shaped wake. Similarly to how you can’t hear the supersonic aircraft before the supersonic boom (because the sound can’t travel faster than the speed of sound and the pressure signal thus gets formed into the Mach cone), waves can’t outrun their wake (which is like their 2D Mach cone). So I don’t believe that those waves were made by those two ships. Rather, I believe that they were made by a ship that is no longer visible in the area we are able to see.
So remember, this is the wave pattern we are trying to explain (Marked is only one wave crest, but you see that there are several parallel to the marked one):
We do nicely see how the wave is reflected by the straight sea walls. But what direction is it traveling in? And what caused it? Let’s speculate!
First: let’s consider the very weird shape of the body of water shown in the picture. Quick search for Tampa on Google Maps lets me believe is that the picture was taken more or less from the position of the white star and the view is the area between the two red lines. Looking at that map, we see that the water we see opens up into four different water ways: One to the north, one to the east, one to the south east, and one to the south west. The two to the south eventually open up into Tampa Bay.
The wave field that we are trying to explain would look somewhat similar to what I drew in below (green):
My best explanation of that green wave field above is this: A boat that went on the course that I drew in in yellow:
So far, so good. Wanna know why I believe this is what happened? Then this is the picture for you!
Assuming the boat followed along the yellow track, the other lines are the wake it would have produced:
green: Those are two parts of the wave field that I marked above that I am fairly confident of: The wake propagated across the body of water, got reflected and came then over towards the photographer. Note how not all waves reach the shoreline close to the photographer yet? That’s because they are the “newer” waves that haven’t traveled for long enough to reach that spot
light blue: The “newest” waves that aren’t very long yet and are traveling in an area where we can’t clearly make out the presence or absence, let alone direction, of waves. They are fanning away from the “green waves” because the ship is turning (similar to here).
dark blue: Those is a part from the wake that originated on the other side of the ship, got reflected, and now traveled across the body of water to reach the point where the picture was taken from. They do so at an angle that looks like they might be reflections of the incoming green waves (which is another possibility which I can’t rule out with 100% certainty). Newer wakes from that side, once they’ve been reflected on the shore, will lead to waves almost parallel to the green part of the wake and would be indistinguishable from those in the picture.
orange: Those are “old” wakes that must have happened when the ship came out of that inlet, but that would not interfere with our picture because their reflection stays caught within the inlet itself.
This is the best explanation of what must have happened that I can come up with, and I have thought about this quite some time (more on that at the end of this post) :-)
But then there are tons of shorter wave length waves that we have to explain, too: See those marked in red, yellow and green below.
I am confident that the ones I marked in red are wind-driven waves coming across the open area. Their direction also agrees quite well with the wind directions the flags indicate (marked with a white arrow above). I believe that the ones I marked in yellow and in green are two separate wave fields at a slight angle, but that might be an optical illusion, I am not quite sure.
If we go back to the map, I believe the wave fields I marked above would look pretty similar to the ones I drew in below (I changed the red waves above to magenta waves below, because red was already taken. Note the wind direction marked with a white arrow: it looks pretty much perpendicular to the now-magenta wave crests):
And looking at the angles in that depiction of the waves, I could imagine that the green wave field is a reflection of the magenta wave field where that one hits the shore on the side where the picture was taken from (see light blue wave crests). As for the yellow one: I still have no idea what caused that. But maybe there need to be some mysteries left to life? ;-)
To end on something that I am confident in: The half circles near the bottom of the picture are the result of something (two buoys? two small boats?) moored on that pier, bobbing up and down in the waves, thus radiating wave rings with shorter wavelengths and higher frequency than the wave that is exciting the movement.
But after all this hard work (more on that at the bottom of this post) — let’s take a minute and look at those beautiful interference pattern again where the wave fields cross each other and create a checkerboard pattern. How amazing is this?
Phew! I love #friendlywaves, but this was quite a challenge! How did I do, Victor? :-)
If you or anyone else have any comments or suggestions — I would love to chat about alternative explanations!
P.S.: Just to give you an idea of what my process was like: It involved late night scribbles on a tea bag (because that was the best “paper” I had available on my bedside table in the hotel in Manchester) and I needed to play scenarios through in my head…
…and some sketches on my phone while I was on a train…
This is the story of a pilot ship, merrily sailing along on a beautiful day, making waves.
Since it’s windy and Kiel fjord is a little choppy, the waves break and both side of the V-shaped wake with the pilot ship at its tip are visible. See the foam of the breaking waves? And in the middle of both sides of the V, visible as a lighter-colored stripe, there is the turbulent wake where the ship’s propeller has set the water into chaotic motion.
Both constituents of the wake — the V-shaped feathery waves and the turbulent wake — stay visible for quite some time after the ship has passed!
Can you spot the one side of the V approaching the shore?
A little while later, the pilot ship returns. nice bow wave (where its bow is breaking the water apart) and all. Also note the wave field inshore of the floating wave breaker — it is a lot calmer than on the outside!
A week ago already, Frauke and I went on an evening walk in Kiel Holtenau. Beautiful wave watching to be done there as always! Here you see the one side of a ship’s V-shaped wake approaching our vantage point. You can see the individual “feathers” of the wake: Short wave crests, all parallel to each other, but slightly shifted to the side to form a straight line (well, two straight lines to form a V with the ship at its tip, but the other side of the V is not visible on this picture).
And this is what it looks like when the wake has moved past us: Looking on the back of the feathery shapes. The ship that made all these waves has long sailed away.
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?