The geometric shape of Lille Lungegårdsvannet makes for perfect wave watching conditions. Not only when wanting to look at waves from all sides, but also when you are just fascinated by reflections and geometric wave pattern.
And also by rainbows. Am I the only one who, when the sun is out and at a good angle, walks around Lille Lungegårdsvannet to see the rainbow that you know must be there?
Oh look, someone built a perfect rectangular wave watching basin into Bergen harbour!
As you see above, waves are propagating towards this little wave tank and into it. They then get reflected at the edge at the bottom of the picture. Then, the original incoming wave and reflection propagate together further into the basin. They are now forming V-shaped wave.
This leads to this really cool interference pattern in the basin: Lots of seemingly disconnected little hills and valleys in a checkerboard pattern.
It looks even cooler when moving! Because it’s so difficult to track individual wave crests and the hills and valleys seem to just be appearing and disappearing randomly:
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…
(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! :-)
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!
Recently, more and more of my friends send me pictures of waves they spotted when walking along a lake side or taking a ferry ride. I love how contagious wave watching is, and I love sharing my fascination with you! :-)
Here are some pictures that Fred sent me of his lovely Sunday walk today. There are at least five interesting things that I notice in the picture below. How about you?
Look at the beautiful interference pattern where two wave fields are almost perpendicular to each other, creating the checkerboard pattern! As you see in the picture below, there is one wave field coming in at a 45ish° angle to the sea wall, so its reflection is at 90ish° to the original wave field.
In the background you see the surface roughness changing and the water seeming darker where there is a breeze going over the water, creating small ripples that reflect the sky in a different way than the smooth surface closer to us.
See the waves the seagull made where it landed on the water?
Looking at the foreground, do you see the tiny ripples that show up not so much on the surface of the water, but rather at the sandy ground, because they focus the light?
And notice how you can look into the water in the foreground but not in the background? That’s the awesome phenomenon of total internal reflection where, if you look at water at an angle that is smaller than a critical angle, you cannot look into the water any more but just see light reflected at the surface! One of the things I never understood we had to learn about in school, but that I find super cool now.
And in the picture below, what do you see?
What I find most interesting in the picture above is how the reflection of that storehouse tower looks different in areas with different surface roughnesses. Where there is a breeze on the water in the background and in the foreground, it’s a lot more spotty than in the calm and smooth surface in between. And the checkerboard waves pattern (now you see the seawall that created the reflection, btw) carries through to the reflections, too, with the blue crisscross going into the white area where a cloud is reflected.
And then the phenomenon of total internal reflection is really clearly visible here with a lot of reflections on the water (or just more interesting things to reflect than just a blue sky in the previous picture) and a view down to the ground only in the very foreground of the picture.
Today we are focussing on tiny waves right near the shore inside the sheltered harbor. See how below there are two wave fields, one with longer waves with crests that are parallel to the water’s edge, and then shorter ones propagating at a right angle relative to the first field?
Where the rope swims on the water you see how the short wind waves are stopped and only start forming again at a distance downwind of the rope.
The same here: Where there are ropes floating on the water, the water’s surface looks a lot smoother because the wind waves that propagate perpendicularly to the ropes are erased. But there are some wave crests parallel to the rope, formed by the rope hitting the surface and being pulled out again!
Below, the ropes don’t actually touch the water’s surface, but we have cool reflections of waves with crests parallel to the two walls that form the corner. The water level is right at the height where there is a little ledge on the wall that gets flooded with wave crests arriving and then falls dry during wave troughs. This causes this cool pattern of wave crests that seem to be interweaved right at the corner.
Sometimes looking really closely at small scale pattern is even more fun than looking at the sea and all the big and flashy (or splashy?) stuff going on there!