I just found this picture that I took back in May near my friend Elin’s cabin on an island in western Norway, and it’s a really nice illustration of how the same wind will cause very different waves depending on whether it’s blowing over the sea for many kilometres, or over a puddle for only a couple of centimetres.
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! :-)
And we are wave watching again!
A ship’s wake and the different zones within
Here is the wake of the little ferry that goes across Kiel canal.
I love how you can see the different parts that a wake consists of: The V with the ship at its tip that consists of wavelets from the bow wave and that spreads outwards. And then the turbulent wake where the ship has physically displaced the water when sailing through, and that then has been thoroughly mixed by the ship’s propellers.
This second, turbulent wake actually changes the water’s surface for quite some time. Propellers put the water in rotation and it slowly entrains surrounding waters, and this turbulent motion looks substantially different from the “normal” sea surface. It can even be spotted from satellites long after the ships are gone. You’ve probably sometimes noticed streaks on the sea even though no ships were present — those might well have been the remains of wakes!
But speaking of ships that have sailed…
Wake of a ship that sailed past a while ago
Here is another example of a wake being visible quite some time after the ship has sailed past. However what we see here is the feather-y train of wavelets from the V reaching the shore.
While we were looking at it, my friend mentioned that the waves seemed to approach a lot more slowly than she had expected. That’s because the movement we first notice is the phase velocity of individual wave crests. But when you look closely, you can’t follow one individual wave crest for a very long time, it always appears and you have to start over. That’s because the signal, the V itself, only moves with the group velocity, which moves at half the velocity of the wave crests. That really looks confusing! Unfortunately I didn’t get a good movie of this. But there is always next wave watching session! :-)
And a mystery wave!
But then what would any wave watching session be without a riddle.
Any idea what caused the wave pattern below? Not the obvious, larger waves, but the concentric circle segments that radiate outwards from somewhere in the bottom right?
This is a case where it is really helpful when you recognize where the picture was taken, because there is some important information missing from the picture: The straight edge continues on for a little to the right, and then it opens up to a fairly long channel coming in.
However what you do see is the wind direction from the way the water is smooth right at the shoreline and then ripples start to form as you look further away: The wind is blowing out onto the water.
Now combine those two informations and you understand how that wave pattern was generated!
Diffraction at a “slit”
Wind-generated waves move as (more or less) straight crests out of the channel that opens into Kiel fjord just outside the right edge of the picture above. Then, suddenly, they aren’t bound at the sides any more, and what happens looks like diffraction at a slit (except the slit is fairly wide in this case): The straight crests turn and form 90 degree circle segments that radiate outwards. Voila!
So many people are surprised when I speak of wave watching as of a “real activity”. But to me it is! So I am going to talk you through a couple of minutes I spent looking out on the water where the Kiel Canal meets the Kiel fjord, right outside the locks at Kiel Holtenau.
A light breeze across the fjord
The “light breeze” part is fairly easy to observe: There are ripples on the water, but no actual waves. “Across the fjord” is also fairly obvious if you look at either side of the wave breaker: On the fjord side, there are ripples, on the shore side, there are none (or hardly any), indicating that the wave breaker is sheltering the shore-side from the wind (and dampening out the waves that come across the fjord).
And then: A ship sails into view!
We watch the ship sail past, dreaming of foreign countries and exciting adventures.
A ship leaving a wake
Behind the ship, the water looks very different from what it looks like everywhere else. The wake is turbulent and waves radiate outwards like a V, with the ship always at its tip.
Then, the ship is gone. But we can still see where it went.
There are no waves in the tubulent wake
The ship’s path is completely smooth. No waves have invaded the turbulent waters of the wave just yet, claimed them back. However, the waves the ship created in that V are about to reach the wave breaker.
Also the wind has picked up a little, as evident from the less smooth water surface shore-ward of the wave breakers.
Diffraction at a slit
Right after the waves from the V reach the wave breaker, they reach the opening at the end between the pylons. And what happens now is that the waves get diffracted at a “slit”: they propagate outwards as semi circles, even though the wave fronts were straight when they reached the slit.
How awesome is that? And all of this happening in a matter of minutes!
The weather changes
I said earlier that there was hardly any wind. Later that afternoon, it still wasn’t very windy, but the wind direction had changed: now the smooth and sheltered part has moved to the other side of the wave breakers. There are a lot more waves on the shore side of the wave breaker now, the ones with crests parallel to the wave breaker due to it moving, and the ones with crests perpendicular to it generated by wind. And you see gusts of wind on the sea side of the wave breakers in the different surface roughness.
So if you were wondering, too: That’s the kind of stuff I look at when I am wave watching. And I still find it super fascinating and relaxing at the same time! :-)
As you know we are currently preparing for future wave riddles. So this afternoon I went out for a wave hunt again and found something beautiful for you!
The ship coming out of the Kiel-Holtenau locks into the Kiel Canal is making waves, but although those are pretty exciting, too, there are more things going on in the picture above…
Many processes can create waves
In addition to waves made by ships, seagulls, the locks opening and closing, and those waves being shaped by reflection, refraction, and all those other processes, most waves look actually pretty similar, and they are all formed by the same process.
Most waves are wind waves
In almost all situations it’s a safe guess that most of the waves you see are caused by the wind. Either locally, or by storms far away. Of course, the waves might look very different from day to day and location to location. But as a rule of thumb, the stronger the wind, and the longer it has been blowing, and the longer its way over water without any obstacles in its way, the higher the waves.
Usually the length of the fetch shapes the wave field
This uninterrupted stretch that the wind can blow over the water is called the “fetch”. And it explains why you don’t have really large waves on small ponds: if the fetch isn’t long enough, waves just don’t have enough time to build up from when they are generated at the upwind side of the pond until they have reached the downwind side.
Sometimes obstacles shape the wind field
Sometimes though, there are obstacles in the wind field that cause interesting wave phenomena. Below you see that the wind that has been coming across Kiel Canal is interrupted by those pylons. Upwind of the pylons the waves are fairly regular and pretty boring.
But remember your Bernoulli? If the area across a flow decreases, for continuity reasons the flow speed has to increase.
Since air is “flowing” in that sense, too, it’s accelerated where it goes in between and around those pylons since it has to squeeze through a smaller cross section than it had to its deposal further upwind.
The wind field is mirrored in the wave field — well, kind of
Do you see how the faster wind causes all these nice little ripples? Maybe “mirroring” the wind field isn’t quite the right way to express it, but you can definitely see where the wind speeds are different from the rest of the Kiel Canal just by looking at the waves! From there the waves then propagate as sectors of circles outwards and leave the areas of the high wind speed, but they quickly dissipate and vanish again.
Wave watching is awesome. Can you think of anything better to do on a Saturday afternoon? :-)
Today I have a couple of photos for you to prepare you for upcoming wave riddles. Since, in those riddles, I usually ask what might have caused the wave on that picture to look a certain way, let’s today look at a couple of relevant processes.
A lot of processes can make or destroy waves
In previous riddles, I have often chosen pictures where waves were made by ships or other objects, or shaped by topography. Today, I want to focus on wind-generated waves, and how the wave field changes without interactions with the bottom or other boundaries.
Well, unless you think of surface films as boundaries, that is. Which, I guess is a valid way to look at them. What do you think?
Surface films act as filter on short wave lengths
Below, you see wind waves running into some sort of surface film. I am not quite sure if “film” is the best way to describe the case you see below: It’s not like an oil film, it’s a lot of tiny objects floating so close to each other that they rub against each other when moved, and since the rubbing eats up more energy than the movement of a completely free surface, waves get dampened. And, as you see below, the dampening happens selectively depending on wave lengths: Short waves are dampened out as soon as they run into the area covered by the surface film, while longer wavelengths propagate into that area without being affected too much.
Dispersion also acts as filter on small wave lengths
But surface film aren’t the only thing that changes a wave field’s spectrum. It can change all by itself: Since the velocity of deep-water waves (meaning that the water depth is large compared to the wave length, which is the case in all the pictures in this post) depends on their wave length, and longer waves move faster than shorter ones, a gust of wind that ripples the surface in one place will not make a ripple pattern that propagates “as is” over the water, but the spectrum of different wave lengths will separate, with the longer, faster waves overtaking the shorter, slower waves.
That’s what you see above: The shorter, slower waves can’t keep up with the longer ones. And then the longer ones run into the area covered by the surface film, and again only the longest ones manage to propagate into that area while the rest is filtered out.
Wind causes ripples which then grow into waves
I’ve kind of assumed that everybody knows this, but here is a nice example of how wind causes waves in the picture below. Just out of the upper edge of the picture below, there is a pier that shelters the down-wind water from the wind, causing a flat and smooth surface close to it.
After the wind has had the opportunity to interact with the water surface for a little while, ripples form. They then grow, and yada yada yada, we are back in the situation shown in the picture above the one above this one.
Growth and destruction of waves
Would you have been able to explain the four different zones shown in the picture above? Would you recognize what’s going on if you happen to observe it “out in the wild”? Then you are well prepared for upcoming wave riddles! ;-)
In the last post, I showed you flow separation on a pylon in Elbe river. Remember?
Today, we are back at the same pylon, only that this time the tidal current is a lot less strong, but there is a lot of wind, so our focus is on wind-generated waves.
It might be admittedly a bit hard to see, but if you watch closely and use your imagination, you might be able to see the waves propagating towards the pylon and then being reflected and radiating radially outward from where they hit the pylon. Pretty fascinating!
Can you see the locally generated waves to the left of the pylon? All those tiny waves where the wind is funneled around the pylon?