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! :-)
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! ;-)
This kind of stuff looks more like a numerical simulation than something actually happening in a tank, doesn’t it? I am pretty stoked that we managed to set up such a nice stratification! Those are the things that make me really really happy :-)
(The setup of this experiment is the same as in this post)
Today I went on a wave-hunt expedition to take pictures for posts on the Froude and Reynolds number over at Elin & team’s blog (which you should totally check out if you haven’t done that yet! I am actually proof-reading my posts there and that is saying something ;-))
Anyway. Let’s look at the picture below. Do you see how there are two qualitatively different flow regimes in the Isère? Closer to the banks, you see waves that look like normal waves, happily propagating wherever they want to. And towards the middle of the river, you see that there is a lot of turbulence, but disturbances don’t propagate wherever they want, they are being flushed downstream.
For comparison below a picture of a part of the Isère where it is turbulent all the way to the sides:
And below a nice example of how phase velocity of waves depends on wave length. See all the small, choppy stuff being flushed downstream and then standing waves caused by some obstacle in the middle of the river? That’s because the longer the wavelength, the faster the wave propagates (assuming that we are in deep water, which I think is a safe assumption in this case). So the river is so fast that the slower waves get flushed away and only waves of the length of those created by the obstacle (or longer) can stay in one place (or even propagate against the current). I think that’s pretty cool.
Below is one of my favourite wave-watching sights: A half slit.
And what I really liked: see the spot below where there are all of a sudden standing waves appearing in the middle of the river? Clearly there is a sill below, but I like that you cannot see the obstacle, just deduce that it must be there from how the waves look :-)
It’s not a hardship to be here, I can tell you ;-)
It is quite a beautiful place! And, by the way, this is my 600th blog post on this blog. Can you believe this?
Do you know the phenomenon that once you start noticing something, you see it everywhere? That’s been the case with me and total internal reflection. Not quite as impressive as last time, but still there:
And what I found really interesting this time: a swarm of tiny fishies making wave rings! I only noticed them because of those tiny waves. And if you look closely you can see so many of them just below the surface right where the wave rings are!
So funny to see the water almost boiling with fish on such a calm morning.
And another thing that fascinated me: how it’s so much easier to see into the water in places that are shaded (or dark) from the reflection of that pier. Not quite sure yet why it’s so much easier to see here, maybe just because there isn’t any glare? Any ideas?
Have you ever wondered why at some angles the sea looks blue (or whatever the color of the sky that day) and at others you can actually look into the water? That’s the phenomenon of total internal reflection. There is a critical angle at which you switch from “being able to look into water” to “total internal reflection”, i.e. the sky being reflected off the water’s surface and reaching your eye. Below you see a nice example of this: The more perpendicular you look at the water surface (i.e. those sides of the wave facing you), the better you can look into the water. Whereas all those parts of the sea surface that face away from you look blue and you can’t look into the water there.
I think this is totally fascinating! Don’t those pictures look almost fake?
And, btw, this doesn’t only happen if you look in parallel to the direction of wave propagation. Although it looks even weirder at an angle:
Can you see how all those tiny ripples on the wave each show the same phenomenon of either reflecting the sky or being transparent and showing the sea floor underneath? How cool is that? :-)