Tag Archives: waves

Why are they so much slower than I thought? Observing the group velocity vs phase velocity of waves

Have you ever seen a speedboat drive past, looked at its wake moving torwards you, then gotten distracted, and when you look back a little while later been surprised that the wake hasn’t moved as far towards you as you thought it would have during the time you looked away?

Well, I definitely have had that happen many times, and the other day I was sitting on the beach with a friend and we talked about why you initially perceive the waves moving a lot faster than they turn out to be moving in the end. While I didn’t film it then, I’ve been putting my time on the GEOF105 student cruise to good use to check out waves in addition to the cool research going on on the cruise, so now I have a movie showing a similar situation!

But let’s talk a little theory first.

Phase velocity

The phase velocity of a wave is the speed with which you see a wave crest moving.

Waves can be classified into long vs short waves, or deep- vs shallow water waves. But neither deep and shallow, nor long and short are absolute values: They refer to how long a wave is relative to the depth of the water in which it is moving. For short or deep water waves, the wavelength is short relative to the water depth (but can still be tens or even hundreds of meters long if the water is sufficiently deep!). For long or shallow water waves, the wave length is long compared to the water depth (for example Tsunamis are shallow water waves, even though the ocean is on average about 4 km deep).

For those long waves, or shallow water waves, the phase velocity is a function of the water depth, meaning that all shallow water waves all move at the same velocity.

However, what you typically see are deep water waves, and here things are a little more complicated. Since phase velocity depends on wave length, it is different for different waves. That means that there is interference between waves, even when they are travelling in the same direction. So what you end up seeing is the result of many different waves all mixed together.

If you watch the gif below (and if it isn’t moving just give it a little moment to fully load, it should then start), do you see how waves seem to be moving quite fast past the RV Harald Brattstrøm, but once you focus on individual wave crests, they seem to get lost, and the whole field moves more slowly than you initially thought?

That’s the effect caused by the interference of all those waves with slightly different wave lengths, and it’s called the group velocity.

Group velocity

The group velocity is the slower velocity with which you see a wave field propagate. It’s 1/2 of the phase velocity, and it is the velocity with which the signal of a wave field actually propagates. So even though you initially observed wave crests moving across the gif above fairly quickly, the signal of “wave field coming through!” only propagates with half the phase velocity.

Usually you learn about phase and group velocities in a theoretical way and are maybe shown some animations, but I thought it was pretty cool to be able to observe it “in situ!” :-)

Thinking about the Doppler effect as of a boat sailing against the waves!

I can’t believe I haven’t written about this on my blog before, thanks Markus Pössel for reminding me of this great way to understand the Doppler effect!

Doppler effect, or why ambulances change their sound as they race past you

Doppler shift is everywhere, but it’s maybe not obvious how to imagine what’s going on if you think of sound waves.

But look at the picture below. Can you imagine the sound of those waves lapping against the shore?

Now imagine taking a speed boat riding out on the water. Can you feel how you are bouncing over the wave crests, and notice how you are meeting them a lot more often than when you were standing on the beach, looking out on the water?

Or imagine being a surfer, riding that perfect wave. You are staying with the same wave crest for a really long time, while in front of you creat after crest breaks on the beach.

Yes, the Doppler effect is as easy as this! As you are moving with or against the waves, their frequency changes. Totally obvious when you think about waves on water, right? But the same happens with sound waves, and in their case, a changed frequency means that the sound appears to change pitch. If the ambulance is coming towards you, the sound gets higher and higher, and then as it races away, it gets lower again. So now you don’t even have to look when you hear an ambulance, you know whether it’s coming or going! (Just kidding! Please definitely look out, anyway, and don’t get run over!)

Wave reflections

This still is one of my favourite kinds of wave field to look at. So calming. (Who am I kidding. All waves are my favourite waves, of course! I am addicted to wave watching…)

Here is a short movie for you where you see the crests coming in from the bottom right and then being reflected at the wall. Isn’t this nice? :-)

 

Wave watching: Refraction and diffraction of waves

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! :-)

Wave watching at the Kiel Holtenau locks

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! :-)

When not the fetch but a funnel shapes the wave field

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? :-)

What makes and destroys waves

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! ;-)

Waves in a density stratification. One of the most beautiful tank experiments I’ve ever seen.

It’s pretty impressive when a mountain moves through a stratification and generates lee waves. But what I find even more impressive: The waves that travel behind the mountain when the mountain is long gone. See here:

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)

Wave watching Sunday in Grenoble

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.

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For comparison below a picture of a part of the Isère where it is turbulent all the way to the sides:

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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.

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Below is one of my favourite wave-watching sights: A half slit.

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And in the picture below, we can kinda see vortices detaching behind the obstacle (or is that just me)?

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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 :-)

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It’s not a hardship to be here, I can tell you ;-)

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It is quite a beautiful place! And, by the way, this is my 600th blog post on this blog. Can you believe this?

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Total reflection and fishies

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?