Category Archives: observation

Roll waves in the sand dunes? Observing erosion

On our trip to the west coast yesterday, I observed something really cool: Sand roll waves (I think!) in the sand dunes!

But before I get to that, this is the setting on Sylt. A sandy beach opening up to the North Sea, that is separated from the land by sand dunes which are overgrown with some kind of beach grass.

Yesterday was a windy day as you see from the waves, but neither was the water level very high, nor was the wind anywhere near as strong as it gets here during winter storms, so the erosion happening yesterday is not very strong compared to what it is like during more extreme weather conditions (and the process I am focussing on here is probably one of the least important ones).

In order to prevent erosion of the dunes which protect the inland from storm surges etc, it is crucial that the beach grass growing on the dunes isn’t stepped on by the hundreds of tourists visiting this beach every day (probably thousands during summer). Therefore there are these wooden staircases installed in regular, short intervals to bring people across the dunes without them doing any damage to the vegetation.

Therefore, in most places, the dunes look like this.

In some places, though, there is little or no grass growing on the dunes, so imagine what kind of damage strong winds can do here, let alone a storm surge!

And in one of these open sand areas I observed what I think are roll waves. Do you see what looks like a drag mark a little right of the center in the picture below?

Check it out in the movie below (it zooms in after 5 seconds to show it more clearly) — there is sand surging down this track! To me this looks very similar to roll waves, and I know roll waves have been observed in sediment flows and lots of other places, so why not in the sand of these dunes? What do you think?

A different kind of drop photography today…

After all the professional drop photography I talked about yesterday, here is some of my own from a walk that I took after the amazing and slightly overwhelming experience of giving the laudation speech at the opening of an art exhibition.

Below, I really liked how the wave rings have such different sizes and amplitudes depending on whether they were made by rain drops or ducks (you might have to click the image to enlarge to see what I am talking about).

And below, I love so much about this picture. The long waves with the very small amplitude that are coming into Kiel fjord from some far-away storm. The short waves and small scale turbulence that is created where wave crests just manage to flood a step on the staircase, but the water then flows off it again during the next wave trough. The small speckles made by rain drops. The fact that it seems to almost be summer again because the beach chairs are back! And, of course, that I caught the splash and the flying drops of the wave.

I read this poem by E.E. Cummings on Saturday that really speaks to me. It ends in

“For whatever we lose (like a you or a me)
it’s always ourselves that we find in the sea”
E.E. Cummings

Vernissage of “liquid art”: The perfect opportunity to combine art & physics to do some scicomm!

If you don’t want to “preach to the choir”, how do you, as science communicator, reach new audiences occasionally?

One way that I tried today is to give the (invited, I swear!) laudation at the vernissage of Wlodek Brühl‘s exhibition on “liquid art“. The idea was that visitors would mainly come to the event because they are interested in art itself, but that I will try to give them a new perspective on the art by exposing them to the science behind it. Which I think is a pretty cool concept!

Yesterday, I got a sneak peek into the exhibition which features new art that isn’t even two weeks old! I took pictures of some of the art to show on this blog (with Wlodek’s permission!).

Let’s start with a sculpture that isn’t even part of the actual exhibition but that is displayed in my living room (and I love it!!!): A very simple drop sculpture. A drop fell onto a water surface. Due to surface tension, the water surface deformed, got pulled down, bounced back, overshot, and a drop shot up again, pulling a thin trail behind it. As the drop was flying upwards, it got hit by a second drop which fell straight on it. That second drop splattered into this umbrella, which is starting to disintegrate into small instabilities that form tiny filaments. A fraction of a second later and the whole thing would have collapsed and look totally different.

My picture of art by Wlodek Brühl, taken and published with kind permission.

That’s part of the art of capturing these sculptures: timing. Not only does one need to be super precise in the timing of drop releases, one also needs to capture the exact right moment to light the dark room with a flash, which is a lot shorter than the exposure time of the camera. Of course it’s all controlled by a computer!

But here is an impression of the exhibition itself.

My picture of art by Wlodek Brühl, taken and published with kind permission.

I’d like to start out with some of the older art from 2016 which is easier to explain: “Simple” drops like you see to the right of the door above, then double pillars to the left of the door, and then reflections, before we move on to the kind of art that you saw at the top of this post.

In the picture below, what happened is pretty similar to what happened in the picture above: A drop fell, bounced back up again and was hit by a second drop. The second drop hit the first one when that one was still fairly fast, therefore the vase-like structure. (And don’t you just love the waves that you see on the water surface? I feel like I see the actual dynamic process of the surface rising up!)

My picture of art by Wlodek Brühl, taken and published with kind permission.

Or below, another similar setup, except here the drops collided in such a way that the larger, bottom one formed an umbrella-like shape, whereas the upper one rose as a vase.

My picture of art by Wlodek Brühl, taken and published with kind permission.

It gets more complicated if two drops are released simultaneously as below, and then a third one hits them in the middle with a little time delay to form the umbrella, and a fourth drop is still falling down and hasn’t reached the sculpture yet.

My picture of art by Wlodek Brühl, taken and published with kind permission.

So much for the “simple” structures, now on to more complicated ones. The ones below are similar in their setup to the ones above, but now they are photographed against a black background and in a large, black dish. Therefore we see the reflection of the sculpture on the water surface. This lets us look at different structures within the sculpture from two angles, making it even cooler to think about all the physics going on here!

My picture of art by Wlodek Brühl, taken and published with kind permission.

But now on to stuff done with more fun toys:

These are the newest works of art that Wlodek did only within the last two weeks! I personally prefer the translucent, fragile, light sculptures like the one in my living room, but I can also really appreciate those bouquets of spring flowers for their dynamic and lively shapes.

My picture of art by Wlodek Brühl, taken and published with kind permission.

Below I am showing a larger version of the sculpture to the very right above. In these new sculptures, Wlodek isn’t “only” working with drops, but now he has started to incorporate colored jets that are driven up by pressurised air. See how the yellow central jet broke through the umbrella formed by the orange drop that dripped on it from above?

Additionally, Wlodek is building vases around the bouquets by pushing dyed water through a rotating turbine. This vase breaks up into tentacles when it gets unstable!

The sculpture below is called “sundae with umbrella” and I cannot un-see this!

My picture of art by Wlodek Brühl, taken and published with kind permission.

But mostly I see flowers, specifically orchids. Below, the yellow drop from the top didn’t hit the green-ish jet from below completely center, therefore the latter broke up and seems to be turning towards us, wrapped in the orangey-yellow vase that has become very unstable on one side, but not so much in the back. Don’t you just love how the rims bulge together due to surface tension?

My picture of art by Wlodek Brühl, taken and published with kind permission.

In any case, I had a blast, even though, judging from the picture below that shows me giving the laudation, it doesn’t seem like it. Do I always look this serious? But the feedback I got was that everybody enjoyed looking at Wlodek’s art through a physics lense, at least after they got over their initial shock that they would have to listen to physics on their artsy Sunday morning. So this is definitely a scicomm format I want to explore more!

Me (in stripes) with the artists Regine Hahn (left) and Wlodek Brühl, as well as the host, chairwoman of Kunstkreis Preetz. Picture by Frauke Voitle, used with permission.

Intriguing interference pattern of waves

Do you see those weird traces going away from us, perpendicular to the wave crests, but in parallel to the bright stripes on the sea floor (I talked about those in yesterday’s post), looking almost like waves but not quite? What’s going on there?

Something very cool! :-)

In the gif below, I have drawn in several things. First, in red, the “weird” tracks that we are trying to explain. Then, in green, the crests of two different wave fields that are at a slight angle to each other. I’m first showing one, then the other, then both together. Lastly, I am overlaying the red “tracks”.

So this is what those tracks are: They are the regions where one of the wave fields has a crest and the second one has a trough (i.e. where we are right in the middle between two consecutive crests). What’s happening is destructive interference: The wave crest from one field is canceled out exactly by the wave trough of the other field, so the sea level is in its neutral position. And the wave fields move in such a way that the sea level stays in a neutral position along these lines over time, which looks really cool:

Some more pics, just because they are pretty and I like how they also show total internal reflection :-)

And don’t you just love the play of light on the sea floor?

And even though these weird neutral sea level stripes are parallel to the bright stripes on the sea floor, I don’t think that the latter one is caused by the first. Or are they? Wave lengths seem very different to me, but on the other hand what are those stripes on the sea floor if they aren’t related to the neutral stripes in the surface??? Help me out here! :-)

Wave watching by proxy — looking at how waves focus light on the sea floor

What is it that we actually look at when we go wave watching? Water is pretty much clear (or at least it is in the spots where I like to go wave watching), so how come we are able to see waves?

What we are looking at are not actually the waves themselves, but at how surfaces oriented in different directions reflect light from different directions towards us, and usually the light isn’t uniformly distributed, so we see lighter and darker areas on the waves that are associated with certain orientations of the surface, i.e. the slopes going up and down to and from the crests.

But this only happens if we look at water at a small angle — then the water surface acts to reflect most of the light from above. However if we look at water at a steep angle, we are actually able to look inside. See this in the picture above? This is due to a phenomenon called total internal reflection.

Now that light easily gets in and out of the water, the water surface does something weird: It acts as a lens and focusses light on the sea floor so we see bright areas and not so bright areas. And looking at how the brightness is distributed on the sea floor, we can figure out what the waves must be to have focussed the light in exactly that way, even though we can’t see the water surface.

Let’s start with an easy example. Below, you see the half circles of concentric waves radiating away from some obstacle at the bottom of the sea wall. The further away from the center you look, the more other waves you notice as the concentric circles become more and more difficult to see.

Moving on to a slightly more difficult case below.

You see the waves radiating away from the seagulls. Behind them, at a shallow angle, you mainly see the ambient light of the sky reflected on the waters surface to let you see the waves. Towards us, though, at a steeper angle, it gets more and more difficult to see the water surface and the waves, but we start seeing the light focussed on the sea floor, mirroring the circles of the waves above.

Here is another example of waves , except this time we see because of reflection of light on the surface further out, vs focussing of light on the sea floor closer to us, except that this time we are not looking at the same waves any more. The waves further out are wind waves and waves the birds made, the waves further in are similar to the ones in the second picture — created by an obstacle at the base of the sea wall.

But then sometimes it gets really difficult to reconcile the waves we see through these two different phenomena. Below, the wave field we see by looking at the light reflected at the surface seems to be dominated by wave crests coming towards us, with the crests being more or less parallel to the sea wall at the bottom of the picture. There is some small stuff going on on top of that, but it doesn’t seem very important.

But now looking at the pattern of light on the sea floor, we pick out something very different: The dominant wave crests are now perpendicular to the sea wall when you look at the middle of the picture below (towards the bottom we see those half circles again that we saw above, too)! Where do those wave crests come from that are perpendicular to the sea wall?

There are actually two things I can think of.

First: they are actually an important part of the wave field, we just don’t pick them up very well because — in contrast to the waves coming towards us with the side going up towards the crest reflecting the dark land behind us and the side going down towards the trough reflecting the bright sky — waves going perpendicularly to that field would mainly reflect the sky, so it would be hard to make out their crests and troughs since they appear to be the same color.

Second: I’m not actually sure this makes sense any more. I was going to say that the surface shape of wave crests moving away from the sun might be more suited to focus light than wave crests moving in a perpendicular direction. But looking at all the examples of circular waves that I posted above and that show up as circles, not just in areas where the wave crest was in specific directions, this probably doesn’t make sense. If anyone is reading this, what do you think??

Below is another example: Here we see a crisscross of waves, a checkerboard pattern of an incoming wave field and its reflection — as long as we look far out onto Kiel fjord. If we look into the water at a steep angle, we see again wave crests that don’t seem to match what we saw on the surface! (btw, don’t let yourself be distracted by the ripples in the sand that might look like they are also caused by light being focussed by the water surface. They are just ripples in the sand…)

Clearly I need to think about this some more to figure out what’s going on here. I’m grateful for any input anyone might have!

Wave watching at the locks in Kiel Holtenau

Yes, we are back to wake watching! Today I went to a new-to-me wave watching spot: The bridge across Kiel canal close to the Holtenau locks, which you see in the background of the picture below. And I should have checked out my favourite ship tracking app for better timing, I had to wait for quite some time before there were any ships apart from the small ferry which you see crossing right at the locks! But the wait was well worth it in the end!

In these pictures, you see very clearly the different parts of the wake. The turbulent wake right behind the ship where the ship has displaced a large volume of water and where the ship’s propeller has induced a lot of turbulence. The turbulent wake is bound by the foam created by the breaking bow waves. And outside of all of this, the V of the feathery wake opens up with the ship at its tip.

I am super excited about these pictures. Do you see the wake reflecting on the right (south) side of the Kiel canal?

And while it was pretty easy to interpret the pictures above, and the one below is still fair game because the turbulent wake of the third ship is still clearly visible, even though the ship is not, it is getting more and more complicated, isn’t it?

But now, with two of the three ships gone, it has suddenly gotten a lot more complicated. And it doesn’t help that the sides of the canal aren’t completely straight which leads to the mess in the lower right corner…

This is definitely a new favourite wave watching spot which you might see more of in the future! This stuff makes me so happy :-)

Vernissage of water sculpture photography by Wlodek Brühl, with explanations of the physics behind the pictures by yours truly!

I am a huuuge fan of Wlodek Brühl’s liquid art: Pictures of water sculptures that are created with focus on the tiniest of details, that only persist for milliseconds, but that are captured forever in all their fragile beauty. And I think these pictures are an awesome tool in science communication — I see so much physics in them (some of which I wrote about here already), and even if you come to an exhibition for the art, who wouldn’t love to learn some physics while they were there, too?

Well, we are about to find out! There is a new exhibition being opened (with brand new pictures!) on March 3rd in Preez. And I will actually give the opening speech for the liquid art half of the exhibition! I haven’t seen all the pictures yet so I can’t tell you exactly what I will be talking about, but whatever I say will definitely have to involve lots of fun physics :-)

Click for pdf

Roll waves, one of the more complicated #friendlywaves I’ve gotten over the years…

#friendlywave is the new hashtag I am currently establishing. Send me your picture of waves, I will do my best to explain what’s going on there!

When it rains, it pours, especially in LA. So much so that they have flood control channels running throughout the city even though they are only needed a couple of days every year. But when they are needed, they should be a tourist attraction because of the awesome wave watching to be done there! As you see below, there are waves — with fronts perpendicular to the direction of flow and a jump in surface height — coming down the channel at pretty regular intervals.

Roll waves on Verdugo Wash. Photo by Mike Malaska

Even though this looks very familiar from how rain flows in gutters or even down window panes, having this #friendlywave sent to me was the first time I actually looked into these kinds of flows. Because what’s happening here is nothing like what happens in the open ocean, so many of the theories I am used to don’t actually apply here.

Looks like tidal bores traveling up a river

The waves in the picture above almost look like the tidal bores one might now from rivers like the Severn in the UK (I really want to go there bore watching some day!). Except that bores travel upstream and thus against the current, and in the picture both the flow and the waves are coming at us. But let’s look at tidal bores for a minute first anyway, because they are a good way to get into some of the concepts we’ll need later to understand roll waves, like for example the Froude number.

Froude number: Who’s faster, current or waves?

If you have a wave running up a river (as in: running against the current), there are several different scenarios, and the “Froude number” is often used to characterize them. The Froude number Fr=u/c compares how fast a current is flowing (u) with how fast a wave can propagate (c).


Side note: How do we know how fast the waves should be propagating?

The “c” that is usually used in calculating the Froude number is the phase velocity of shallow water waves c=sqrt(gH), which only depends on water depth H (and, as Mike would point out, on the gravitational constant g, which I don’t actually see as variable since I am used to working on Earth). (There is, btw, a fun experiment we did with students to learn about the phase speed of shallow water waves.) This is, however, a problem in our case since we are operating in very shallow water and the equation above assumes a sinusoidal surface, small amplitude and a lot of other stuff that is clearly not given in the see-saw waves we observe. And then this stuff quickly gets very non-linear… So using this Froude number definition is … questionable. Therefore the literature I’ve seen on the topic sometimes uses a different dispersion relation. But I like this one because it’s easy and works kinda well enough for my purposes (which is just to get a general idea of what’s going on).


Back to the Froude number.

If Fr<1 it means that the waves propagate faster than the river is flowing, so if you are standing next to the river wave watching, you will see the waves propagating upstream.

Find that hard to imagine? Imagine you are walking on an elevator, the wrong way round. The elevator is moving downward, you are trying to get upstairs anyway. But if you run faster than the elevator, you will eventually get up that way, too! This is what that looks like:

If Fr>1 however, the river is flowing faster than waves can propagate, so even though the waves are technically moving upstream when the water is used as a reference, an observer will see them moving downstream, albeit more slowly than the water itself, or a stick one might have thrown in.

On an escalator, this is what Fr>1 looks like:

But then there is a special case, in which Fr=1.

Hydraulic jumps

Fr=1 means that the current and the waves are moving at exactly the same velocity, so a wave is trapped in place. We see that a lot on weirs, for example, and there are plenty of posts on this blog where I’ve shown different examples of the so-called hydraulic jumps.

See? In all these pictures above there is one spot where the current is exactly as fast as the waves propagating against it, and in that spot the flow regime changes dramatically, and there is literally a jump in surface height, for example from shooting away from where the jet from the hose hits the bottom of the tank to flowing more slowly and in a thicker layer further out. However, all these hydraulic jumps stay in pretty much the same position over pretty long times. This is not what we observe with tidal bores.

On an escalator, you would be walking up and up and up, yet staying in place. Like so:

Roll waves

Tidal bores, and the hydraulic jumps associated with their leading edges, propagate upstream. But they are not waves the way we usually think about waves with particles moving in elliptical orbits. Instead, they are waves that are constantly breaking. And this is how they are able to move upstream: At their base, the wave is moving as fast as the river is flowing, i.e. Fr=1, so the base would stay put. As the base is constantly being pushed back downstream while running upstream at full force, the top of the wave is trying to move forward, too, moving over the base into the space where there is no base underneath it any more, hence collapsing forward. The top of the wave is able to move faster because it’s in “deeper” water and c is a function of depth. This is the breaking, the rolling of those waves. The front rolls up the rivers, entraining a lot of air, causing a lot of turbulent mixing as it is moving forward. And all in all, the whole thing looks fairly similar to what we saw in the picture above from Verdugo Wash.

But the waves are actually traveling DOWN the river

However there is a small issue that’s different. While tidal bores travel UP a river, the roll waves on Verdugo Wash actually travel DOWN. If the current and the waves are traveling in the same direction, what makes the waves break instead of just ride along on the current?

What’s tripping up these roll waves?

Any literature on the topic says that roll waves can occur for Fr>2, so any current that is twice as fast as the speed of waves at that water depth, or faster, will have those periodic surges coming downstream. But why? It doesn’t have the current pulling the base away from underneath it as it has in case of a wave traveling against the current, so what’s going on here? One thing is that roll waves occur on a slope rather than on a more or less level surface. Therefore the Froude number definitions for roll waves include the steepness of the slope — the steeper, the easier it is to trip up the waves.

Shock waves: Faster than the speed of sound

Usually shock waves are defined as disturbances that move faster than the local speed of sound in a medium, which means that it moves faster than information about its impending arrival can travel and thus there isn’t any interaction with a shock wave until it’s there and things change dramatically. This definition also works for waves traveling on the free surface of the water (rather than as a pressure wave inside the water), and describe what we see with those roll waves. Everything looks like business as usual until all of a sudden there is a jump in the surface elevation and a different flow regime surging past.

If you look at such a current (for example in the video below), you can clearly see that there are two different types of waves: The ones that behave the way you would expect (propagating with their normal wave speed [i.e. the “speed of sound”, c] while being washed downstream by the current) and then roll waves [i.e. “shock waves” with a breaking, rolling front] that surge down much faster and swallow up all the small waves in their large jump in surface elevation.

Video by Mike Malaska

In the escalator example, it would look something like this: People walking down with speed c, then someone tumbling down with speed 2c, collecting more and more people as he tumbles past. People upstream of the tumbling move more slowly (better be safe than sorry? No happy blue people were hurt in the production of the video below!).

Looking at that escalator clip, it’s also easy to imagine that wave lengths of roll waves become longer and longer the further downstream you go, because as they bump into “ordinary” waves when they are about to swallow them, they push them forward, thus extending their crest just a little more forward. And as the jump in surface height gets more pronounced over time and they collect more and more water in their crests, the bottom drag is losing more and more of its importance. Which means that the roll waves get faster and faster, the further they propagate downstream.

Speaking of bottom drag: When calculating the speed of roll waves, another variable that needs to be considered is the roughness of the ground. It’s easy to see that that would have an influence on shallow water. Explaining that is beyond this blog post, but there are examples in the videos Mike sent me, so I’ll write a blogpost on that soon.

So. This is what’s going on in LA when it is raining. Make sense so far? Great! Then we can move on to more posts on a couple of details that Mike noticed when observing the roll waves, like for example what happens to roll waves when two overflow channels run into each other and combine, or what happens when they hit an obstacle and get reflected.

Thanks for sharing your observations and getting me hooked on exploring this cool phenomenon, Mike!

My escalator analogy for Froude numbers

The Froude number Fr=u/c is the ratio of a typical velocity of a current (u) and the phase velocity of the typical waves in that area (c). It thus describes whether a flow is subcritical for Fr<1 (i.e. with a current that is slower than the waves, so waves can propagate in any direction), or supercritical for Fr>1 (the current is moving faster than the waves, so waves can’t propagate upstream and are washed downstream with the current), and the transition between the two, where a hydraulic jump occurs (Fr=1).

Since many people find this hard to imagine, I like to use the “escalator analogy” (and please don’t try this at home or wherever you find the next elevator). But I think it works rather well as an analogy.

For Fr<1, the person on the elevator is walking faster than the elevator is moving. The person can thus get to where it wants to get, even though the elevator is running the opposite direction.

At Fr=1, the escalator moves as fast as the person, so the person is stuck in place.

And then for Fr>1, the escalator is moving faster than the person is, so the person gets “washed downstream” with the elevator.

What do you think? Is this analogy working for you? If yes, I might spend some more time on the animations. If no, well, I still had fun :-)