# Visualizing boundary layers using rheoscopic fluid

Or: How does momentum get transferred from a rotating tank to the water?

I recently noticed — and it was confirmed by observations and student feedback that my friend Kjersti got — that it is not at all obvious to students how momentum gets transferred from a rotating tank into the water. For me, the explanation “friction” always seemed sufficient. But Kjersti asked her students about it, and for them friction was something that can only slow down things, not speed them up. So I’ve been trying to find a good way to show how the water is actually spinning up and down: From the sides towards the center, and from the bottom up.

I am using a rheoscopic fluid here (prepared after Borrero-Echeverry, 2018, plus blue food coloring). Rheoscopic fluid is “current showing”, as in it looks homogeneous as long as there is no current shear, but as soon as there is shear, these silvery structures show up, thus showing all the small turbulent motion going on in the tank. (The rheoscopic fluid is not transparent, so you can only see the surface and cannot look into the tank)

Here is a movie, where I am first switching on the rotation and spinning up the water, (then bumping against the rotating table, sorry!), then switching the rotation off again and spinning the water down.

Can you see how when the tank starts spinning, shear instabilities at the side wall of the tank form? This turbulent boundary layer grows over time. I didn’t let the tank spin up to solid body rotation but switched it back off maybe half way there. When the tank stops rotating, a similar thing happens: A turbulent boundary layer forms and slows down the water from the outside in (and bottom up).

So basically this:

Borrero-Echeverry, D., Crowley, C. J., & Riddick, T. P. (2018). Rheoscopic fluids in a post-Kalliroscope world. Physics of Fluids, 30(8), 087103.

# 7 years of blogging! Celebratory wave watching with A LOT OF #friendlywaves

It doesn’t feel like it, but today marks the 7-year-anniversary of my first blog post on my “Adventures in Oceanography and Teaching”! To celebrate, I sent out this call to action (and please feel free to respond, no matter when you are reading this):

Below, I am sharing the pictures that people sent me plus my thoughts on them, newest on top. Pictures that reached me after August 28th 2020 will be posted in follow-up posts! (Keep them coming, I love it!)

## 23:58 — Kristina

Oooh, I love the internal waves on the interface between the milky part of the coffee and the not-yet-milky part! Looking at them moving very slowly always feels like being caught in slow motion, when of course the phase speed has to be very slow because of reduced gravity

## 21:55 — Phil (San Francisco)

Ooooh, this is awesome! Phil writes “photo of an awesome phenomenon that I took just before landing at SFO. San Mateo Bridge, San Francisco Bay on an evidently quickly rising tide!” and I am love the vortex streets! Count 4 pylons up from the bottom — that’s such a nice and clear von Kármán vortex street, absolutely beautiful! And then the bottom one does seem to show som shear instability. Now. In some spots vortex streets develop, while in others they don’t. But why?

## 21:06 — Clark (Bay of Fundy)

Clark wrote an entire thread explaining this awesome observation in the Bay of Fundy. You should totally check out the whole thread & explanations on Twitter, but I had to share this video so you can see what an exciting situation it is!

## 20:51 — Elin (Bergen)

Oh, nice one! Lots of tiny air bubbles in a vase or jug filled with water. Now. Is the line crossing through the water level? It kinda looks like it at first glance, because it seems to show a meniscus. On the other hand, there are bubbles sitting above that line, and they don’t look qualitatively different from the ones “under water”, so that seems unlikely. But then light seems to be refracted substantially differently above and below that line, so maybe we are looking at the water surface at some weird angle? Intuitively I would say that we are looking in from underneath the water level, but see the water line on the opposite side of the vessel. But that doesn’t seem to make sense with the (most likely level) table top? I will have to think about this some more!

## 18:14 — Simone (Hamburg)

How beautiful — in this drop we see the tip of the leaf it is hanging on pointing uo from the lower end of the drop! Nice example of how drops act as lenses and show us the world upside-down!

## 15:43 — Dong

Oh! Nice long waves coming in from far offshore. From the shape of the wave profiles I would guess that this was taken close to shore in shallow-ish water. This seems to be confirmed by the waves changing direction from further away coming towards us, which would indicate that the depth is changing over that distance

Unfortunately I could only screenshot that gif, check it out in the original tweet! What I find fascinating here is how there are two waves breaking offshore running towards us, but then there are several wave crests even closer to us that are still distinct and pointy (so the waves clearly didn’t loose all their energy breaking), but not breaking. I think there must be a shallow area where those two breaking waves are, making them break, and then deeper water again so that they are only temporarily tripping up and breaking, but then propagating further towards the shore without too much of an interruption

## 15:18 — Nena (Bodensee)

Oh, waves and a piece of driftwood! I wonder if it’s floating, it looks like it’s grounded. Otherwise I’d expect it to move with the waves, creating a dipole pattern when the ends take turns coming further out and then sinking deeper into the water.

And now a larger wave, breaking as it reaches the shore and also washing over the driftwood. I love how the water that came washing over the driftwood “in one piece” then disintegrates into drops when it falls down the other side!

## 15:13 — Jeffrey (Boulder)

Wow, this video is super tricky! Please check it out — volume up!

At first, I thought that the periodicity was set by eddies shedding periodically after water had washed over the obstacle. But after about the 50th time I looked at the video, the obstacle (is it driftwood?) seemed to start moving. If it is actually moving, the periodicity makes sense: The wood is trapped in place (you see that on the far side of the river) but it can move a little. It’s bopping on the water, floating at whatever height the waterlevel is at, but at the same time acting as a dam and trapping water on its upstream side, thus influencing the waterlevel. So this is basically a recharge-discharge oscillator. Maybe. Or maybe not. Any ideas, anyone? This is really tricky!

## 12:38pm — Gabriela (Lüneburg)

I would be so jealous of those kids playing with the locks and weirs and water channels if they weren’t my adorable nieces. Now I just can’t wait to go visit & play with this really cool toy!

## 11:49am — Gabriela (Lüneburg)

Somehow raindrop photography seems to be the topic of the day today? Here we see really well how a drop shows us an upside-down image of the world. See the sky at the bottom and the shed at the top, with the wine branches in the middle?

## 11:39am — Gabriela (Lüneburg)

Oh, a rain barrel! I think someone touched the side (possibly kicked it) so we get waves radiating from the outside in. Could also be that someone moved the ropes, but I would expect shorter wavelength waves then

This would be sooo difficult to interpret if I didn’t have inside knowlege: There are rocks hanging at the end of those strings to keep them in the center of the barrel, to guide the rain water in. What happened here is that someone pulled one of the strings to the side and let go of it. We see that the rock that was lifted when the rope was pulled out, is pulling the rope down again. That’s why the rope still has this weird bow shape, and that’s why we get kinda a wake where the rope moved from the outside of the barrel towards the center. All the other smaller ring waves are either drops that fell from the wet rope, or the ones that are centered around the other rope are caused by that rope vibrating because it’s attached to the first rope somewhere up on top

Here, my niece is demonstrating how to make wakes by swinging weighted ropes through water

Same as above, but we nicely see the capillary waves that radiate away

## 11:20am — Katharina (Hamburg)

I guess I said I liked a challenge… Screenshots with comments below! And check out the sound in the movie! Volume up!

At first I thought this was going to be a movie with pretty rainbows and reflections — water can create awesome prism effects!

But no! She dropped a fizzy tablet in! Here we see the first gas bubbles bubbling up to the surface. The bubbles get bigger the closer they get to the surface, because the pressure decreases and they can therefore expand

Already a lot of bubbling and fizzing going on! On the right side of the glass we can see that the gas bubbles are released in bursts. We also hear that when listening to the sound in the movie. Also funny to see how the bubbles raise in the middle of the glass and the flow is really turbulent there. Only at the rim can bubbles persist without bursting for a little while

The tablet has almost completely dissolved now, and what little is left has floated up to the surface (upper right). Btw, that fizzing sound is not really made by the water itself, it’s all the tiny bubbles bursting. Since sound are pressure waves and bursting bubbles radiate pressure, as the gas inside of the bubble is at higher pressure than the surrounding air and expands until the bubble bursts and then the pressure equilibrates. That’s what we hear!

## 10:46am — Astrid (Hamburg)

Astrid has a great taste! Both in her choice of reading materials (my blog!) and in her taste of coffee, with the beautiful swirls of milk in it. Here we see that molecular diffusion is slow when it has to physically swap whole molecules around — the swirls of milk are still distinguishable in the coffee (she clearly didn’t stir). But I would be prepared to bet that the milk has the same temperature as the coffee, because molecular diffusion of heat is fast (and also because she likes her coffee hot, the milk most likely went in hot)!

## 10:38am — Sara (Klein Waabs)

Phew, this is a difficult one! The first structures that jump at me (besides the wind surfers, of course) are the shadow of the sail (from the board to the left) and the reflection of the sail (from the board towards us), which are kind of distracting from the waves. And the waves are kind of messy, there is no clear direction visible. There is some wind causing the waves. Not very much, but enough to make it difficult to distinguish wind waves from others caused e.g. by the surf board.

Now we have some wind! We see waves breaking at the stones offshore (and looking at how high the foam is flying, those waves were not too shabby!), but we don’t actually see a lot of those waves because everything from the wave breakers towards us is in the lee and thus sheltered. But we see some long waves that have propagated into this bay that break on the beach

## 10:37am — Florian (all over the world!)

Cabo da Roca in Portugal; westernmost point of the continent. This is beautiful! Waves from far offshore arrive at the beach. As they reach the shallower water, all of their properties except their frequency change: Their wavelength gets shorter, their height larger, their steepness larger. When one part of a crest is in shallower water than the rest, the crest bends towards the shallower areas. The breaking waves create a lot of foam, indicating that there was some biological activity creating a surface film

Falesia Beach, Algarve. Oh how beautiful! Breaking waves on the other side of those rocks, and only the longer waves make it into the calm, sheltered space this side of the rocks. Interesting example of a filter that only lets long wavelength come through!

Algarve-Coast. What strikes me here are the beautiful colors! Near the beach, we can look into the water and see the sandy sea floor as well as some larger rocks, that seem to be partly overgrown. The further we look offshore, the bluer the sea gets, because at shallower angles the reflection from the sky increases, until at a critical angle, we only see reflections and can’t look into the water any more.The different shades of blue in those areas show where breezes rough up the water, darker areas are those where there is currently more wind and the surface roughness is higher. Another thing I am noticing are the waves that the person in the water makes — circles around them.

Timmendorfer Strand, Baltic Sea coast. On a windy day! We can see that from the whay the waves are breaking, not only right at the beach and in areas where the water is shallower, but also in smaller, more random bursts. Also waves don’t have the same regular shape as they would have had this wave field traveled to the beach from far away, it seems to be somewhat regional. Also love how far the waves run up the beach (as you see from the large area covered in foam). This must have been a fun day to play at the beach!

Maschsee Hanover — I love how you see different things in this picture: First, how stuff floating in the water dampens out the waves (see how there are a lot more waves behind the plants floating in the water than on this side). And then the wakes that this cute family of swans is making as they are swimming towards us!

## 9:09am — Gabriela (Lüneburg)

Honestly, what jumps at me most is my ADORABLE niece who’s saying Kaffefoto (“coffee pic”). But then there is also the puzzle of why the coffe coming out of the machine looks so much lighter than when it’s in the mug (underneath the foam)? Well, the foam is the clue here! When there are a lot of airbubbles in the coffee still, they reflect light differently (i.e. from all different directions, making it look white, rather than directional, showing either the color of the coffee or a reflection) than when the coffee has settled down and the air bubbles have gone away.

## 9:01am — Kristin (hiking somewhere near Bergen)

Did you ever wonder why waterfalls (or really turbulent rivers) always look white, while a lake or the ocean can look all kinds of different colors depending on what is dissolved in the water and what they are reflecting on the surface? The answer is that in waterfalls (or the really turbulent, “white water” rivers), there are tons of tiny air bubbles trapped in the water. All the surfaces of those air bubbles and also the turbulent flow itself make the water surface very irregular. Since the surface is so irregular, it reflects light from all different directions, rather than just one. As we receive all that different-colored light, our eye interprets it as white. Fun exception: Sometimes we see rainbows in water falls. Then the sun as light source is so dominant that we see the sunlight reflected in the falling water drops and a rainbow appears!

Oh I love this! I think that what Sid doesn’t show us on the very right is a narrow connection to a second body of water, on which waves are generated by wind. (Alternatively, there might be something there at the very right just outside the frame that is making waves, such as a bird or a fountain, but I don’t think that’s the case. Birds usually don’t move this regularly for long enough to generate this wave field even before you started filming and then throughout the whole movie. Fountains usually generate concentric waves (unless there are several fountains, in which case this would be a trick question ;-))) So let’s assume that wind-generated waves from a second body of water pass through a narrow inlet onto this pond. As they pass the narrowest part, they start spreading to all directions, forming concentric waves that grow over time. Well, almost concentric, because the narrowest part isn’t a perfect point source. Therefore we don’t see diffraction at a slit, but rather at a wider opening.

## 8:58am — Torge (Kiel)

Not a picture, but even better: He managed to fix the problem we had been having with the co-rotating video of our rotating tank. Super excited! If I wasn’t so busy today (slightly underestimated how many pics my dear friends would send me!) I would go try it out right away!

## 8:51am — Sam (Manchester)

Raindrops on the window! I love how, especially with the ones in the upper part of the window, you can see the world upside down: the bright sky at the bottom of the drops, the darker trees at the top. In the drops further down the window you see the sky at the bottom, then the darker bushes and trees, and then the brighter gravel & car! So cool!

## 8:28am — Ronja (Nordsee)

On this beautiful picture you clearly see wave crests meeting up at an angle, even though further offshore they all seem to be coming in parallel to the beach. Why? Because there is this groyne going out perpendicular to the shore. You see some of the stones at the bottom of the picture, but from the wave field we see that it reaches further offshore and is just submerged there. Where it is submerged, the water depth suddenly decreases. Waves running close to and on top of it therefore change their speed, and with changing speed, the wave crests bend towards the obstacle (as they are being slowed down more on the obstacle side than on the deeper side). Since this happens on both sides of the groyne, we get this cool checkerboard pattern!

Same explanation as above, but another beautiful picture! :-)

## 8:13am — Elsa (Bergen)

Ha! Knowing where this picture was likely taken, the fist thing I notice is the reflection of the masts of the sailing ship Statsraat Lehmkuhl! And how pretty the light is looking in between the hulls of the catamaran. And how there are waves radiating away from where other waves bumped against the bottom of those tyres

Bergen is so beautiful! I love how we see the reflection of the colorful houses of Bryggen, then the dark mountain of Fløyen behind it, and then a blue sky with pink clouds! And how the structures of waves are clearest where there are strong contrasts in brightness of the reflected light, for example at the pink/blue boundaries!

More beautiful Bergen. The dark mountain’s reflection does not have a sharp edge, because the water surface isn’t flat. So depending on the angle of the surface, some spots still show mountain while others already show the sky

Same as above, PLUS isn’t it cute how the floaty bits in the foreground have their own little wave rings around them???

What jumps at me here is the turbulent (white) water, most likely caused by a speedboat

Here I love how the surface appears smooth even though there are very clearly waves on it. That means that the waves we see haven’t been caused locally by wind, otherwise there would have to be smaller wavelength stuff on them. Instead, they were generated further offshore and traveled here

## 7:26am — Kati (Schönbrunn, Wien)

First thing I notice here: How pretty this looks with the reflection! And beautiful weather! Hardly any waves, but there are some structures in the lower right that look like there are possibly plants growing in the water, just breaking the surface

## 7:07am — Marisa (Hamburg)

Looks like it’s raining in Hamburg! What I always find super cool about rain drops is how they act as tiny lenses and show us an upside-down picture of the world

## 6:26am — Désirée (Möhnestausee)

This is a picture taken at the Möhne reservoir — a river that has been dammed to create this lake. The water level is regulated, which you see in the horizontal stripes on the opposite side of the lake, each representing what the water level was like at some point in the past..

What an awesome pic! But wait — aren’t water drops (or anything, really) supposed to fly in a straight line, unless there is a force acting on them? There is obviously gravity acting, but why the curve? This riddle is solved by looking at the flying droplets, which are individual droplets. And even though they look as if they are following a curved path one behind each other, this is just our eye being tricked into that. Each drop is flying on a parabola (thanks, gravity) away from the spot where it detached from the end of the flying wet hair. But the drops are not following each other, they just happen to have detached from the hair along a path.

## 6:17am — FrozenBike (Khajoo Bridge in Isfahan)

I’m posting a couple of screenshots from that video to make it easier to discuss…

First, doesn’t this lake look absolutely beautiful? The calm surface is an almost perfect mirror of the sky because we are looking at the water at a shallow angle, thus we only see reflections and can’t look into the water

Then, we look down. See the plants in the water in the top left of the picture? They indicate quite a strong flow from top left to bottom right of the picture. But wait, there is an obstacle in the way! That stone introduces turbulence. There are waves that are created as water washes past, and there are also eddies shed because the current shear between the flowing water and the more stagnant water in the shelter of the stone is so strong. See that one water plant thingy right below the train of eddies? It seems to be moving in the turbulent flow, too!

And we reach the next obstacle! At the top left, water is still flowing slow(ish), thus the surface is flat and we can clearly recognize the tree reflected in the water. But then we reach the threshold, and all of a sudden the flow goes from laminar to turbulent. See how the whole right side of the picture seems to be full of tiny bumps? That’s where the water is influenced by the structure of the bottom underneath

I absolutely LOVE that my blog and twitter have helped me meet and connect with so many wonderful people all over the world! Here we see Khajoo Bridge in Isfahan, Iran. So beautiful! As for wave watching: In the left side of the picture we see what was the right side of the picture above, the very fast, turbulent flow down the slope. And then at the bridge, there is a jump in surface height: As the water is deeper there, the flow slows down to subcritical speed and a hydraulic jump develops

Last screenshot: The hydraulic jump shown in the last picture, only more prominently pictured. Also visible: The influence of that stone edge on the flow. See all the waves that radiate from it as it is restricting the flow? Super awesome!

## 6:06am — Chirine (Kiel)

What I notice first is the tiny white sliver of light, close to where the spoon breaks the coffee’s surface. That’s showing us that the surface isn’t perfectly straight, but that it is deformed where the metal of the spoon and the coffee meet. The effect — cohesion between molecules — makes the coffee rise up a little at the edgs of the cup and also where the spoon breaks the surface. You might know this from the meniscus that shows up in test tubes and makes it difficult for the untrained eye to estimate how full a test tube really is

# One of the most difficult #friendlywaves I’ve ever gotten! Did I get it right?

Florian sent me a #friendlywave — a wave picture he took, with hopes that I might be able to explain what is going on there. And this one had me puzzled for some time!

This is what the picture looks like:

What I knew about it: Florian was on the ferry from Wisschafen to Glückstadt, crossing the Elbe river.

In the picture itself, there are several features that jumped at me. First, drawn in with the lightblue line below: A sand bank parallel(-ish) to the island’s coast line.

Then, the ship’s wake (shown in red) breaking right near the ship (orange) and turning (green) and breaking (yellow) where it runs on the sand bank.

Florian wrote he was watching the ferry’s wake and noticed something curious: There seemed to be a shallow part, where the waves suddenly became a lot faster! And could I explain what was going on?

Looking at the picture, there were two possibilities for what he might have meant (and, spoiler alert — I completely jumped on the wrong one first!).

Below, I’ve drawn in the part of the wake that is running on the shallow sand bank (green) and how those wave crests continue on the other side of the sand bank (red). I’ve also drawn in some mystery wave crests in blue. Those were the ones I chose to focus on first, since Florian had written that he noticed waves behaving weirdly and suddenly becoming much faster. So if we are talking fast, we are talking really fast, right?

So how do we explain those blue wave crests?

There is a limit for the maximum speed a wave can have. That limit depends on the wave’s wave length: The longer a wave, the faster it travels. In deep water, i.e. water deeper than 1/2 the wavelength, the wave travels at this maximum speed (see green lines in the plot below).

But as it comes into shallower water, it gets slowed down (see black lines in the plot below — those are just a quick sketch, there are complicated equations to calculate it exactly).

In shallow water, i.e. water that is smaller than 1/20th of the wave length, the phase speed only depends on water depth: The shallower the water, the more the wave is being slowed down (see the red lines in the plot below).

Sorry about the quality of the sketch — I don’t have Matlab or anything else useful on the computer I have available right now, so I drew this in ppt! Take it with a pinch of salt, but qualitatively it’s correct!

So looking back at Florian’s picture, for the blue waves to have been caused by Florian’s ferry, there are two options:

A) they would have to have wave speeds faster than the ferry’s bow wave and wake

B) the ferry would have had to come from the direction of the island, so that the waves propagated in that deeper channel behind the sand bank before the ferry made its way around the sandbank.

Option A is impossible, because wakes travel at maximum wave speed (similar to a sonic boom in the atmosphere, where sound is travelling at maximum speed, forming a cone with the air plane at its tip, only here it’s a 2D version, a V-shaped wake with the ship at its tip). So if the wake is traveling at maximum speed already, then the blue waves can’t go faster than that.

For option B, looking Florian’s ferry up on a map, I saw that that ferry goes around a small island, which is the land you see in his picture. But a quick glance at the map shows that even though the sand bank seems to end where the ship would have had to have gone in order to create those waves, the island is still very much in the way. So this can’t be the solution, either.

This map is published at http://map.openseamap.org under a CC BY-SA 2.0 license

So let’s take another good look at the original picture.

Remember those wave crests that I marked in blue? Well, upon closer inspection it turns out that they are tidal gullys and not wave crests! (Which is what Florian confirmed when I asked whether he remembered the situation) Guess I have been barking up the wrong tree all this time!

So back to the wave crests that I marked in red:

What we see here is exactly the depth dependence of the phase speed that I plotted above. Right at the sand bank, the water is shallowest and waves are slowed down (we see that both in the green wave crests that seem to be falling back and start breaking as they get closer to the sand bank [both indicating that the water is getting shallower], and in the red wave crests right at the sand bank). But as the water gets deeper again on the far side of the sand bank (which depth measurements in the map above seem to confirm), the phase speed picks up again (as it has to — see my plot above) and the wave crests accelerate again. Hence we have the weird phenomenon of waves suddenly speeding up!

Very long explanation, I know, but still pretty cool now that we solved it, right? I love #friendlywaves — if you have any mystery wave pictures, please do send them my way! :-)

# Such a pretty #friendlywaves!

My long time Twitter friend Anne shared these beautiful pictures and I absolutely had to do a #friendlywaves post where I explain other people’s wave pictures.

Take a moment to admire the beautiful picture below. Wouldn’t you love to be there? I certainly would!

What can we learn from this picture? First — it’s a windy day! Not stormy, but definitely not calm, either. See how the water outside of the surf zone is dark blue and looks a little choppy? That’s the local wind doing that.

And then there are the waves that we see breaking in the foreground. Without knowing where the picture was taken, I would think that they traveled in from a large water body where there was a long fetch so they could built up over quite some distance. And then they meet the coast!

You see breaking waves of two kinds: the one marked with red ovals below, where there is hardly any buildup of the wave before it meets a rock and breaks into white, foamy turbulence. The other type of breaking waves, the ones where I marked the crests with green lines, build up over a short distance before they break because there is a more gradual decrease in water depth. The stope is still quite steep so the waves change from deep water (where they can’t feel the sea floor and have a fairly low amplitude, so we can’t distinguish wave crests further offshore than the two I marked in green) to shallow water waves that feel the sea floor and build up to break.

In contrast, let’s look at the lovely picture below.

Here, we have a sandy beach on which the waves can run out. There slope right at the water’s edge is not very steep, but seeing that we can only really spot two wave crests there has to be a change in gradient. About where the offshore wave crest is in the picture below, or possibly a little further offshore, the water depth must suddenly increase, otherwise there would be more wave crest visible further offshore. Since there aren’t any, water must be a lot deeper there.

But what I found really cool about the picture above are the trains of standing waves in the little stream that flows into the sea here. I find it so fascinating to see standing waves break in the upstream direction — so completely unintuitive, isn’t it? So much so that I dug out some pics from January for you and posted them last Friday in preparation for today’s post. Sometimes I actually plan my posts, believe it or not!

Standing waves don’t move in space because the flow of the current they are sitting on is exactly as fast as they are moving, only in the opposite direction. What is happening in the picture is that in those standing waves sit on ripples in the sand. The waves become so steep that they are constantly falling back down onto the current, get carried up the ripples again, in an endless loop. So fascinating!

# A #friendlywaves from Lofoten

A #friendlywaves post: you send me the pictures, I talk about physics! Today: My friend A sent me these lovely pictures from Lofoten, knowing I love wave watching. And there is so much to see!

Let’s begin with the picture above, where we are looking out over the stern of a ship towards a bridge. There are two different kind of things that jump out to me: The ship’s wake and the tidal current.

The ship’s wake consists of two parts: The turbulent wake we see right in the middle of the picture, behind the A-frame crane (in between the red lines below), and the feathery V-shaped wake (some of the individual “feathers” are marked in green).

And then there is the turbulent backwater behind the bridge’s pylons that’s caused by the tidal current going through underneath the bridge. Pretty cool, isn’t it?

And now on to the next picture, that is one of the most beautiful wave pictures I’ve seen the last couple of weeks: Now we are sailing in the wake of a second ship.

We are following the other ship a bit off to the side, therefore the perspective is a little confusing. Between the red lines, we see the other ship’s turbulent wake. Additionally, it has an interesting V-shaped wake that actually consists of two stacked Vs, a bit like this: <<

One of the Vs is the actual bow wave radiating from where the ship’s bow cuts through the water, the second one detaches further backwards from the ship. Both Vs are marked in dark green below. But to the left of the picture, in light green, I marked some of the individual “feathers”, wavelets that make up the V-shaped wake.

Isn’t it fascinating? I love this.

# A beautiful #friendlywaves from Spain

A reader of my blog, Rocío*, sent me this beautiful image from Arnao beach (Castrillón- Asturias-Spain), and I asked if I could use it in a #friendlywaves post. He agreed, so here we go!

First, let’s check out the original image in all its beauty, before I start scribbling on it. What features of the waves stand out to you that you find especially interesting?

For me, what I think is especially awesome here, is how the behaviour of the waves lets you draw conclusions about the sea floor underneath. Look at all the wave crests coming in nice and parallel. Far offshore, it’s difficult to even see wave crests (marked orange, for example), only when they come closer to the shore and the sea gets shallower, they start to build up, get a distinct shape. Yet in some places they become a lot steeper and start breaking a lot further offshore (red marks) than in others — why?

Because in those spots the sea is shallower, thus the interaction with the seafloor is a lot stronger. If you look at the yellow mark, for example: Offshore of it the wave crests are still very shallow and not pointy, and then all of the sudden they break. Here the water is deep until there is a very fast change and then it’s suddenly very shallow (and probably rocky, hence all the turbulence).

And then, if you come closer towards the shore, there is an area that has only a very gradual incline, where the shape of the waves hardly changes any more (blue marks).

And then there is a small inlet to a large puddle that acts as “slit” (albeit a fairly wide one) and lets waves radiate as half circles from where they enter through the slit.

I love how in such a beautiful image of such a beautiful landscape, there is so much physics that we can discover if we only choose to look! :-)

*I asked how I could credit the picture to Rocío, but he doesn’t have Twitter or a website and wrote “I only want you to explain it for people i love your blog and your information you are doing a great job”. Aaaaw, thank you!!! :-) And thanks for sending me this beautiful picture!

# Christina’s #FriendlyWaves from Panama!

Christina writes on Twitter: “#wavewatching from a plane, approaching #Panama. @Meermini, do you know what causes those regular ‘wrinkles’?” and how could I resist writing a blog post about what I think might be the explanation?

Below is the picture Christina shared on Twitter.

Picture by Christina Oettmeier @sulfurium

What I think we see here are basically two wave fields: The regular “wrinkles” and then a lot of small crinkle.

The small crinkle are boring: local, wind-generated waves. They are not what Christina asked about.

But the wrinkles are swell: Waves that were formed in a storm far, far away and that have propagated here over a long distance. While propagating from the area where they were formed to the beach where Christina took these pictures, the waves got sorted by wave length. The longer a wave, the faster it propagates in deep water. So long waves from a distant storm will arrive first, and over hours or days the wave lengths of the waves arriving at the beach will get shorter and shorter. The wave lengths we see here seem to be about the height of the high rise buildings we see on the shore. The highest high rise in Panama is almost 300m high, so the wave lengths might not be that long, but at least 100+m.

Why do they look so “wrinkly” and not like proper breakers? When waves are in water that is shallow compared to their wave length (so say water depth would be less than 50m for these waves if we assume they are 100m long, which I think are both reasonable estimates), their shape changes from the normal sine-shape that they would show in deep water, to steep crests and loooong troughs. You might have observed waves with this shape for example in the very shallow waters of a beach on the wadden sea coast or any other beach with a really small slope, where waves look like sausages or pool noodles that are being shoved onto the beach (compare for example to pictures in this post).

What makes me confident that we are really seeing what I’ve just described above? Mainly that I can see the interaction of the waves with the sea floor. If you look at the pic above, do you see the area where the waves bend? That’s where the water is shallower. I’ve tried to sketch that below: The red lines are — in first approximation — the wave crests (I’ve only drawn in every third or so for clarity). Red dashed lines are kinda the second approximation of the wave crests: Those are the deformations that I want to talk about. And those deformations are caused by a shallower area, which I’ve drawn in with the green dashed line. This little submerged headland slows that part of the waves down that runs above it (because in shallower water the wave’s speed only depends on water depth, not on wave length any more), but not the rest of the waves that propagate towards the beach with the straight crests intact.

It’s even easier to be confident when we look at the next two pictures that Christina shared with me. Now we are a little closer to the beach and can see the area where the waves break and where it is shallow enough that the wave lengths drastically decrease (since the waves are slowed town more and more the closer they come to the beach, waves that are further out are still faster and can catch up to waves in front of them). This is very typical for the parts of a beach where the depth changes rapidly.

Picture by Christina Oettmeier @sulfurium

And on the next pic, we see even more clearly that the waves change from pool-noodle shaped offshore to breaking waves close to the beach:

Picture by Christina Oettmeier @sulfurium

In case you don’t see what I am trying to point out, here an annotated version of the pic above. Green dashed circles: Smudges on the window, or possibly reflections on the window, but nothing to do with the waves. Red circles: Here we see foam on the back side of breaking waves, so there was definitely some wave breaking going on here. And blue circle: Cool structures in the flow of water that is retracting downslope from the beach, back into the ocean.

So much for now. No idea if that made any sense to anyone except myself. Please let me know! :-)

# #friendlywaves: You send me a picture, I (try to) explain the wave field!

Do you like observing wave fields and pondering what might have caused them? Why they look the way they do? What caused them? What they can tell us about the wind, the sea floor, the trajectory of a ship?

This is actually not an easy task and takes a lot of practice and a good understanding of the physics involved. If we observe the waves in real life, we can observe the wave field developing over time, turn our heads or walk a little to see what’s happening around that corner, feel the wind or hear the ship. But it might still be difficult to figure out what is going on.

If you really want to know what is going on, though, or want to send me a little friendly challenge to see if I can figure something out that you already have the solution to, you might enjoy to send me a #friendlywaves#friendlywaves means: You take a picture of waves, send it to me via email or social media, and I write a blogpost, explaining as much as I possibly can related to the wave field. And you get to tell me if I got it right, because you were there and I wasn’t!

Check out the blogposts tagged #friendlywaves for examples of previous #friendlywaves that people sent me.

If you have any interesting pictures, please don’t hesitate to send them my way, I love a good challenge! :-)

# Astrid sent me a #friendlywaves from Whitstable for remote #wavewatching

Astrid, #wavewatching supporter from Day 1, sent me these pictures for a #friendlywaves post. Today, I want to start with a spoiler picture (or, rather, I did start with a spoiler picture already — see above) that shows you the setting at low tide to help us explain the wave pattern that we then observe at high(er) tide.

Note the headland in the picture above? Below shows what it looks like when it is covered in water:

Astrid, as a real #wavewatching pro, also sent me a video, so I can show you the super cool interference happening here.

Wave crests from far offshore (probably caused by a storm somewhere far away) arrive in shallower water and get broken up into parts on either side of the (now submerged) headland. But on either side, the wave crests also change their shape, being refracted towards the headland. And some of the wave crests make it over the headland, now at an angle to each other, meeting waves from the other side. And where they meet, they steepen up and even break occasionally. Doesn’t it look super cool to watch waves run towards each other in such a way, creating these interference pattern?

This wave pattern always reminds me of one that I saw years ago — coincidentally with Astrid! — when we were in Iceland in 2013, the day after my dad’s heart surgery. And while watching those waves then was beautiful and calming, seeing this pattern still always reminds me of a pretty traumatic time. So I am happy that this new wave pattern will now at least partially overwrite some of those memories with a very happy day: Herzlichen Glückwunsch und alles alles Gute, liebe Simone* & family!

*That is Astrid’s friend Simone, not my own sister Simone, although of course alles Gute to her, too :-)