# 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! :-)

# 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 #friendlywaves from Cyprus

My friend Alice (of the awesome Instagram @scied_alice and the equally awesome blog, which you should totally follow) sent me a #friendlywaves from her trip to Cyprus. She said that this was a simple one, so I am looking forward to what else she has up her sleeve once I pass this test ;-)

So here we go with the pictures she send.

Clearly, she is on a boat trip, and she’s looking back at the wake of the ship. You see the one side of the feathery V of the wake, pretty much in the middle of the picture. On the “feather” closest to us, you can still make out the turbulent part of the breaking bow wave, where the water surface looks all crumpled up and not as smooth as it does further away from the ship. Actually, this is a really nice example to show that the waves are traveling away in the wake, but the water is not: All the other “feathers” further away have smooth surfaces as they have run away from the ship’s trajectory, while the turbulent wake traces out the exact path where the ship went (as long as there aren’t any currents moving around the water, which we’ll assume for now).

Picture by Alice Langhans, used with permission

The waves in the V-shaped wake are fairly steep, you can see them very slightly tipping over on occasion.

And Alice sent a second picture: Similar situation, except now it’s a little more windy. The turbulent wake is a little more foam-y than in the previous picture. This could be because the ship is sailing faster, or because it’s more windy. I would guess the first.

And when I say “sailing”, I am using this as the technical term for a ship driving. I am assuming that the boat Alice is on is not a sailboat. I’m thinking this because the wake looks fairly turbulent and sail boats usually don’t cause this much turbulence; also the little bit of the boat that I can see doesn’t really scream sailboat to me. We’ll have to wait to hear what she tells us, though!

Picture by Alice Langhans, used with permission

On both pictures, there is hardly any swell visible. Waves are usually not as visible when the water is deep as when they run up on a beach, and so far off shore we can assume that the water is fairly deep. But that also means that it isn’t very windy, hasn’t been very windy recently, and hasn’t been very windy anywhere near recently, either, so no large waves have traveled into the region.

So much for these #friendlywaves. How did I do, Alice? :-)

# Wave watching on Kiel Canal: Bulbous bows and how they shape the wave field

Even when I fully intend to just go for a Saturday afternoon walk to catch up with a friend, this is what happens…

I get distracted by waves. Like the crisscrossing pattern of waves and their reflections that you see below.

Or the amazing bow waves of ships passing by. Isn’t it fascinating what a huge amount of water is displaced by the ship’s bulbous bow, piling up into a mountain in front of it, then the sharp dip where the actual ship begins? (If you want to read about why ships are built with a bulbous bow, check out this old blogpost).

Having a bulbous bow alone does not always lead to the same bow wave. Which is fairly obvious when you think about it, of course the speed of the ship or the shape of the bow influence the wave field that is created, but also how heavily the ship is loaded, i.e. how deep the bow is in the water.

What you can see very nicely on the sequence of pictures of bows and bow waves in this post are bulbous bows going from fairly far out of the water (above) to fully submerged (towards the end).

And I just love the sharp contrast of the smooth water piling up and then the turbulence and breaking waves right there. Interesting example of subcritical and supercritical speeds, btw: The ship travels faster than the bow wave (so the bow wave can’t overtake the ship, but always stays behind it, forming a two-dimensional Mach cone).

The ship in the picture below is the odd one out in this blogpost: It does not have a bulbous bow but just pushes water in front of it. This is an interesting example of a bow shape that is clearly not optimized for energy efficiency when traveling large distances, but then the purpose of that ship is obviously a different one. But isn’t it amazing how such a small ship creates waves larger than all the other much bigger ships do, just because they have better bow shapes?

But beautiful wakes nonetheless. I love those tiny ripples riding on top of the wakes!

And, of course, the checkerboard pattern of a wave field and its reflection.

Here is another example of a ship with a bulbous bow, this time it is almost submerged. Since they are designed to be fully submerged, this ship is loaded in a way that is closer to what it was made for, and you see that the generated waves are smaller than the ones in the pictures up top.

And look at its wake — really not a lot going on here, especially when compared to the much smaller ship a couple of pictures higher up in this post!

Now for a ship that is hardly creating any waves at all, the mountain of water that it’s pushing in front of its bow looks especially weird since the bulbous bow isn’t visible any more.

See? (And isn’t it cool how the chronological order of pictures in this post just coincided with ships laying deeper and deeper in the water? I love it when stuff like that happens :-D)

And then, of course, I had to include some more pictures of beautiful wakes…

Do you see, comparing the picture above and below, how the first one was taken when the wake had just reached the shore, and the second one the wake was reflected on the shoreline already?

Not many things make me as happy as wave watching :-)

P.S.: Ok, one last bonus picture (non-chronological, we saw it some time during the walk. But that’s ok, I wasn’t going to include it until the post was already done and I decided that you just HAD to see this): Someone who is clearly not using their bulbous bow to their advantage. But at least I get to show you what they look like when they are not in the water. And we got to speculate about how annoying it is to be on a ship with such a strong tilt all day :-D

# Feathery wavelets and wakes

My sister took this amazing picture — and from a train no less! And I got super excited. Can you see the feathery wavelets* of the bow wave of that large ship? And then the wakes of both ships, spreading out at the same angle? I should definitely start spending time on high bridges going across canals, there is so much unused potential for wave photography!

*I was super convinced at first that they were called “winged wavelets”. But then doubt started to kick in, so I asked google. Turns out they are called “feathery”. However, apparently “winged wavelets” is a very poetical expression, all google hits are in some poem or other! And one that I really liked by Mary Bamburg, where it goes like this (as part of a longer poem):

“… waves wring sand from the shore,
strew shells, strech after them
white wash and wild winged wavelets
glass green, blaze blue, slick silver …”

Does it create the same beautiful image before your inner eye as it does for me?

# Wavelets on bow wave

The other day (well, the other day when I was still at sea and wrote that blog post. Been quite a while since…), when sailing in calm waters, I noticed the wavelets of a bow wave.

And I cannot not see them these days! No matter how much the other waves try to disguise any trace the boat might be trying to leave to prove its existence, the bow wave wavelets put up a fight to be noticed.

Below, you see the direction the ship is sailing in (yellow), the wash from the broken bow waves (green) and the wavelets that form the bow wave (red).

And they look extremely pretty in the setting sun, too!

If you like pictures like this, you’ll love my book! Stay tuned!