The thing that really blows my mind about kelvin wake patterns is that they don't depend on the details of the fluid or even the strength of gravity. The Wikipedia page has amazing photographs of volcano islands disrupting a layer of clouds in exactly this way with the same 19.5° angle. And if Titan has alien ducks swimming on its liquid methane seas, they will make the same pattern too.

FAQs Q. Doesn't a fast motorboat have a much smaller angle? Yes, it does. For fast boats, the stationary waves following it would also be fast, so they need to be very long. But an object typically does not produce significant waves of a wave length longer than its size. So for a fast boat, we would be missing part of the stationary contributions. There still seems to be some debate about the best way to understand fast boat wakes, see physicsworld.com/a/physicists-rethink-celebrated-kelvin-wake-pattern-for-ships/ Q. Doesn't this break down for really slow objects? Yes, it does. Think about a duck barely moving: its waves propagate in all directions. For very slow objects, stationary waves would need to be very slow as well, so they'd need be very short. The issue is that waves shorter than a few cm are governed mainly by surface tension instead of gravity. When surface tension is the main force, shorter waves actually move more quickly than longer ones, so the story changes completely! Indeed, very short waves can get ahead of a moving object. Often you can see such ripples just in front of a swimming duck. Q. What about very small objects? For very small objects (insects, young ducklings), the pattern is different because the waves are mainly driven by surface tension instead of gravity. See the answer above about slow objects. Q. How does the picture change depending on viscosity? Everything in the video assumes zero viscosity. This is a very good approximation for larger objects moving through water. Adding a little viscosity would just dampen the pattern, making it fade out as it gets further from the source. I don't know what exactly would happen in a fluid with large viscosity, except that the duck would get tired very quickly trying to swim through it! Q. How does the picture change depending on the density of the fluid? It doesn't. Just like mass disappears from the equations when you calculate the trajectory of a falling object (in vacuum), the density drops out from the wave equations here. Q. Do sound waves form the same patterns? Sound waves are quite different. For sound waves the restoring force is pressure, not gravity, so the dimensional analysis in the video doesn't hold. In fact, for sound waves the speed does *not* depend on the wavelength (but it does depend on the material). With sound waves you only get a V-shaped pattern if the object is moving at supersonic speed. Such a V-shape (called a "mach cone") is a shock wave instead of the smooth feathery V behind our duck.

Glorious transition from simulation to duck picture well done!

All of this video is excellent, but possibly my favourite part of it is the title. It's so much fun to say, almost even to sing.

Thank you for your explanation. I always thought that the angle depended on the speed of the swimming object. But, you are right, it doesn't matter, whether it's a duck or a boat. It always looks the same. Nice animations and nice explanations. I'm a big fan of dimensional analysis😎

it's 3am and i am learning thing i didn't even know i could learn. thank you

Let the algorithm bless this video

Hydrodynamics simplified, this is gold

None of the ducks were hurt during the making of this video, they still are happily making those waves...😁. Couldn't help myself. Mats, thank you so much for the excellent explanation. 👍

At first it looks obvious, just like the sonic boom forms a cone behind a fast airplane, but then you realize that the shape and angle is independent of the speed. I think the most unintuitive thing about water waves is that unlike other waves, the speed is proportional to the wavelenght and not constant.

I remember being very enlightened by the rainbow video a year ago, glad to say I was equally in awe by this year’s production quality! Keep the great videos coming!

This channel reminds me of Posy but his channel says he doesn't have any other channels so probably just similar.

I love the math and stuff! Just a reminder to normalize your audio before posting the video, otherwise the user might not be able to make the volume high enough to hear

Very interesting video! You should consider posting more frequently ;))

That's really cool!

Thanks for the video. It was a bit of an eye opener for me as I was always taught that wave velocity only depended upon the medium through which the wave propagated and was independent of the wavelength [ie (v = f * (lambda)) where v= constant for a particular medium]. So you "blew me out of the water" with the initial premise that v is proportional to squareroot(lambda) right at the very beginning. Tomorrow I'm heading down to the lake to throw some pebbles and watch the ducks,

You gained a sub thanks for the video!

Really cool! Thank you for sharing these amazing insights!

Great video Mats, Goed gedaan!

this is pretty great. You are gonna be big on here

Keep in mind that speed is equal to omg over k

Small correction at 2:46 g is not the same as gravitational constant, gravitational constant is the big G in the formula for universal gravitation, the g on screen (in m/s²) is earth's gravity

Nice work

Thanks for the video, it is very interesting. However I disagree on the dimensional analysis at 2:20. In fact, it is normal for fluids to have specific sound velocities. E.g. air has 300m/s and water has 1400m/s. So, one may claim that a fluid-dependent constant should appear in the equation too.

That could be very helpful for someone who wants to develop wave simulators for photorealistic rendering

Am I the only one to who the shape of waves reminded how the warp engine works?

Very cool video! I wonder though how that picture changes depending on density/viscosity(e.g. dirty water, aerated water etc.). There is btw a video describing this same shape but as the duck breaking the terminal velocity of water similar to a sonic boom.

Brilliant! Thanks for preparing this.

Right Click -> Shade Smooth 🙏

That digital duck looking funny.

Very instructive ! Thanks. Just a suggestion : i have learned somewhere that the waves on the ocean propagate by rotation and that rotation is visible when a wave crashes on the beach. can you explain why ocean waves propagate by a rotational movement and not simply by a strictly vertical ups and downs ? Thank you

Very nice! More please!

I'm still not sure I've understood the animations from 8:18 Dunno if it's because of my level in English or something else

Excellen explanation, excellent work, excellent presentation. May I ask what software you used for creating the animation?

Very nice but why no reference to Lord Kelvin at the university of Glasgow who solved this blooming years ago? He also built a mechanical machine to work out tides anywhere on the planet.

dumb question - doesn't this break down for really slow objects (think about a duck barely moving - its waves propagate in all directions...) or really fast ones (doesn't a fast motorboat have a much smaller angle?)

More simulations and visualizations would be great in the video. perhaps showing a visualization each step of the video as it builds up?

I had thought it was based on the speed similar to a jet going super sonic exceeding the speed of the fluids wave speed but this is really eye opening

I guess a lot of this goes for sound waves too?

Great video, especially loved the look of your fluid simulations. What did you use to render them ?

Not really convinced. Like why did you choose beta as (k-k')/2 *x - (w- w') / 2 *t ? Where does the 1/2 at 8:00 come from?

what about 3-D , a fish inside water?

beautifull

So if a ship can float on water, like a duck... That means it weighs as much as a duck.... Which means.... She's a witch

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