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.
@MatsVermeeren2 жыл бұрын
Allright NASA, forget about the moon and mars, we need you to find some alien methane ducks!
@MatsVermeeren2 жыл бұрын
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.
@blacklistnr12 жыл бұрын
Interesting, I thought density/viscosity would have played a role to make the cone thinner like a parabola until the limit of the duck just creating a straight canal at low density high viscosity. Is there any parameter that could damp the waves' *frequency* to 0 as they spread out from the central duck line?
@ponjavic11 ай бұрын
Glorious transition from simulation to duck picture well done!
@andrerenault Жыл бұрын
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.
@Number_Cruncher2 жыл бұрын
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😎
@tryctan2399 Жыл бұрын
it's 3am and i am learning thing i didn't even know i could learn. thank you
@Apertureadhdiction2 жыл бұрын
Let the algorithm bless this video
@rafaelnobrega1340 Жыл бұрын
Hydrodynamics simplified, this is gold
@joeyho5134 Жыл бұрын
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. 👍
@pyglik2296 Жыл бұрын
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.
@tissuepaper9962 Жыл бұрын
It is actually true for other waves, it's called dispersion and it's what causes chromatic aberration in photographs.
@tanchienhao Жыл бұрын
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!
@lyrimetacurl02 жыл бұрын
This channel reminds me of Posy but his channel says he doesn't have any other channels so probably just similar.
@loganhodgson6343 Жыл бұрын
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
@gorilla1q4172 жыл бұрын
Very interesting video! You should consider posting more frequently ;))
@johnchessant30122 жыл бұрын
That's really cool!
@Nibor9992 жыл бұрын
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,
@MatsVermeeren2 жыл бұрын
It depends on what the restoring force is (the force which tries to bring the waves back to equilibrium). In water waves with a wave length of more than a few centimeters, the restoring force is gravity. What you had in mind is true when the restoring force is pressure, for example for sound waves: the speed of sound does not depend on the wavelength, but it does depend on the medium. Enjoy the lake!
@adam_salah2 жыл бұрын
You gained a sub thanks for the video!
@Rationalific2 жыл бұрын
Really cool! Thank you for sharing these amazing insights!
@koendos32 жыл бұрын
Great video Mats, Goed gedaan!
@GEdluge Жыл бұрын
this is pretty great. You are gonna be big on here
@pro_-lx2bf2 жыл бұрын
Keep in mind that speed is equal to omg over k
@elnico562311 ай бұрын
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
@realcygnus2 жыл бұрын
Nice work
@Spocchio Жыл бұрын
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.
@MatsVermeeren Жыл бұрын
These aren't sound waves though. For sound waves the restoring force is pressure due to compression, and the speed depends on the compressibility (and density) of the fluid. The dimensional analysis in the video assumes that the restoring force is gravity, which is the case for surface waves (if they are long enough that we can ignore surface tension). Of course, what we get out of dimensional analysis could always be wrong by a dimensionless factor, so to be sure that there is no fluid-dependent constant you'd have to do the full analysis using a mathematical model of fluid mechanics.
@stereopolex2 жыл бұрын
That could be very helpful for someone who wants to develop wave simulators for photorealistic rendering
@dimanyak373 Жыл бұрын
Am I the only one to who the shape of waves reminded how the warp engine works?
@blacklistnr12 жыл бұрын
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.
@MatsVermeeren2 жыл бұрын
Thanks! I've just added some FAQs in a pinned comment, including your question on density and viscosity. The sonic boom only makes sense if you consider one fixed wavelength, because you'd need a fixed wave speed (a speed of "sound"). You could construct the pattern as a superposition of sonic booms for different wavelengths. But not all possible sonic booms contribute (some would make a wider angle) and I think you'd still need the argument of stationary waves to explain which ones do.
@myozinaung Жыл бұрын
@@MatsVermeeren In shallow water at critical speed and super critical speeds, the wave speed is constant. Similar phenomenon like sonic boom happens.
@IgnacioPisso Жыл бұрын
Brilliant! Thanks for preparing this.
@Leymora Жыл бұрын
Right Click -> Shade Smooth 🙏
@Green24152 Жыл бұрын
That digital duck looking funny.
@visualchallenge241311 ай бұрын
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
@jimday666 Жыл бұрын
Very nice! More please!
@weak7897 Жыл бұрын
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
@soroushmoallemi77411 ай бұрын
Excellen explanation, excellent work, excellent presentation. May I ask what software you used for creating the animation?
@MatsVermeeren11 ай бұрын
I used Manim. Source is linked in the description.
@jonathanlister564411 ай бұрын
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.
@TheVirIngens2 жыл бұрын
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?)
@MatsVermeeren2 жыл бұрын
Not a dumb question! You are right, and the reasons why it breaks down are quite interesting as well. For fast boats, the stationary waves would 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. For very slow or tiny objects, the issue is that very short waves are governed by surface tension instead of gravity. For such waves, the shorter ones more more quickly, so the story changes completely. Indeed, these waves can get ahead of a moving object. Often you can see such ripples just in front of a swimming duck.
@magnuswright55722 жыл бұрын
@@MatsVermeeren I'm curious, what is the relationship between speed and size and the contributions to the wave from gravity and surface tension? Surely there isn't just some cut off where gravity stops mattering and surface tension starts?
@MatsVermeeren2 жыл бұрын
@@magnuswright5572 Yes, strictly speaking all water waves are influenced both by gravity and surface tension. For waves longer than about 7cm, surface tension effects are negligible. For waves of a few mm or less, gravity is negligible. For waves of an intermediate wavelength you need to take into account both gravity and surface tension. Where exactly you put the cutoffs depends on how much of an approximation error you are willing to tolerate. (See en.wikipedia.org/wiki/Dispersion_(water_waves)#Surface_tension_effects if you want to get into the details)
@alborzdesign2 жыл бұрын
More simulations and visualizations would be great in the video. perhaps showing a visualization each step of the video as it builds up?
@ThevenimX2 жыл бұрын
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
@RodyvanGemert Жыл бұрын
I guess a lot of this goes for sound waves too?
@MatsVermeeren Жыл бұрын
Sound waves are actually 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. 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.
@blergblergblerg1343 Жыл бұрын
Great video, especially loved the look of your fluid simulations. What did you use to render them ?
@balls28482 жыл бұрын
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?
@MatsVermeeren2 жыл бұрын
This is the unique choice of α and β such that α+β=kx-ωt and α-β= k'x-ω't. The factor 1/2 comes from differentiating the square root.
@balls2848 Жыл бұрын
@@MatsVermeeren thanks
@vikramvishalstorywallah3251 Жыл бұрын
what about 3-D , a fish inside water?
@bpavanellic2 жыл бұрын
beautifull
@kevmasengale6903 Жыл бұрын
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