Helmholtz Principle and Vortex Motion with
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- Опубліковано 1 жов 2024
- Oxford Mathematician Dr Tom Crawford teaches @DrTrefor about Helmholtz' Principle and how it can be applied to calculate the motion of a vortex in 2D potential flow.
Watch part 2 of the collaboration where @Dr. Trefor Bazett teaches me a little algebraic topology, specifically the fundamental group: • Intro to the Fundament...
We being by looking at the setup for 2D potential flow which is both incompressible (zero divergence) and irrotational (zero curl). This gives rise to a velocity potential and a streamfunction which can be combined using the theory of Complex Analysis and the Cauchy-Riemann Equations to form a complex potential.
The situation studied is for a vortex in the positive quadrant which is bounded below (along the x-axis) and to the left (along the y-axis). Using the Method of Images we derive the full complex potential and differentiate to get the velocity field. Helmholtz' Principle is then applied to give the trajectory of the vortex as it moves in the fluid.
Helmholtz' Principle states that a vortex will move due to the velocity field of everything except itself.
For more information on 2D potential flow and the Method of Images see this video with @3blue1brown: • Potential Flow and Met...
Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: www.seh.ox.ac....
For more maths content check out Tom's website tomrocksmaths....
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths. / tomrocksmaths
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beautifulequat...
Watch part 2 of the collaboration where Trefor teaches me a little algebraic topology, specifically the fundamental group: ua-cam.com/video/IpkzNeS8G20/v-deo.html
Thanks for having me Tom, learning some fluids was so much fun!
wait.......Trefor said it was the first part....
I‘m actually trying to find periodic solutions near critical points in arbitrary domains of the N-Vortex problem for my PhD, so I love this example :))
learning cal is really fun because before a handful of months ago these symbols on the board had no context now i can see that everything is starting to become apparent.
If Orochi (King of Fighters 97) was a math professor 😎. Thanks for making Mathematical Sciences very cool
Fluid mechanics...Game companies would love you Tom!
Retired postgrad eng scientist here - what a delightful, clear explanation. More enjoyable though was to see two such skilled mathematicians interacting like this. Well done both of you, most enjoyable.
glad you enjoyed it :)
Another quicker way of visualizing (1/x^2)+(1/y^2) = constant is:
Kinda visualize 1/x or the Hyperbolic curve, x^2 or any power changes the smoothness of the bend towards the origin.
Maybe this is not a quicker way I don't know but the video was amazing and how the math just fits in with physical observations & absolutely beautiful part was being able to drop the term where the value of function goes to infinity (pole) in the given contour and how the method of images became usefull.
Thankyou.💜
nice!
looks so cool! i bet i'll enjoy this :)
Ver very cool! Looks like a full derivation (no jumping lol) would have taken a couple of hours or more, but Trefor was following very well. More then I was at times.
I did it in my thermal machine course in ME and it took us 5 modules of lessons each being 1.5 hours
@@federico1183 You mean thermodynamics? I’m not sure if it took us that long, but it has been awhile since I took that class.
@@iteerrex8166 well, yes and no.
I already had a thermodynamics class a year ago and we barely touched the subject. Earlier this year i had a thermofluidynamic class in which we studied in detail the workings of turbines.
I really enjoyed this video! A first for a TomRockMaths for me. I wish more videos were this kind of content, rather than the clickbait stuff of taking off your clothes or doing GCSE maths papers
Ohh the jung best professor. Your moving is very interesting Bravo 👍
Nice!! Like you've said very intuitive, but explained throu science. Loved it!
:)
Vortex dynamics is such a beautiful subject within fluid dynamics, and I am happy to see you are giving this theory exposure to a wider audience through your amazing videos!
1/y^2 + 1/x^2 = C reminds me of the circle equation but inverted
So so good!! Very helpful for my studies too! Thanks
For those wondering, the way you go the other way with curl is related to the topology of the space and is related to something called the De Rham Cohomology of the space.
"I'm the fluid guy..." Tom, 2021
always
Your hairstyle is mine favourite Tom
I have absolutely NO idea whats going on but I just find it interesting.
that's all that matters!
Bro, has anyone ever told you that u look like an epic anime mathematician
lol i'll take it
Oh, I need to revisit vector calculus! Lol.
yes it would certainly help in this one!
Very NOICE 👍
Veramente fico, I went through the entire video and it was a lot of fun!
Glad you enjoyed it!
can you do a video explaining all the math in your tattoos please?
i explain a lot of them here: tomrocksmaths.com/tattoos/
Until I seen your videos I thought it was only possible to be a cool math teacher XOR a good math teacher. You have disproven me.
Oh no try not to think of fluid dynamics when you next go swimming😂
Or if you like you can teach people at the pool but they may want to sunbathe I DK how they would react LOL
Where were you when I studied this at school? Oh yeah, you weren't even a good movie and a nice bottle of wine on a Friday night yet.
Amazing video!
Thanks!
This was amazing!
glad you enjoyed it!
I enjoyed this. Thank you very much.
Tom is so pretty
Pls dont go to the residue theorem Im' actually understanding so far!
Now add a magnetic field...
what extras do you add in to look at when the wall may break? This assumes the wall is indestructible
and, i assume that a black hole would compact all opposing fields in 2D into 1 and the wall would be meaningless? Any tips for that sort of Math?
i would like to have a unisex Tee tshirt with your face instead of einsteins or tesla. xD
ha that would be fun!
Why complex function where it come from ??????
rotation
Dr. Trefor is an Absolute Goat!
amen
Amazing!
You should be ashamed to sell your name and, even worse, to dare to talk in the name of mathematics in such a clearly biased and improperly made bogus "study" like the one you did for Live Score, establishing Cristiano Ronaldo as the "best football player in history" using one of the most flawed maths I've ever seen in my life.
What a shame for Oxford University to have something like that linked to them and what a shame for mathematics in general. Truly shameless, utterly pathetic... all just for money. If you have any kind of decency left and actual love for mathematics, you should get that video down. Spreading misinformation like that only goes against what you're supposed to be doing with your channel and against actual critical thinking. No one should be using their academic renown in such a negligent and disrespectful way. Reconsider your actions...
calm down boi