# How to Make a SQUARE Vortex Ring! ft. 3blue1brown

[MUSIC PLAYING]
Hey, I'm Diana.
And you're watching "Physics Girl, Vortex Edition"
[POP] with special guest who doesn't usually show his face.
But here he is--
Grant Sanderson from the Math Channel--
you should check out if you haven't--
"3Blue1Brown."
So 3Blue1Grant flew out to San Diego
to make vortex rings with me.
But we very quickly got distracted with a question.
Well, we could make a square hole.
That-- hm.
That's interesting.
What would happen if you made a vortex
ring through a square hole?
What do you think would happen?
A vortex ring is typically made by pushing
air or some other type of fluid through a circular hole.
And if you put a little smoke, you can see the ring.
Here's me and Math Boy Grant and my friend
Dan trying to make vortex rings for the first time with an air
cannon and a colored smoke grenade.
Eek.
Dan.
[LAUGHING]
Let's go.
DIANA: Oh, yeah, fill it up.
That's probably enough.
No, no, no, I want more.
DIANA: That thing's really hot.
[POOF]
Oh!
I think it's too hot for that-- to do that.
GRANT: I don't learn lessons that quickly.
[LAUGHING]
DIANA: Oh no.
You know what, Grant?
Am I about to get some sass here?
DIANA: So let's see the damage.
[LAUGHING]
After it burned, do you put it straight back on top?
GRANT: Repetition is the key to education.
[SLAPS]
That was our only vortex cannon.
But luckily for Math Boy, the supplies
to make an even bigger vortex cannon
could be found at any hardware store.
[MUSIC PLAYING]
So how many more air cannons do you
think Grant is going to burn through?
Seven?
We've got a tarp.
If I burn through the tarp, I deserve an award.
[MUSIC PLAYING]
[POOF]
DIANA: Whoa!
That was really fast.
Oh!
That is so cool!
What!
GRANT: Oh, whoa.
That was interesting.
[MUSIC PLAYING]
Ah!
You're not going to see it that easily.
You have to predict what happens.
Let me know in the comments what you think
happened when we tried to make the vortex
through the square hole.
Here were our guesses.
I think it's just not going to work.
I would guess the, like, square hole would have trouble
around its corners and that those would
be points where it breaks.
I think it'll work.
I don't think it's going to stay square.
But I think they'll be, like, four leaf clover.
You think it's not going to work?
DIANA: Yeah.
A four leaf clover.
Is this a good angle?
DIANA: Yes.
[POOF]
What!
No way.
Look, it's wobbling!
DIANA: I don't believe it.
DAN: That's awesome.
DIANA: That is really awesome.
I was wrong.
And so was Grant-- taking him down with me.
But Dan was right.
The square hole works!
And it wobbles.
And by standing in front of the vortex,
we can see that it wobbles not randomly, but from a square,
to a diamond shape, and back, and forth.
I wonder what happens if we make it, like,
even shorter on one end.
Surprise!
We made it shorter on one end.
[POOF]
Whoa!
The ring wobbles even more with the rectangular hole,
from a tall oval to a squashed oval.
But more interestingly, it wobbles front to back, too,
going from, like, a C to a backwards C shape.
You guys!
GRANT: That's juicy.
DIANA: Oh, my gosh.
GRANT: Wa-wa-wa-wa.
[INAUDIBLE]
DIANA: Yeah.
GRANT: Oh, there we go.
DIANA: Wow.
So the question is, why?
Why does the vortex have that wiggly wa-wa-wa behavior?
That's the technical name for it.
Come out!
[GIGGLING]
Come at me, fluid dynamicists.
OK, first, we have to talk about, what is a vortex ring?
A vortex is the result of a bit of fluid swirling around
where it's all swirling in a circle around a line, called
the vortex line.
But in a vortex ring, the line is then wrapped around
in a closed circle.
But it really only has to be a closed shape.
And I said a bit of fluid.
But it could be the size of Oregon,
like a hurricane, which is just one giant vortex.
In fact, the eye of Jupiter is a vortex.
And it's about one and a half times the size of Earth.
So it could be a lot bit of fluid.
So now what's the deal with the wobble?
Imagine you've got a vortex like a hurricane blowing clockwise.
Some unsuspecting debris on the top
will be blown to the right and around.
Now if we bring in another identical hurricane instead
of the debris, it would move the same way to the right.
And in fact, the two hurricanes would dance around each other
like they're orbiting.
This has happened with real hurricanes,
since hurricanes in the same hemisphere
are always spinning the same direction.
And the closer together they are, the faster they'll orbit.
a hurricane that's spinning in the opposite direction,
we see that the two hurricanes, in fact,
move together to the right.
Oh, oh, ho!
This looks quite like what you'd get if you cut a vortex
ring in half--
if you look at the cross section,
which is what you get if you just
cut the vortex ring in half like a donut,
and look at the innards.
The lesson is that a vortex ring pushes itself forward,
because every part of the ring is pushing on every other part.
And the parts that are closer together push each other more
than parts that are further away, which
also means that small vortex rings tend to move faster.
Because the parts are all close together.
That's for circular rings.
But what happens with the square ring?
Since parts of a vortex that are closer
together push on each other more,
that means that sharp turns in a vortex
get ahead compared to other parts of the ring.
Looking at the square vortex, the corners are sharp turns.
So these parts of the ring are going to get a head start.
And as that happens, the bend or kink from the corners
moves along the ring until the corners reach
the sides, and the top, and the bottom,
and we have a diamond shape.
Then the process repeats until you get back to a square shape.
This effect of the bend moving along the ring
is even more pronounced with a vortex formed
from a rectangular hole, because the curvature
from the two short sides of the rectangle is even higher.
Consequently, those parts of the ring get a huge head start.
And we see a pronounced saddle-shaped wobbling
behavior.
Understanding exactly why the ring wobbles
can be done using the Navier-Stokes equation, which
is a common fluid dynamics equation actually being
studied by a ton of researchers to this day.
So this is a bit of a subtle problem.
What we describe is a simpler model pretending
that the air has no viscosity, which--
well, it does.
But it gave you an idea of what's happening conceptually.
Now the last thing we tried when we were playing around
What do you think is going on here?
I had a laser laying around--
as you do.
And I shined it with a diffraction grating
through the fog, which looked pretty cool
and gave Dan an idea to make a plane of light.
We used that to show a cross-section, or a slice
of the vortex, or of any of the fog moving around in the air.
I can't tell if your mind is blown right now.
But in person, this looked ridiculously cool
and brought up so many new questions.
So now is the right time to check out Grant's video
on 3Blue1Brown, where he goes into depth
on how we made the contraption to see the fog slices
and talk about some of the weirdness
in the math and the physics of fluid flow, like turbulence.
What the heck is turbulence?
All right, yo, Grant, now that I have duct taped my air cannon
and forgiven you, I had a lot of fun.
Thank you for coming down.
Thanks to Dan, my friend who's always down for the physics--
the best kind of friend.
Thank you, guys, for watching.
Subscribe to Physics Girl if you want more physics.
Now head down into the description,
where you can check out Grant's video.
See you later.
[MUSIC PLAYING]