[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?
Here's what I'm talking about.
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]
 [INAUDIBLE] You ready?
DIANA: Yeah, I'm ready.
 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.
Then we asked another question.
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.
But if we go back
and instead add
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
like kids was this.
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]
