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用正方形的孔制造涡流环 – 译学馆
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用正方形的孔制造涡流环

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

PBS Digital Studios
PBS数字工作室
Hey, I’m Diana.
嗨 我是Diana
And you’re watching
你正在收看的是
“Physics Girl, Vortex Edition”
《物理女孩 涡流特辑》
[POP] with special guest who doesn’t usually show his face.
[嘭] 这期邀请到了一位不常露面的
But here he is.
特别嘉宾
Grant Sanderson from the Math Channel. You should check out if you haven’t.
他就是来自 《三蓝一棕》的
“3Blue1Brown.”
Grant Sanderson
So 3Blue1Grant flew out to San Diego
我们一起前往了圣地亚哥
to make vortex rings with me.
进行涡流环试验
But we very quickly got distracted with a question.
但很快踫到了难题
We could make a square hole.
我们可以做一个正方形的孔
That’s, emm, that’s interesting.
嗯 有意思
What would happen if you made a vortex ring
如果通过正方形的孔来制造涡流环
through a square hole?
会发生什么呢?
What do you think would happen?
你觉得呢?
Here’s what I’m talking about.
我想说明的是
A vortex ring is typically made by pushing
通常涡流环是通过圆形孔制造的
air or some other type of fluid through a circular hole.
将空气或其他流体推入圆形孔而产生
And if you put a little smoke, you can see the ring.
如果放入一些烟 就能看见它啦
Here’s me and Math Boy Grant and my friend Dan trying to make vortex rings for the first time
一开始时 我 Grant和Dan试着
with an air cannon and coloured smoke grenade
用涡旋炮和彩色烟雾弹来制造涡流环
The more doubt I express,
我问得越多
the farther away you walk
你就走得越远
Dan.
Dan
– Are you ready? – Yeah, I’m ready.
— 准备好了吗? — 是的
Oh, yeah, fill it up.
噢 对 把它填满
That’s probably enough.
这应该够了
No, no, no, no, I want more.
不 不 我想要多点
That thing’s really hot.
这东西真热
[POOF]
[嘭]
Oh!
噢!
I think it’s too hot for that– to do that.
我觉得温度太高了
I don’t learn lessons that quickly.
我应该早点听你的
[LAUGHING]
[哈哈哈]
Oh no.
喔 不
You know what, Grant?
Grant 你知道发生了什么吗?
am I got to get some sands here
难道我要放点沙子吗
So let’s see the damage.
让我们看看它造成的破坏
[LAUGHING]
[哈哈哈]
After it burned, do you put it straight back on top?
烧完之后 你会把它放回去吗?
Repetition is the key to education.
重复是学习的关键
That was our only vortex cannon.
那是我们仅有的涡旋炮
But luckily for Math Boy,
但幸运的是
the supplies to make an even bigger vortex cannon
在任何五金店都可以买到材料
could be found at any hardware store.
来重新做一个更大的涡旋炮
[MUSIC PLAYING]
[音乐播放]
So how many more air cannons do you
所以你觉得还会有多少涡旋炮
think Grant is going to burn through?
会被Grant烧穿?
If I burn through the tarp, I deserve an award.
如果我能烧穿油布 那我真应该得个奖
[MUSIC PLAYING]
[音乐播放]
[POOF]
[噗嗤]
Whoa!
哇哦!
That was really fast.
好快
Oh!
喔!
That is so cool!
这太酷了!
What!
什么!
Oh, whoa.
哦 哇
That was interesting.
这太有趣了
[MUSIC PLAYING]
[音乐播放]
[around a ball]
[环绕球面]
[leapfrogging rings]
[穿越铁环]
[shooting straight at a wall]
[直射墙面]
[vortex through a square hole]
[让涡流穿过方孔]
You’re not going to see it that easily.
想看结果 可没这么容易
You have to predict what happens
先来预测一波吧
Let me know in the comments what you think happened
当用正方形的孔制造涡流环时
when we tried to make the vortex through the square hole.
你觉得会发生什么呢 快来评论吧
Here were our guesses.
我们的猜想是这样的
I think it’s just not going to work.
我觉得不会成功
I would guess that like square hole would have problems around its corners
我猜正方形孔的四角会出现问题
and that’ s really points when it breaks.
而且这是关键所在
I think it won’t work
我认为不会成功
I mean I don’t think it’s going to stay square.
我的意思是它不会保持方形
But I think they’ll be, like, four leaf clover.
而是会 像四叶草那样的形状
You think it’s not going to work?
你觉得不会成功吗?
Yeah.
是的
Is this a good angle?
这个角度可以吗?
Yes.
可以
[POOF]
[哇哦]
What!
什么!
No way
这不可能
It’s wobbling
它在摇晃
I don’t believe it.
我不相信
That’s awesome.
这太酷了
That is really awesome.
真的超酷
I was wrong.
我猜错了
And so was Grant– taking him down with me.

Grant也错了 把他带过来
But Dan was right.
但Dan猜对了
The square hole works!
它成功了!
And it wobbles.
而且还在摇晃
And by standing in front of the vortex,
站在涡流环的前面观察
we can see that it wobbles not randomly,
可以看到它并不是随机晃动的
but from a square,
而是从正方形
to a diamond shape
变成一个菱形
and back, and forth.
再回到正方形 再变成菱形
Then we asked another question.
然后我们提出了另一个问题
I wonder what happens if we make it,
我想知道如果让正方形的某一边
like, even shorter on one end.
变短一点 会怎么样
Surprise!
惊喜!
We made it shorter on one end. [POOF]
它的某一边变短了 [嘭]
Whoa!
哇哦!
The ring wobbles even more with the rectangular hole,
从矩形孔出来的涡流环晃动地更剧烈了
from a tall oval to a squashed oval.
从长的椭圆形变成扁的椭圆形
But more interestingly, it wobbles front to back, too,
更有趣的是 它也会前后晃动
going from, like, a C to a backwards C shape.
像是从C变成反向的C
You guys!
大家看!
That’s juicy
太有趣了
Oh, my gosh
喔 我的天
Wa-wa-wa-wa.
哇-哇-哇-哇
Yeah.
是的
Oh, there we go
噢 快看
Wow.
哇哦
So the question is, why?
问题来了 为什么?
Why does the vortex have that wiggly wa-wa-wa behavior?
为什么涡流环会出现摇晃的现象?
That’s the technical name for it.
它的专业名字就是
Come out!
来!
[GIGGLING]
咯咯咯
Come at me, fluid dynamicists.
跟我念 流体力学
Ok, first, we have to talk about,
好 首先 我们必须弄明白
what is a vortex ring?
什么是涡流环?
A vortex is the result of a bit of fluid swirling around
涡流是由少量流体围绕着涡流线
where it’s all swirling in a circle around a line, called the vortex line.
不断绕圈旋转而产生的
But in a vortex ring, the line is then wrapped around
在涡流环中 涡流线会被
in a closed circle.
包裹在闭环中
But it really only has to be a closed shape.
但不一定是圆形 只需是闭合的形状
And I said a bit of fluid.
少量流体的大小
But it could be the size of Oregon,
也有可能像俄勒冈州那样大
like a hurricane, which is just one giant vortex.
比如飓风 它其实就是一个巨大的涡流
In fact, the eye of Jupiter is a vortex.
事实上 木星之眼也是一个涡流
And it’s about one and a half times the size of Earth.
它的大小约为地球的一点五倍
So it could be a lot bit of fluid.
所以它可能是大量流体
So now what’s the deal with the wobble?
那晃动又是怎么回事呢?
Imagine, you’ve got a vortex like a hurricane blowing clockwise.
假设有一个像飓风般顺时针旋转的涡流
Some unsuspecting debris on the top
在其顶端有些不明残骸物
will be blown to the right and around.
会被吹到右侧或者四围
Now if we bring in another identical hurricane instead of the debris,
如果我们放入另一个飓风来替代残骸物
it would move the same way to the right.
它会以同样的方式移动到右侧
And in fact, the two hurricanes would dance around each other
事实上这两个飓风会互相起舞 就像在
like they’re orbiting.
按轨道运行一样
This has happened with real hurricanes,
真实情况中的飓风也是如此
since hurricanes in the same hemisphere are always spinning the same direction.
处于同一半球的飓风总是朝相同方向转动
And the closer together they are, the faster they’ll orbit.
他们相互靠的越近 就会转得越快
But if we go back and instead add
但如果我们一开始放入
a hurricane that’s spinning in the opposite direction,
一个反向旋转的飓风
we see that the two hurricanes, in fact,
实际上我们会看到这两个飓风
move together to the right.
仍会一起向右侧移动
Oh, ho, ho!
喔吼吼!
This looks quite like what you’d get if you cut a vortex ring in a half
如果把涡流环对半切开 会是这个样子
If you look at the cross section, which is what you get
观察它的横截面部分
if you just cut the vortex ring in half like a donut,
就像在看一个对半切开的
and look at the innards.
甜甜圈切面一样
The lesson is that a vortex ring pushes itself forward,
我们还发现了 涡流环会推着自身向前
because every part of the ring is pushing on every other part.
因为它的各个部分都会相互推动
And the parts that are closer together push each other more
靠得较近的部分会比靠得较远的部分
than parts that are further away,
相互推动的力更大
which also means that small vortex rings tend to move faster.
这也意味着小的涡流环往往会移动地更快
Because the parts are all close together.
因为它的各部分靠得都很近
That’s for circular rings.
以上是圆形环的情况
But what happens with the square ring?
那正方形环又是怎么样呢?
Since parts of a vortex that are closer
由于涡流环中靠得更近的部分
together push on each other more,
相互推动力更大
that means that sharp turns in a vortex
这意味着涡流环的拐角部分
get ahead compared to other parts of the ring.
会比其他部分提前转动
Looking at the square vortex, the corners are sharp turns.
正方形涡流环的四角 也就是拐角部分
So these parts of the ring are going to get a head start.
会先开始转动
And as that happens, the bend or kink from the corners
从拐角处沿着涡流环的边缘
moves along the ring until the corners reach
开始弯曲或扭结 直到延伸到
the sides, and the top, and the bottom,
侧面 顶部和底部为止
and we have a diamond shape.
变成菱形的形状
Then the process repeats until you get back to a square shape.
这个过程会不断重复 直到变回正方形
This effect of the bend moving along the ring
这种沿环移动的弯曲效果
is even more pronounced with a vortex formed from a rectangular hole,
在矩形孔形成的涡流环中会更加明显
because the curvature from the two short sides of the rectangle is even higher.
这是因为矩形的两个短边的曲率更高
Consequently, those parts of the ring get a huge head start.
因此 涡流环的这些部分会转动得更快
And we see a pronounced saddle-shaped wobbling behavior.
并且能看到一个明显的马鞍状晃动现象
Understanding exactly why the ring wobbles
为了准确理解为什么涡流环会摇晃
can be done using the Navier-Stokes equation,
这可以用纳维-斯托克斯方程来解释
which is a common fluid dynamics equation
这是一个常见的流体力学方程
actually being studied by a ton of researchers to this day.
直到今天 大量的科研人员还在研究它
So this is a bit of a subtle problem.
这是一个微妙的问题
What we describe is a simpler model
我们设想的是一个假设空气没有粘度的
pretending that the air has no viscosity, which– well,it does.
更为简单的模型-当然 假设是不成立的
But it gave you an idea of what’s happening conceptually.
但它帮助你对概念中的事情有所了解
Now the last thing we tried
当我们像孩子一样玩乐着做试验时
when we were playing around like kids was this.
最终是想要了解原理所在
What do you think is going on here?
你觉得这是怎么回事?
I had a laser laying around– as you do
后来我用衍射光栅穿过雾气
And I shined it with a diffraction grating through the fog,
来照射我们周围存在的激光
which looked pretty cool
这酷炫的操作
and gave Dan an idea to make a plane of light.
让Dan产生了制造光平面的想法
We used that to show a cross-section,
我们用它来表示横截面
or a slice of the vortex,
或者说涡流环的一部分
or of any of the fog moving around in the air.
又或是任何空气中漂浮的雾气
I can’t tell if your mind is blown right now.
我不知道现在你是否很激动
But in person, this looked ridiculously cool
但在我看来 这非常酷
and brought up so many new questions.
也产生了很多新问题
So now is the right time to check out
所以现在是时候去看看
Grant’s video on 3Blue1Brown,
Grant在《三蓝一棕》中的视频
where he goes into depth on how we made the contraption
深入研究了我们如何通过
to see the fog slices
巧妙的装置来看到雾片
and talk about some of the weirdness in the math
并讨论了在数学和流体物理学中的
and the physics of fluid flow, like turbulence.
一些怪异现象 例如湍流
What the heck is turbulence?
湍流到底是什么?
All right, yo, Grant,
好吧 Grant
now that I have duct taped my air cannon
现在我已经用胶带把涡旋炮粘好了
and forgiven you,I had a lot of fun.
原谅你 我玩得很开心
Thank you for coming down.
谢谢你能来
Thanks to Dan, my friend
感谢我最好的朋友Dan
who’s always down for the physics– the best kind of friend.
他总是对物理充满热情
Thank you, guys, for watching.
感谢你们的观看
Subscribe to Physics Girl if you want more physics.
想了解更多物理知识 就点击订阅吧
Now head down into the description,
查看结尾字幕
where you can check out Grant’s video.
可以找到Grant的视频哦
See you later.
下期再见
[MUSIC PLAYING]
[播放音乐]

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译制信息
视频概述

涡流环如何制造,为什么涡流环会摇晃以及涡流环形成的原理是什么,用正方形孔制造出的涡流环会有什么不一样呢,这些问题会由Diana和她来自《三蓝一棕》栏目的朋友们通过实验进行解答。

听录译者

收集自网络

翻译译者

Lancy

审核员

审核员 EM

视频来源

https://www.youtube.com/watch?v=N7d_RWyOv20

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