科里奥利力，在北半球这个漩涡

Be very, very careful what you put into that head,
because you will never, ever get it out.
Thomas Cardinal Wolsey (1471-1530)

   Bad Coriolis
Click on the symbol for its explanation.
前边浣熊提了一些有意思的物理问题，其中一道是：
: 把洗手池中的水放掉时，水在漏水口的上边会形成一个漩涡，这是为什么？
: 从上面看下去，这个漩涡是顺时针还是逆时针转（在我国）？
相信不少人对此会象我这样回答：
: 科里奥利力，在北半球这个漩涡是顺时针，南半球是逆时针。
的确，这个说法很常见，和我们的日常经验也比较吻合，想起来也挺有道理，
我也曾经看过一篇文章，准确的记不清了，大致是有人做了实验，在一个封闭
的房间内，在形状规则的水池里蓄上水，待水完全静止后，将池底的开关打开
排水，验证了形成的漩涡旋向与科里奥利力一致（好象是南北半球都做了）。
不过我这样回答之后，虽然有一位高手赞同，却也有两位高手反对，说：
: 不管在地球的任何地方，水都可能左旋和右旋，因为旋涡形成的主要原因不
: 是地转偏向力。
: 这种漩涡的形成的主要原因是流体流动中的内生不稳定性，科氏力只是提供
: 了一个定向的初始扰动，使得在大多数情况下漩涡的方向总是顺时针或逆时
: 针的。
看来有必要对这个问题重新考察一番，我已经记不清那篇文章是哪里看的了，
也检索不到专业文献，只好四处胡乱翻找一通，发现这个问题真的很有意思。
首先解释一下科里奥利力，它是在转动的非惯性参考系下，运动的物体受到的
一种惯性力，科氏力的公式为：
F=2mv*ω，式中v*ω为矢量积，v为物体相对转动系的速度，ω为转动系的角
速度。
在实际中，地球就是一个转动的非惯性系，当地球上的物体运动时，如果运动
速度与地球自转轴不平行，就会受到科里奥利力。举例来说，从高处自由落下
的物体，会由于科氏力的作用发生向东的偏移，计算可知，物体从赤道上空高
100米处下落，到达地面时将偏东2.2厘米。
看得出来，通常情况下科里奥利力是一个比较微弱的力，只有物体相对地球的
运动速度比较大、时间比较长时，科氏力作用的效果才比较显著。而水池排水
的过程中，一般水流速度并不大、时间也不长，受到的科氏力是很小的，况且
水形成漩涡，也的确主要由于流体流动中的内在不稳定性，科氏力提供的只是
一个定向的微扰，在上面那种尽量排除了其他外界扰动（如风吹、搅动等）的
严格的实验条件控制下——光是待水完全静止就花了近二十个小时——科氏力
才有可能对漩涡旋向的形成产生决定性影响。而我们的水池，显然不具备这么
理想的条件，排水的漩涡应该可能是顺时针，也可能是逆时针。对位于北半球
的我们，如果看到排水漩涡是顺时针，虽然表观上符合科氏力作用的结果，但
并不能心满意足地以此解释；如果排水漩涡是逆时针，那就更说不过去，需要
好好琢磨琢磨了。
不过我的水池平时排水总是顺时针的，从无例外，我观察了一下，原来水龙头
位于排水孔右上方，而池底的坡度使得水流下来自然就会沿着顺时针运动——
漩涡的初始旋向已经被这么决定了。还有抽水马桶，如果也始终顺时针排水，
那么准是水冲下来时就产生了初始旋向。
对司空见惯的现象、习以为常的解释，还得留个心眼再注意观察、多想想呢。
Be very, very careful what you put into that head,
because you will never, ever get it out.
--Thomas Cardinal Wolsey (1471-1530)
附：推荐一些相关网页，请各位感兴趣的朋友去看看。
http://www.ems.psu.edu/~fraser/Bad/BadCoriolis.html
——对该问题进行了很好的解释澄清，上面那段Be very, very careful...的
话就抄自它的题头:P
http://eagle.cc.ukans.edu/~keithweb/640_2.html
——注意Toilet tricks一段，其中提供详细解释的链接指向上面的地址，而
另一个链接指向下面的抽水马桶……
http://www.personal.psu.edu/users/r/p/rpe100/toilet.htm
——for the real reason the water swirls a certain way in your toilet
http://www.physics.ohio-state.edu/~dvandom/Edu/coriolis.html
——注意E. Water Going The Wrong Way Down The Sink一段
http://www.treasure-troves.com/physics/CoriolisForce.html
http://www.windpower.dk/tour/wres/coriolis.htm
http://satftp.soest.hawaii.edu/ocn620/coriolis/
http://zebu.uoregon.edu/~js/glossary/coriolis_effect.html
http://www.schools.ash.org.au/paa/coriolis.htm
——讲解科里奥利力
Bad Meteorology:
The water in a sink (or toilet) rotates one way as it drains in the
northern hemisphere and the other way in the southern hemisphere.
Called the Coriolis Effect, it is caused by the rotation of the Earth.
First on this page is a discussion of the issue. Towardsthe bottom of the page you can see examples of incompetence from PBS,NPR, and Sports Illustrated.
TheCoriolis force does influence long-lasting vortices.

Hurricane Andrew
On the scale of hurricanes and large mid-latitudestorms, the Coriolis force causes the air to rotate around a low pressure centerin a cyclonic direction. Indeed, the term cyclonic not only means that the fluid(air or water) rotates in the same direction as the underlying Earth, but alsothat the rotation of the fluid is due to the rotation of the Earth. Thus, theair flowing around a hurricane spins counter-clockwise in the northern hemisphere,and clockwise in the southern hemisphere (as does the Earth, itself). In bothhemispheres, this rotation is deemed cyclonic. If the Earth did not rotate,the air would flow directly in towards the low pressure center, but on a spinningEarth, the Coriolis force causes that air to be deviated with the result thatit travels around the low pressure center.
In the accompanying picture of the Caribbean, one cansee the cyclonically spiraling clouds of Hurricane Andrew (at the mouth ofthe Mississippi) and of another vortex in the Atlantic.
But, the Coriolis force is very small, indeed.

water draining in the supposedly wrong way
Compared to the rotations that one usually sees(tires on a travelling automobile, a compact disc playing music, or a drainingsink), the rotation of the Earth is very small: only one rotation per day. Thewater in a sink might make a rotation in a few seconds and so have a rotationrate ten thousand times higher than that of the Earth. It should not be surprising,therefore, to learn that the Coriolis force is orders of magnitude smaller thanany of the forces involved in these everyday spinning things. The Coriolis forceis so small, that it plays no role in determining the direction of rotationof a draining sink anymore than it does the direction of a spinning CD.
The direction of rotation of a draining sink is determinedby the way it was filled, or by vortices introduced while washing. The magnitudeof these rotations may be small, but they are nevertheless gargantuan by comparisonto the rotation of the Earth. I decided to include a picture of a drainingsink, and the first one I tried in my house was found to drain clockwise (theopposite of what the silly assertions would have it do here in the northernhemisphere). This direction was determined entirely by the way the tap filledthe sink. The direction of rotation of a draining toilet is determined bythe way the water just under the rim is squirted into the bowl when it isflushed.
Is it possible to detect the Earth’s rotation in a draining sink?
Yes, but it is very difficult. Because the Coriolisforce is so small, one must go to extraordinary lengths to detect it. But,it has been done. You cannot use an ordinary sink for it lacks the requisitecircular symmetry: its oval shape and off-center drain render any resultssuspect. Those who have succeeded used a smooth pan of about one meter indiameter with a very small hole in the center. A stopper (which could be removedfrom below so as to not introduce any spurious motion) blocked the hole whilethe pan was being filled with water. The water was then allowed to sit undisturbedfor perhaps a week to let all of the motion die out which was introduced duringfilling. Then, the stopper was removed (from below). Because the hole wasvery small, the pan drained slowly indeed. This was necessary, because ittakes hours before the tiny Coriolis force could develop sufficient deviationin the draining water for it to produce a circular flow. With these procedures,it was found that the rotation was always cyclonic.
Why do teachers claim that a draining sink reflects the rotation of the Earth?
A surprisingly large number of my undergraduate studentstell me that their high-school teachers told them that sinks drain in oppositedirections in the two hemispheres owing to the rotation of the Earth. Whywould a teacher offer such garbage to students when it is so easy to check.A trip to the school washroom (let alone the ones at home) will reveal drainagein both directions (which would certainly require the equator to assume atortuous track through the countryside).
Is knowledge just a bunch of abstractions to be memorizedwith no recourse to the relevance of everyday experience?
Sigh... I don’t know why teachers do this.I can but assume that those who do so just never feel any need to wash theirhands --- or their minds.
Incompetence from those we trust
Incompetence from PBS (USA)
Fakery of the first water (so to speak).
There are charlatans operating at a tourist trap inNanyuki, Kenya. In this little town, located right on the equator, a localmountebank works for tips as he glibly cons busloads of tourists into believingthat the rotation of the Earth causes water draining from a container tospin clockwise in the northern hemisphere and counter-clockwise in the southernhemisphere. (Yes, you read that correctly, the charlatan fakes it backwards.You would think that if he were going to sucker people, he would at leastget his directions the same as what really happens in large weather systems.)
This man’s nonsense was captured (and endorsed)by Michael Palin in one episode of his BBC TV special, From Pole to Pole, which is often aired on PBS. The presentation went as follows:
faker:
This is the northern hemisphere (gesturing to his left), and thisis the southern hemisphere (gesturing to his right). If you drain asink when you’re on the northern side of the equator, and you watchthe water as it drains, you will see that the water always rotates clockwise[sic]. (Shot of a pan with water draining clockwise. Floating matchsticks are used to make the motion easier to see.) This phenomenon iscaused by the rotation of the Earth. The effect becomes stronger accordingto how far you move to the north or to the south and becomes weakeraccording to how close you go towards the line [the equator]. So that’swhy we have to give some distance from the equator so that the rotationcan be noticeable.
Palin:
This is known as the Coriolis effect and Peter McLeary has given thissame lecture every day for the last six years. It’s delivered inthe burnt out shell of an old hotel. The equator used to run throughthe middle of the bar. I bet they were always floating match sticksin the middle of the beer. (The faker has been carrying his pan andwater about ten meters to the south of the spot marking the equator,and turns to face the audience.)
faker:
So, this changes to counter-clockwise [sic] indicating that now weare on [sic] the southern hemisphere. (Shot of the water in the pandraining counter-clockwise.)
(Transition to a scene where the faker is placing the water-filledpan directly on the equatorial marker.) So, now we are right on theequator, and as we drain the water, you’ll see there will be norotation. It just drains straight down. And that’s how we provethat we are right on the equator. (Water draining with no apparent rotation.)
Palin:
It does work.
Sure it does --- in the hands of a mountebank,that is. And now we have Michael Palin acting as a shill for bad science--- and on PBS, no less. Huh?
A correspondent has written me to say that in the version of the program she saw, that "Mr. Palin proceeded to describe how the demonstration was pure bunk and told how the charlatan pulled off his little deception..." Yet, in my version of the program, Palin unambiguously endorses the demonstration.
Could it be that there are two versions out there, the original and an amended one in which Palin attempts to address some of the criticism of the original? Does anyone know?
So far, the only readers who have written me on this point are ones who have seen the Palin-endorsing version. There are no further reports of a version where Palin is claimed to have pointed out that the demonstrator had cheated.
But, how is the fraud accomplished? The Coriolis forceis so tiny that it cannot cause the rotation in the faker’s drainingpan; indeed at only ten meters to either side of the equator, it is so tinythat it could influence neither the carefully performed experiment (describedabove) nor the large scale motions of weather systems.
So, the faker must be forcing the rotation by othermeans, and by a sufficiently unobtrusive way that the busloads of touristsdo not spot the means. Indeed, a colleague of mine, who witnessed the performancefirst hand and knew it was a cheat, was not able to spot how the fraud wasperpetrated. (It is an interesting sidelight that when back on the bus,he informed his fellow tourists that they had just witnessed fakery ---the Earth did not cause the rotation they had just seen --- there was widespreaddisappointment. The tourists preferred the fantasy to the reality.)
Do-it-yourself fakery.
There are two clues to the successful fakery of thedrainage changing direction at the whim of the mountebank. One is revealedin each of the two images (above) which I captured from the TV program:
Non-circular pan
The non-circular pan allows the faker to easily introduce rotationinto the pan after he begins. Let us imagine that the pan is filledvery carefully so that there is no rotation initially. Indeed, onewants to be able to show the audience that any rotation introducedwhile filling has died out. Now what? If the pan were circular, itwould be harder to start the water spinning by turning the pan itself,but by having the pan nearly square, the water must turn if the pandoes.
Turn to face the audience
But how does one turn the pan without the audience becoming suspicious.Obviously, it must be done in such a way that the audience does notattribute the action to part of the fakery, but to a courtesy whichenables them to see better.
The procedure is as follows:
Find the materials
You want two plastic containers: one which is to be the pan to bedrained, and the other is a bucket for the storage of water. The panshould be non-circular. I found a quasi-square one (made by Sterilite)for $1.28 in the local Wal-Mart. It is the three-cup size (.7 liter).It works well. Drill a hole (say, 1/4 inch or 3/8 inch) through thecenter bottom. You don’t need a special stopper for the hole:your finger placed underneath works just fine. The other containercan be any small plastic bucket with the only restriction that yourpan should be able to sit on top of it so that the bucket can catchthe water as it drains.
Fill the pan
Choose the spot that you wish to claim is the equator (the centerof your classroom will do). Fill the pan from the bucket there andlet the motion from filling die out. (You can insert and then gentlyremove a vertical object, such as index card, into the water to dampenthe motion.) You can then show that there is little or no circulationby floating a match stick (or sprinkling pepper) on the water.
Covertly add the chosen rotation
If you are going to the north side of the equator, stand in frontof the pan facing south. Pick it up, turn around by turning toyour left, walk to the north end of the room, turn aroundby turning to your left, and face the audience. As you have anon-circular pan, you have now introduced counter-clockwise rotation(which is cyclonic in the northern hemisphere) into the water.
The coup-de-grace
Add a tracer (such as matches or pepper). Remove the stopper (yourfinger) and let the water drain. Lie through your teeth by claimingthat it is the rotation of the Earth here in the north which is causingthe water to circulate the way it does.
The other hemisphere
Go back to the equator but this time stand on the south side lookingnorth. After filling the pan, turn around by turning to your right,walk south, again turn around by turning to your right toface your audience (cyclonic rotation in the southern hemisphere isclockwise), and remember to complete the demonstration by lying again.
The equator
This is the hardest part of the fakery, because it is actually verydifficult indeed to eliminate all rotation from a pan of water. Itreally should sit for a very long time (and your finger might gettired). If the pan is fairly deep, and the hole small, it takes amoment or two before the rotation is apparent. This seems to be thedodge followed by the Kenyan faker.
What can I say, it all worked the very first timeI tried it. If any of you can devise any improvements in the procedure,please send me a note.
Incompetence from Sports Illustrated
One does not normally turn to Sports Illustrated for insightinto the natural world, unless, possibly that bit of the natural worldwhich sometimes wears swimming suits. However, one does not expect incompetencefrom the magazine either. Yet, the special Winter 1998 swimsuit issue offersmuch more than its standard set of salacious images, it offers geographicand scientific swill. In an article by Jamie Malanowski, entitled, ZeroLatitude, (starting on page 16) we learn:
Say you’re vacationing at a nice hotel in Costa Rica [sic]. Feelingrestless, you go for a walk, heading in a generally southern direction.After a few days and a few beverages of your choice, you stop at anappropriate facility and do what you do whenever nature calls. Whenyou flush, you note that the water whirls down the bowl in a counterclockwisedirection. Now resume your walk. Go far enough south, and the next timeyou hit the head, the water will spin clockwise down the drain. Andthen it hits you: Somewhere back there you crossed the equator!
Apart from the fact that the equator is one very long (and difficult)walk from Costa Rica, any difference in the behavior of toilets on thejourney is the result of happenstance and not the crossing of the line.
Incompetence from NPR (USA)
On October 16, 1996 the NPR program, Rewind,blotted its escutcheon with their nonsensical discussion of the Coriolis force. The librarian who prepared it supportedher position with references to the book, Rainbows, Curveballs and otherWonders of the Natural World Explained, by Ira Flatow, host of NPR’sTalk of the Nation - Science Friday and with a previously aired PBS (cumBBC) program called, Pole to Pole (or, Full Circle). You can read aboutthe silliness in Pole to Pole, above. I have yet to see just what it isthat Flatow had to say. Note: The program has since retracted itsmistake.
Incompetence from the author of a standard undergraduatephysics textbook.
A physics student from Nottingham University,in the U.K., wrote to tell me that the physics textbook they are assignedin one of his courses states:
"...on a smaller scale, the coriolis effect causes water drainingout a bathtub to rotate counter clockwise in the northern hemisphere..."
Sigh, this mind-numbing example of scientific incompetence is offeredby author, Paul A. Tipler, on page 128 of his book, Physics for Engineersand Scientists, 4th Edition. One wonders if Tipler gets the relativemagnitude of the other forces in nature wrong, or if he reserves thisprivilege for the Coriolis force. In the U.S.A., the book's publisheris W.H.Freeman, and in the U.K. it is Worth Publishers. SHAME ON BOTH PUBLISHERS.
But, competence from teachers
Sowhat do you tell your students.
The direction of rotation in draining sinks and toiletsis NOT determined by the rotation of the Earth, but by rotationthat was introduced earlier when it was being filled or subsequently beingdisturbed (say by washing). The rotation of the Earth does influence thedirection of rotation of large weather systems and large vortices in theoceans, for these are very long-lived phenomena and so allow the very weakCoriolis force to produce a significant effect, with time.
Bad Coriolis FAQ
Before writing me with a question about this page,please check the Bad Coriolis FAQ to see if the issue has already been addressed satisfactorily.