This article is from WeChat official account: science home (ID: steamforkids), author : seven Jun, the original title: “You Didn’t you notice anything wrong when making tea? Einstein used it to publish a paper and create a discipline”, head picture source: Visual China
Have you noticed a peculiar phenomenon: When making tea with tea leaves, if you stir the tea, the tea leaves will gather at the bottom center of the cup instead of being scattered near the wall of the cup due to centrifugal force. How is this going?
This interesting phenomenon is called the tea paradox (tea leaf paradox). You may not be able to imagine what the tea paradox has to do with winding rivers. One hundred years ago, Einstein explained this phenomenon ingeniously and connected it with the nine bends and eighteen bends of the river.
When stirring the tea in circles, we usually think that the tea will rotate with the spoon and stick to the wall of the cup due to centrifugal force.
Secondary stream (blue) Picture source: wikipedia
But actually, due to the friction between the liquid and the teacup,A secondary flow (secondary flow) will appear in the water cup, that is, a circle of water perpendicular to the rotating surface. Tea leaves are drawn into this secondary stream and swept to the center of the bottom of the cup. In the secondary flow, the liquid near the bottom of the teacup has a lower speed, and the tea leaves there are not fast enough to rise, and they are eventually swept into a ball.
Picture source of the flow direction of the secondary stream in the teacup: (DOI) 10.1007/BF01510300
So, what does the tea paradox have to do with the river?
The riverbed of a small river is eroded. Picture source: wikipedia
This is the case. In the mid-19th century before Einstein, there was a popular opinion among geographers that in the northern hemisphere, the erosion of the riverbed mainly occurred on the right bank of the river, and the southern hemisphere was on the left bank, and this is the earth Caused by Coriolis force caused by rotation. Because of the rotation of the earth, objects in the northern hemisphere tend to turn to the right, which is the Coriolis force.
These geographers believe that because of the Coriolis force, the sediment on the river bank on the right side of the northern hemisphereIt is easy to be taken away, and the southern hemisphere is just the other way round. This once popular theory is called Bell’s law (Baer’s law).
The earth rotates counterclockwise, like the disk in the picture. Under the action of Coriolis force, objects in the northern hemisphere will deflect to the right when moving, as shown in the white ball.
However, Einstein’s 1926 paper (Die Ursache der Mäanderbildung der Flußläufe und des sogenannten Baerschen Gesetzes) eroded the river bank for the first time Phenomenon gave the correct solution, put Bell’s law into the cold palace and gave a bonus.
Einstein pointed out that the imbalance of erosion on the left and right of the river is because the river also has a secondary flow similar to that in a teacup.
There will be a clockwise secondary flow in the cross section of the river AB, similar to the situation on the right side of the teacup cross section. Picture source: (DOI) 10.1007/BF01510300
Assuming that there is a bend like AB in the above picture, and the river flows counterclockwise, then this bend is like the right half of a teacup, where the direction of the secondary flow is clockwise, this As a result, the sediment was taken from the right side to the bottom of the left side to accumulate. As a result of this accumulation of time, the originally curved river will become more curved.
In the end, the bottom of the river bed above will become like this–
Picture source: (DOI) 10.1007/BF01510300< /p>
The direction of the river is the same in reverse, and the B side is also eroded. How to understand this? Just like when you use a spoon to make a circle in a cup, no matter whether it is clockwise or counterclockwise, the direction of rotation of the secondary stream will not be affected, and eventually the tea leaves will gather in the middle. For rivers, the direction of the secondary flow will not change.
In other words, in this case, the left side of the river’s flow direction is eroded. Obviously, Einstein’s explanation is inconsistent with Bell’s law.
In short, Einstein predicted that regardless of the direction of the river, whether it is in the southern or northern hemisphere, the outer curve of the river will always be eroded, and sediments will gradually accumulate in the inner curve, causing the river to become more and more Curved, like a pustule.
Later research found that the change of the river is indeed like this.
The evolution of the Ucayali River in Peru has caused the river to become more and more curved. Image source: geogarific
In the end, the meandering will even give birth to an oxbow lake that separates from the main river. It’s just as pictured–
The life cycle of meandering will eventually form an oxbow lake (the bottom semicircle). Image source: wikipedia
The secondary flow described by Einstein was later named the spiral flow(helicoidal flow).
Einstein further explained that Coriolis force does have a certain effect on erosion, but it is not judged by Bell’s law.
I just said that the river is a little bit curved. But even if a river is originally straight, it may be bent, and the reason for being bent is the secondary flow. You may find it strange that in a straight river, the water does not turn, and there is no centrifugal force. How can there be a secondary flow?
The principle is this: due to the rotation of the earth, the flow of the straight river is weakly affected by the Coriolis force, which will produce a secondary flow.
The horizontal component of the Coriolis force that makes the river abduct is 2vΩsinΦ. v is the water flow velocity, Ω is the earth speed, and Φ is the latitude. The higher the water velocity and the higher the latitude, the greater the Coriolis force received.
Under the action of Coriolis force, the forward-moving water flow and the bottom of the river bed will have left and right friction, and the water flow at the bottom will decelerate compared with the water surface, resulting in secondary flow and corresponding erosion. In other words, as long as the earth is spinning, the straight river will involuntarily want to bend.
In this concise and powerful paper, Einstein also made several predictions of river erosion.
For example, because this secondary flow has inertia, the strongest erosion should occur downstream of the river bend. In this way, the bends of a river will continue to move downstream, like a snake twisting and twisting. The larger the cross-section of a river, the slower the effect of frictional resistance on the river bed, and therefore the larger the bend diameter of the river. These are consistent with the facts.
Meandering and Oxbow Lake Picture source: eos.org
After Einstein, many scholars gave a quantitative description of this problem. In 1950, Einstein’s eldest son and professor at the University of California, Berkeley, Hans Einstein (Hans A. Einstein) at his father’s Based on the theory of sediment movement mechanics, the father and son made a foundational contribution to river sediment engineering.
In addition to explaining river erosion, the tea paradox also has important applications in beer brewing.
Trub (left) of impurities in beer brewing. Picture source: grainfather
In brewing beer, the protein and fat of the malt will condense to form impurities such as hop lees (trub). In order to facilitate the removal of these impurities, the wort is poured into a large rotating tank called a whirling sedimentation tank. The dregs will accumulate in the center of the bottom and are easy to remove. This technique is called hydrocyclones.
The first person who thought of this trick was the Canadian brewing company the Molson, and now most beer breweries use this idea.
The cyclone sedimentation tank uses the tea paradox to separate hop lees. Picture source: hofbrauhaus
This article is from WeChat official account:Bring science home (ID: steamforkids), author: seven Jun