On March 5, 1966, a Boeing 707 aircraft flew smoothly off the ground at Haneda International Airport in Japan.
This plane belongs to British Overseas Airlines (BOAC), the flight number is actually called 911, like metaphysical friends you have another material. Shortly after the flight took off, the captain was pleased to inform the passengers: due to weather conditions, the air traffic control bureau changed the route of this flight, we will fly over Mt. Fuji, I hope that passengers will not miss the view of Mt. Fuji from above. There were a few cheers from the cabin, and it was a rare thing to know that flying at that time, and being able to overlook Mt. Fuji from a high altitude was a rare opportunity for the 124 passengers and crew on board.
A few minutes later, the plane climbed to an altitude of 5,000 meters, the sky was clear, the beautiful Mt. Fuji appeared in the eyes of passengers, and passengers close to the aisle stuck their necks in the direction of the porthole. At this moment, the plane suddenly jolted violently, a degree of intensity that had never been encountered by an experienced captain with 6 years of driving experience. The passengers sitting at the rear of the aircraft looked through the porthole and were horrified to see that the rudder of the aircraft actually snapped in the violent shaking, and quickly smashed into the elevator on the left side of the aircraft, smashing the elevator in an instant, and the two important rudders were separated from the fuselage at the same time and disappeared into the field of vision in an instant. Then, even more terrible things happened, the four engines hanging under the wings also fell off one by one in a violent shaking, and the plane at this time was like a big bird that dropped its feathers while flying, completely out of control, swinging left and right towards the ground, and finally crashing on the ground, all 124 people on board were killed, and none of them were spared.
What exactly happened to this plane? Why did it disintegrate in such a clear sky? This is the nightmare of the aviation industry – clear skies and turbulence. Although the strength of the aircraft's fuselage is now unlikely to be disintegrated by turbulence, flight accidents caused by clear sky turbulence still occur from time to time. For example, on August 11, 2015, a Hainan Airlines flight from Chengdu to Beijing encountered strong turbulence in the clear sky as it descended to an altitude of 4,200 meters. According to the recollection of the crew, some passengers were directly bounced onto the ceiling without wearing seat belts, smashing the ceiling, and the accident caused a total of 30 people to be injured to varying degrees. According to the International Air Transport Association, clear sky turbulence is the biggest cause of injury to passengers and crew in non-fatal flight accidents.
Many people may think: Now that science and technology are so developed, can't we predict in advance that there is a clear sky turbulence in front of the voyage to avoid it? As soon as I told my story today, I didn't dare to sit on the plane. At present, there is really no way to do this. Why? That's the subject of this article— turbulence.
The famous British fluid gemechanist Horace Lamb put it this way:
I'm very old, and when I go to heaven to meet God, I ask Him two questions, one about quantum mechanics and the other about turbulence. I reckon that the first question has an answer.
If you have read some popular science articles that introduce turbulence, it is estimated that you have an impression of the above sentence, but most popular science articles have misrepresented the person who said this sentence as Heisenberg, and I examined it and found that it was not Heisenberg who said it. This misunderstanding has spread so widely that some of the famous scientists I have read online have mistakenly thought that Heisenberg said it.
Physicist Feynman wrote in a 1963 article:
In the field of classical physics, there is still one last problem left unsolved, that is, the computational problem of turbulent structures.
Turbulence is a classic problem that fluid mechanics needs to solve, and the flowing liquid and gas are actually not much different for physicists, they are all fluids.
In real life, turbulence can be seen everywhere. In the creek ditch, you can see the flow of white flowers everywhere. In the flowing water of those white flowers, there are countless small swirls swirling. Many times, when a piece of flowing water encounters a small obstacle, it will become white, changing from laminar to turbulent.
The phenomenon of turbulence of gases can also be seen everywhere. If we look at the smoke coming out of a blazing incense, you will see that the smoke is columnar at the beginning, and when it rises to a certain height, the smoke begins to become unstable and forms turbulent currents.
In fact, in general, the entire atmosphere of the Earth is a turbulent system.
The spots on Jupiter's surface are actually a vortex of gas, and the entire surface of Jupiter is also a typical turbulence system.
Physicists have long observed: when the flow rate of the fluid is very small, it is a hierarchical flow, not mixed with each other, called laminar flow, or sheet flow; gradually increasing the flow rate, the flow line of the fluid begins to appear wave-like oscillation, the frequency and amplitude of the swing increase with the increase of the flow rate, this flow condition is called transitional flow; when the flow rate increases to a large, the flow line is no longer clearly recognizable, there are many small whirlpools in the flow field, called turbulence.
At various scales, turbulence is a movement that is disordered in time but statistically regular.
The so-called turbulence problem is to mathematically model the entire process of the fluid, so that humans can accurately know the cause of the turbulence and predict its direction. In layman's terms: given the initial conditions, can we figure out how turbulence occurs, when it occurs, how big it happens, when it ends, and so on.
Human research on the problem of turbulence has lasted for more than 200 years, and it has become a famous pit in classical physics, and I don't know how many young talents have plunged into this pit and never climbed out again. The solution to this problem, from a small age, can make the aircraft fly more smoothly, the submarine noise is smaller, the wind farm layout is more reasonable, the weather forecast is more accurate; in the larger term, it can even help astronomers simulate the movement of galaxy clusters and solve various celestial body formation puzzles.
To solve the turbulence problem, the first question that people must first figure out is: under what circumstances will laminar flow become turbulent?
The first to answer this question was The British physicist Osborne Renault. He found that when the fluid flows, it will be subjected to two forces at the same time, one is the force that pushes the fluid forward, which is called the inertial force; the other force that prevents the fluid from flowing forward is called the viscosity force.
In 1883, Renault made an important landmark discovery. Experiments have shown that when the ratio of inertial force to viscous force of a fluid exceeds 2300, laminar flow becomes turbulent. This ratio is known in academia as the Reynolds number. This value remains one of the most important parameters for describing fluids to this day. But Renault's discovery didn't allow us to calculate the evolution of fluids, nor did they allow us to accurately predict changes in fluids.
The next challenge for physicists is to find equations that accurately describe fluids, just as they would find a gravitational formula that describes the motion of celestial bodies.
This is obviously an extremely difficult one, and it has attracted many physicists. In 1827, the French physicist Claude Louis Navier was the first to find a breakthrough in solving the problem. In 1845, the Irish physicist George Stokes made significant progress. The joint work of these two physicists has been dubbed the Navier-Stokes equation by academics. Abbreviated as the N-S equation.
I will not explain this equation, ordinary people do not need to be so proficient. We just need to know that this equation is nonlinear, the so-called nonlinearity is that the relationship between the dependent variable and the independent variable is not a linear relationship, and the function diagram drawn cannot be expressed in a straight line. Nonlinear equations are generally difficult to find precise solutions, only approximate solutions. This N-S equation is even more difficult to solve.
In most cases , its solution is unstable , resulting in multiple forks of the flow , forming complex flow states , and the nonlinearity of the equations couples flows of different scales to study separately. So engineers and scientists often use simplified theoretical models or resort to numerical simulations to predict the motion of fluids.
For example, it's a bit like playing Go, we know all the rules of the game, but it's extremely difficult to tell if there's an optimal move for each step. That is, the Navier-Stokes equation can describe fluids, but it is extremely difficult to solve, and it is the common dream of generations of mathematicians and physicists to completely unravel the hidden mysteries in this equation.
There is a saying in the physics community that the N-S equation is not the end point of turbulence research, but the starting point of turbulence research.
One of the 7 Grand Prize questions selected by the prestigious Clay Institute of Mathematics is whether there is a unique solution to the Navier-Stokes equation. I use an analogy where I take out a small ball and lift it up, and as soon as I let go, it falls somewhere. It is also a mathematical equation that determines where the ball falls, and it has a unique solution, meaning that as long as the initial conditions are the same, the location of the drop is exactly the same. If there is no unique solution to this equation, it means that even if the initial conditions are exactly the same, the position where the ball falls may be different each time. Whoever can prove it mathematically will receive a $1 million prize.
Mathematicians have done a lot of research on the N-S equation for a century, but not many major results. In the 1950s, Mr. Zhou Peiyuan, a pioneer in the study of turbulence, pioneered the idea of "solving first and averaging later", and is known as the father of turbulence pattern theory and one of the four major instructors of world turbulence research.
If you're familiar with solving mathematical equations, you might be wondering, "Aren't there supercomputers now?" If the equations are not resolved, then we can use computers to find one specific solution after another and numerically simulate the N-S equations. "It's like having a lock, I make all the possible keys that can open this lock, and then try one by one, I don't have to understand the principle in the middle, anyway, try to calculate one."
Of course, this idea is correct, in fact, in order to get a better hydrodynamic shape of an aircraft or ship, we are constantly experimenting, accumulating data, and then constantly correcting, which is called fitting in engineering mathematics. However, the turbulence problem is still much more complicated than we think, and if we want to use this method to find the complete flow field of aircraft and ships, including turbulence in their boundary layer, then the speed and storage capacity of the computer are at least 2 orders of magnitude higher than the current supercomputer, that is, more than 100 times. At present, it is very unrealistic.
In the early 1940s, the Russian mathematician Kormogorov proposed a theory of homosexual "turbulence level strings", which can describe the transfer of energy from large whirlpools to small whirlpools, that is, with his method, he can study the rupture of large whirlpools into smaller whirlpools, and then the small vortexes break into smaller whirlpools, so that layer by layer cycle. The transmission of kinetic energy is like a running relay race, except that each time the handover athlete becomes smaller, and the number becomes more, and eventually the kinetic energy is dissipated in the form of thermal energy by molecular viscosity. Based on this hypothesis, Kormogorov built a preliminary mathematical model of turbulence.
He is equivalent to decomposing a big problem into many small problems: now only study how the energy of each large vortex is transmitted and dissipated after it has broken into several small whirlpools; when this small unit is figured out, it can be put together into a complete turbulence model.
The idea is good, but the method must make some basic assumptions about how the great vortex broke, and Kormogorov's mathematical model is based on several assumptions that have not yet been tested. In other words, his method can only solve the problem of turbulence in some idealized situations, but the real situation is much more complex than these idealized cases. The shortcomings of the Koch model are also obvious.
Although this is such an old and important problem, because of its obvious difficulty, many physicists dare not easily touch this problem.
I have seen physics professionals answer the question "Why are there so few turbulent scientists" and say: It cannot be said that physicists dare not be interested, but it is too difficult to break through. Turbulence burning in particular is even more perverted. Therefore, there are fewer physicists who specialize in turbulence theory, think about how to support your family if you can't produce results in a lifetime?
Another user said to the post: Although it is a physical problem, it will cause a lot of physical and psychological problems.
Another person said to the post: Unless a genius suddenly finds a breakthrough, the turbulence will become a hot issue in theoretical physics research again.
But turbulence is so important. Academician Zhuang Fenggan said: Turbulence has become one of the key bottlenecks affecting the success or failure of national aerospace and navigation projects, and is a major application basic topic that the country urgently needs to solve.
It is in this context that in July 2017, the National Natural Science Foundation of China (NSFC) "Major Research Program on the Generative Evolution and Mechanism of Action of Turbulent Structures" was officially approved, led by Academician Chen Shiyi, and Chinese scientists teamed up to challenge the problem of the century , the mystery of turbulence.
That's why I chose the theme "Turbulence" in the second season of "Finding Nature".
Throughout 2021, I've been reading all kinds of material about turbulence. In order to introduce this first problem in classical physics to the majority of science enthusiasts. I have nibbled on many papers this year and interviewed many of our country's top scientists in the field.
During a visit to Professor Li Cunbiao, director of the Turbulence Laboratory at Peking University, Professor Li gave me a particularly subversive new concept, saying:
Even if the problem of whether the N-S equation, one of the Cray Millennium Prize problems, has a unique solution solved, it does not mean that the turbulence problem has been solved. Turbulence problems are commonly equated with the N-S equation, but this equality does not hold. Turbulence is turbulence, and the N-S equation is the N-S equation, which involves a deeper philosophical question of whether the nature of the universe is mathematical.
To put it in layman's terms, we all know that when Newton had just found the formula for gravitational attraction, people thought that the problem of celestial movement was completely solved, and that mathematics could accurately predict the orbit of celestial bodies. But then we found that when precision rose to an order of magnitude, Newton's formula failed. Later, Einstein proposed general relativity, using Einstein's field equations to greatly improve the accuracy of the laws of celestial motion, although so far, we have not found any failure of the broad phase. But who can guarantee that after the observation accuracy continues to rise, will the broad phase also fail?
As you think along this line of thought, you come to the ultimate question: is there a definite mathematical equation that can describe our universe with complete precision. That is to say, we can ask: Is the nature of this universe mathematical? Can mathematical and physical problems be equated?
Professor Lee believes that, at least for the foreseeable future, there will be no answer to this question...
End