I just want to be a quiet scholar

Chapter 460 A Point of View on the Navier-Stokes Equations

Summarize the Navier-Stokes equation in one sentence, that is, this equation is used to explain fluid motion.

Fluid motion is everywhere, from the motion of airplanes and ships, to the way blood flows in veins and arteries.

After the death of two scientists, Navier and Stokes, people continued to study the NS equation and made important progress.

There is only one problem left, and it is the most fundamental problem: no one can find a formula to solve the NS equation.

To be precise, no one can prove in principle whether the NS equation has a solution.

The stubbornness of scientists lies in the search for the truth. Human beings have developed many theories, manufactured various tools, and applied them to various engineering scenarios over the past 200 years using an equation that is unknown whether it has a solution.

Scientists always feel a little flustered, especially scientists like Shen Qi and Wei Teng who have far-reaching considerations.

A meeting room in the centre.

Zhou Yu'an talked eloquently: "Fluid motion satisfies mass conservation, linear momentum conservation, and angular momentum conservation. As a result, six additional motion characterization quantities must be introduced, which are three independent components of Reynolds stress, two dynamic viscosities, and one independent component. pressure."

"However, I think there is a problem here. While satisfying these three conservation laws, it negates the NS equation, and there is a choice of Reynolds stress for the dynamic viscosity and dynamic pressure, which means that there are 6 The 6 degrees of freedom can be selected! As a result, the velocity field is a function of these [-] degrees of freedom." Zhou Yuan had his own ideas, and he stated his ideas.

Xiao Junlong went on to say: "Old Zhou, this problem is a fatal internal injury of fluid mechanics. The original derivation of the NS equation only needs the conservation of linear momentum and the conservation of angular momentum, and the fundamental reason for adding the conservation of mass is that it cannot represent the conservation of angular momentum. You I must have understood the two mechanical viewpoints of the NS equation when I was studying for a Ph. D., first, conservation of mass + conservation of linear momentum. Second, conservation of linear momentum + conservation of angular momentum."

"The first point of view leads to the concepts of material velocity and Euler velocity, so as to maintain the basic structure of three equations to find three velocity field components. This is the current popular theory of fluid mechanics. However, I regret to find that based on the first As a mainstream theoretical system, the NS equation has no solution." Zhou Yu'an shook his head with a puzzled expression.

"You're so right, Lao Zhou, heroes see the same thing!" The collision of ideas produces a steady and progressive friendship, and Xiao Junlong is also at a loss: "The second point of view also has problems, it introduces vorticity vectors, But still maintain 3 equations to find 3 velocity field components, so this is very contradictory. At this time, the derivation of velocity to space coordinates is not interchangeable! Although someone introduced the form of Lie algebra, the engineering value is not great, because the theory Basic concepts are confused."

"So, the NS equation has no solution?" Zhou Yu'an and Xiao Junlong summed up and deduced such a conclusion.

Shen Qi and Wei Teng who had been listening all the time smiled and said nothing.

In order to let Wei Teng understand, the conversation between Zhou Yu'an and Xiao Junlong just now was in English.

Through intense and rigorous deduction, communication, and discussion, the two deputy team leaders Zhou and Xiao believed that the NS equation had no solution.

In fact, this is also the status quo in academia.

Engineers can always introduce additional conditions to the equation for specific problems, so that the NS equation has a solution.

However, the obtained results were correct for their specific problem, but not general.

This is why the vast majority of scholars believe that there is no general solution to the NS equation.

The general solution is the golden key with universal laws. Finding this golden key, or giving convincing evidence to thoroughly prove that this golden key does not exist at all, is an operation of scientific value.

Zhou Yu'an and Xiao Junlong looked at each other, shook their heads and smiled.

It's still too naive. A $1000 million project will definitely be beaten.

Zhou Yu'an and Xiao Junlong looked at Shen Qi and Wei Teng.

According to the conventional script design, after the red-faced supporting role has finished its questionable lines, the calm and steady protagonist should come forward to give the final correct answer and lead the team to a broad road.

"Edward, you go first." Shen Qi said to Wei Teng.

"This is not a system problem, but an algorithm problem." Wei Teng said calmly.

Shen Qi, Zhou Yu'an, Xiao Junlong: "Hmm."

Wei Teng walked to the water dispenser, took a paper cup, put the paper cup under the water outlet, and pressed the water outlet switch.

The water column drains down at a fixed flow rate and flows into the paper cup.

After the paper cup is filled with pure water, the water overflows when it is full.

"This is the first experiment." Wei Teng handed the paper cup full of water to Zhou Yu'an, and said, "Zhou, drink it."

Gooooooooooooooooooooooooooooooooooh.

Zhou Yu'an drank the water in the glass in one gulp. This glass of water has no sweet or salty taste, just the original taste of ordinary bottled pure water.

Wei Teng took the empty cup in Zhou Yu'an's hand and came to the water dispenser again.

This time Witten crushed the paper cup, but it wasn't completely deflated, but half deflated.

Crash.

Under the operation of Weiteng, the water outlet of the water dispenser flows out of the water column at a small water flow rate, and leaks into the half-deflated paper cup.

Because Weiteng exerted an external force on the paper cup, the paper cup did not expand to its original shape when it was continuously filled with water.

Weiteng maintains the external force exerted on the paper cup and maintains the irregular water-filled shape of the paper cup.

"This is the second experiment." Wei Teng walked up to Xiao Junlong, pretended to be feeding water, and said, "Xiao, drink it."

"But... Zhou just used this paper cup!" Although Xiao Junlong is not handsome, he is a man who loves cleanliness and hygiene.

"Don't worry about the details," Witten said.

"Okay, Edward, I'll drink." Xiao Junlong glanced at Zhou Yu'an, and asked in Chinese: "Old Zhou, you don't have hepatitis, right?"

"Look at your future, what kind of scientific research are you doing?" Zhou Yu'an forced himself not to laugh.

Xiao Jun closed his long eyes, his heart sank, and he drank the water in the glass under the service of Wei Teng.

Witten said: "Through two successive experiments, we found that under the same water dispenser system, the same paper cup can hold less water in the second time than in the first time because of the different additional conditions."

Zhou Yu'an and Xiao Junlong: "Hmm."

Shen Qi smiled, but didn't hum.

Witten likes to use simple props at hand to demonstrate and explain some profound scientific principles: "You mentioned before that engineers can always introduce additional conditions to the equation for specific problems, so that the NS equation has a solution. But , these additional conditions are deliberately made, even if the solution of the NS equation is solved, it can only meet the specific situation originally set by themselves, and it is not universal."

"The two fillings of the same paper cup have obvious differences in the amount of water due to different additional conditions. But it is undeniable that they all have engineering effects, and they solve the thirst problem of Zhou and Xiao. So I think that the fundamental of the NS equation The problem is not a system problem, but an algorithm problem.”

Wei Teng came to the water dispenser and restored the paper cup in his hand to its original shape: "Who can design a third experiment, also based on this water dispenser system, to obtain a universal solution?"

(End of this chapter)