In the morning of the Academy of Sciences in Paris, the spring sun shines through the classical-style window lattices, casting dappled light and shadow on the polished marble floor, like an oil painting with a gold frame.

Outside the window, the ancient plane trees sway gently in the breeze, and the tender green new leaves complement the clear blue sky, adding a bit of vitality and tranquility to this temple of knowledge.

On the tree-lined path under the plane trees, two French gentlemen are walking together.

They didn't walk very fast, their pace was slow, and the rustle of the leaves in the breeze could be heard, and the occasional laugh and conversation could be heard.

The younger gentleman, who was about forty years old, had thin and resolute cheeks, a high nose, and deep blue eyes in his sockets. Wearing a black silk top hat with meticulously combed silver-gray hair under the brim, he wore a dark blue double-breasted tuxedo coat with a thick and well-cut fit, and a dark silk tie tied around his neck, which accentuated his scholarly demeanor. Underneath a white turtleneck shirt, the delicate lace trim at the cuffs reveals his attention to detail.

As for the older gentlemen, he simply wore a black wool robe with wide cuffs and a loose hem that swayed gently in the wind, showing his calm and calm academic temperament.

Occasionally, they would be accompanied by a teaching assistant, and almost every teaching assistant would politely take off their hat and say, "Good morning, Mr. Navi." Good morning, Mr. Coriolli. ”

Hypothesis:

Coriolis said, "I haven't done that yet, I've been experimenting with rotating systems like water wheels for a while, and from the results of the experiments, this assumption is very likely to be correct." If you don't mind, I'd like to invite you to join me in researching the relationship between energy conversion and conservation in similar rotational systems. After all, as you know, not everyone is Euler, Fourier, Poisson, or Cauchy, and it can take years for most researchers to reach the threshold of mathematical expressions. ”

When Navi heard this, he didn't delve into it, but stepped into the door and said, "That's it, what do you care about this?" Let's talk about something interesting. You sit down first, and I'll find out where I left that manuscript. ”

The first, Navier, knew it, because it was a system of equations derived by Cauchy.

When Coriolis heard this, he suddenly remembered something: "Ah! So, the allowable stress method you proposed for the design of civil engineering structures was summed up after the failure of the construction of this bridge? ”

"Early."

For most of the people at the Paris Academy of Sciences, just two simple surnames are enough to give an idea of the outstanding academic abilities and tenure of these two gentlemen.

"It's better to be respectful than to obey."

Navi was about to open the door to the library, only to find that the door had been pushed open from the inside.

From the perspective of practical experience, the pressure does not significantly affect the resistance caused by the molecular interaction between the parts of the moving fluid, and these resistance is more due to the difference in the velocity or direction of adjacent molecules. So, based on this premise, I further deduced the categorical expression of the force acting on the molecule by the motion of adjacent molecules on the basis of Euler's equations.

I had just finished doing this work, and the next day I was excited to show Cauchy my latest research, and he happened to be very interested in this aspect, and he saw at a glance the fly in the ointment of the formula—it was only a set of equations describing the balance and motion of incompressible hydrodynamics, and it was obviously not enough to describe the laws of fluid motion at the macroscopic level. I am also aware of this flaw, but with my ability, the deduction to this point is already the limit.

When Liu Wei saw the two academic bigwigs, he was stunned for a moment, and then immediately took off his hat and saluted: "Ah! Good morning, two gentlemen! ”

Seeing this, Arthur also said good morning: "Good morning, gentlemen. ”

Gustave Coriolis is a stalwart of French science under the tutelage of Augustine-Louis Cauchy, a member of the Mechanics Department of the Académie Française, a former professor of geometric analysis and general physics at the École Centrale des Crafts, and currently a professor of applied physics at the Ecole Nationale des Roads and Bridges.

Coriolis said helplessly, "Mr. Navier, you know, that's impossible. You and Mr. Cauchy are old friends, Mr. Cauchy is my mentor, we both know his temper and position, he is an out-and-out orthodox dynastic who has devoted his life to supporting the Bourbons. While Napoleon could have made him willing to serve, his Majesty the King was Louis Philippe, who was clearly not as attractive to Mr. Cauchy as Napoleon, and therefore could never have sworn allegiance to the July Dynasty. ”

2. When the fluid is at rest, the normal stress is equal to the static pressure.

Coriolis asked, "Who is the award presenter?" ”

Sir Arthur Hastings, a young British researcher of electromagnetism. I have heard that he has a very good relationship with Mr. Faraday, and that he is often involved in Faraday's laboratory, and that he should be considered one of the best among the current young researchers of electromagnetism in Britain. It's a pity that I don't have much research on electromagnetism, otherwise I would definitely pull him to tell me about the current situation and breakthroughs in the research of electromagnetism in Britain. ”

Speaking of this, Navi suddenly stopped and asked, "Then again, why did you suddenly have time to come to the Academy of Sciences today?" Today is neither Wednesday nor Saturday, so there should be no meeting in the mechanics department, right? Could it be that you have achieved something new? ”

Navi put down the book in his hand and walked towards Coriolis, who took the calculation paper from the other man's hand.

"Well, that library is so remote that few people go there. But like me, Ampere, and Cauchy, we all like quiet places, so we all want to get together there. What do you think? ”

He turned sideways to get out of the way, watched Liu Wei leave with Arthur, and just as he was about to enter the door, he heard Navi speak, "That young man is the new assistant teacher?" ”

Liu Wei led a gentleman they didn't know out of the library and bumped into the two of them.

On the calculus paper, which should only exist in his personal derivation process, there are three more systems of derivation equations, and at the top of each system, their scope of application is also intimately indicated.

Navi was surprised, "If it's a teaching assistant, how can I not know him?" I have been teaching at École Polytechnique for so many years, and I know every student in the Department of Mathematics and Natural Philosophy in every class, but I have no impression of this person at all. ”

Navi was also helpless about this, but out of concern for his old friend, he asked Coriolis about Cauchy's current situation: "Is Cauchy still in Prague?" Still working as a tutor for the Bourbon Crown Prince 'Duke of Bordeaux'? ”

Coriolis was a little envious: "With this level of honor, it is estimated that the Academy of Sciences will hold an award ceremony for Mr. Poisson, right?" ”

Later, Cauchy told Mr. Poisson about my new discovery in the chat, and it took Poisson only a few months to establish an equation of motion describing compressible fluids by deriving Euler's equations under the same conditions. ”

But the third ......

After all, in the French Academy of Sciences, teaching assistants come and go every day, and it is not unusual for new people to come and old people to leave.

Coriolis joked, "Do you mean to say that the Academy of Sciences has recruited a teaching assistant who did not graduate from École Polytechnique?" You're not kidding, Mr. Navi. Even if they are only the most ordinary teaching assistants of the Academy of Sciences, they must be the best among researchers of the same age, and almost all of the best scholars in each age group are graduates of École Polytechnique. This is true of Mr. Cauchy, this is true of Mr. Poisson, this is true of you and me, and even the same is true of Liu Wei, who has just left the house. Do you mean to say that in our group of Polytechnique students, there are graduates of a motley school? I don't think the Academy of Sciences is so stupid and incompetent as it gets. ”

Speaking of this, Navi felt happy and his head hurt at the same time, and he spoke: "The greatest luck of the French Academy of Sciences is that we have two mathematical monsters, Cauchy and Poisson, so in the process of studying many problems, they have saved us a lot of trouble, intentionally or unintentionally. If it weren't for both of them, I believe that much of the current research in the Academy of Sciences would have been only at the stage of hypothesis and derivation. The biggest misfortune of the French Academy of Sciences is that one of these two mathematical monsters left last year. Rather than having me return to the Bridge Construction Committee, I still think the government should first find a way to bring Cauchy back. ”

The second, which Navier also knew, was because it was a system of equations derived by Poisson.

1. Fluids are isotropic.

Almost every highly educated guy will be in awe in front of these two gentlemen, but unlike the collision of ideas between the academic masters in everyone's imagination, the two of them do not always discuss academic issues when they are together.

Claude-Louis Navier, a master disciple of his mentor Jean-Baptiste Joseph Fourier, is a member of the French Academy of Sciences, a former member of the Higher Committee on Bridge Construction of the Paris High Court, and is currently Professor of Calculus and Mechanics at the Ecole Polytechnique and Professor of Mechanics at the Ecole Nationale de France Road and Bridge.

As soon as Navi entered, he headed straight for the bookshelf behind him, remembering what book he seemed to have tucked the calculus paper into.

Coriolis walked over to the chair, which had not yet cooled down, and as soon as he approached, he found calculus paper on the oak table full of calculations and derivations.

Coriolis knew Liu Wei, but it was the first time he had seen the tall young man in front of him, but he had no interest in asking about the other party's identity.

"Three assumptions?"

Coriolis felt the cool morning breeze and asked, "Mr. Navi, are you really not considering returning to the bridge construction committee?" ”

I thought that this would be the end of my research on Euler's equations, but to my surprise, one day a few months later, Cauchy suddenly walked into my office with a stack of papers. He said that he introduced the concept of the stress tensor of fluid micro-clusters into the Euler equations under the premise I gave him, and then found a set of formulas that could accurately reflect the difference between fluid motion and solid motion through this set of formulas.

Navi shook his head lightly with his cane, "It's not that I don't think about going back, it's that the bridge construction committee will probably not accept me again." When I was in charge of the design of the Invalides Bridge, I did not leave a certain safety margin in the calculation, which led to the cracking of the bridge and its demolition and reconstruction. Since then, government committees have been skeptical of my design skills, arguing that my designs are too mathematically calculated, and sarcastically that I am sometimes not as realistic as an ordinary mason in terms of construction. Although the committee was reorganized after the July Revolution, most of those people were re-elected, and with them, most of the bridge construction committee did not consider letting me go back to preside over the construction of the project. ”

When Coriolis heard this, he couldn't help but laugh and said, "You are right, Monsieur Cauchy's temporary departure is a misfortune for the entire French scientific community, but it is a blessing for all French scientists. When he was at the Academy of Sciences, it was like the Alps, pressing on everyone's heads. It is estimated that the only person who can care about him is a genius of the same level like Mr. Poisson. ”

"That's a good thing, right? After all, if he uses his brain so much to produce papers, his body can't last too long. You don't know that when he was young, he wrote papers like a printing press, because he wrote so many papers that he almost had to occupy the pages of the journal alone, so the Academy of Sciences passed a special resolution, stipulating that each paper should not exceed 4 pages in length in the future. It would be a good thing for young scholars who were eager to show themselves on the stage. ”

Coriolis shrugged his shoulders and said, "Probably yes, can there be any outsiders in the Academy of Sciences?" Even if there were, it was some officials, but it was well known that officials would not come to the library. ”

The two chatted and laughed along the way, and soon followed the tree-lined path to the door of the library.

"Is he still doing research?"

Na Van pouted slightly, "Whatever, I don't like to get involved in this kind of thing anyway, I just hope that the ceremony can end quickly, and don't delay us from doing business." And, I was obviously more interested in the award ceremony than the award ceremony, which was the guest from London. ”

"Speaking of Mr. Poisson, I've heard that the Royal Society of Britain seems to be planning to award him this year's Copley Medal," said Navi. Yesterday they sent someone to contact the Academy of Sciences to ask when Mr. Poisson would have time to receive the medal. ”

"Really?" Navi seemed to be in a good mood: "Then I'll take you to have a look, most of the people in the mechanics department think this is an unpopular direction, and it would be strange if you were interested." My manuscript on the equations of motion of fluids is in the library, and if you're interested, we'll go over now. By the way, let's talk about the issue you just mentioned, introducing a completely new force into the rotation system. ”

Coriolis also smiled and said, "I'm the same, I think mechanics is more interesting than electromagnetism." Electromagnetic induction is magical, but I'm obviously more interested in the equation of fluid motion that you just mentioned. ”

Navi was also quite helpless about this: "You are right, if Monsieur Cauchy is still in Paris, as long as your assumption is correct, he will find the law of mathematical expressions in a few months." When I was studying Euler's equations, I thought that the reason why Euler's equations did not match the real fluid motion was because the Euler equations treated fluids as a collection of molecules, and this assumption only applied to perfectly uniform flows, which in reality are usually inhomogeneous.

When Coriolis heard this, he couldn't help but laugh and said, "I really can't hide anything from you, do you remember the discovery I mentioned to you earlier?" When an object moves in a straight line in a rotating frame of reference, the object tends to maintain its original direction of motion due to inertia. However, due to the rotation of the frame of reference itself, the actual trajectory of the object is shifted. You said my discovery was interesting and suggested that I keep working on it. I've been pondering this question for a while, and in order to explain this phenomenon, I think it would be desirable to introduce an additional force into the research process to describe the object offset in a rotating frame of reference. ”

"I should have done less lately, at least not as crazy as I did when I was in Paris. He now devoted most of his attention to educating the Duke of Bordeaux. ”

Coriolis asked, "You mean the easternmost library?" ”

Coriolis shook his head and said, "No, he went to Graz with the Bourbon royal family a while ago, and Metternich of the Austrian Empire ordered all the orthodox dynastic exiles in the territory to be moved there. ”

Navi frowned and thought for a while, "Introduce a brand new force?" It's a bold idea, but I can't say it's wrong until it's been completely falsified. Well...... Have you found a mathematical expression for this force? ”

Coriolis picked up the calculus paper and glanced up and down, and soon let out an exclamation, "Mr. Navier, you must be looking for this, this derivation is indeed exquisite. However, you seem to have missed something from me, and you have recently put forward three more hypotheses based on the original derivation? ”

Navi nodded slightly, "The same mistake, making it once is a mistake, but making it twice is stupid." I'm not a smart person, but I don't want to be seen as stupid, so of course I have to learn a lesson. After all, I still have a teaching position at the National Road and Bridge School, and although I may not have the opportunity to lead the bridge design again, at least I can't let the students repeat my mistakes. ”

3. Stress is linearly related to the deformation rate.

Based on the above assumptions, the constitutive relationship of fluid stress can be derived, and the following derivation can be carried out by substituting the above-mentioned differential equations of fluid motion, and the system of motion equations applicable to viscous fluids with compressible variable viscosity can be obtained......

(End of chapter)