Into Unscientific

"."

This moment.

Look at the face that appeared next to him.

Unguarded.

Ye Duzheng almost didn't put his hand into his pocket, and took out the natal wooden tablet that his mother gave him back then and threw it at the other party - it is said that it is made of peach wood and can ward off evil spirits.

Of course.

Ye Duzheng reacted before taking out the wooden sign.

The guy who appeared in front of him was not a mummy, but a man who had recently become famous in the base.

Acquaintance Han Li.

See this situation.

While Ye Du was secretly relieved, he also used his slow speech to cover up the initial panic in his heart, and said:

"Comrade Han Li, I thought who it was, it turned out to be you."

to be honest.

Ye Duzheng's impression of Xu Yun was actually quite good.

After all, without the weather Doppler radar he produced, the weather center might never have the chance to prove itself again.

if so

Then it is foreseeable that the entire meteorological center will lose its fighting spirit for a long time.

Also from an industry point of view.

The help of meteorological Doppler radar to the whole meteorology is also obvious.

The emergence of this kind of equipment is likely to open up a brand-new avenue for the meteorological field that has never seen the future-it is still the one that China dominates.

Therefore, no matter from his job or personal feelings, Ye Duzheng has a good impression of Xu Yun, and even has a trace of gratitude.

So after being taken aback.

Ye Duzheng did not show any dissatisfaction, but asked Xu Yun with a smile:

"Comrade Han Li, why are you here? By the way, have you had dinner yet?"

At this time, more than seven or eight hours have passed since the first batch of data was released, the sky has already changed from day to night, and it will be almost twelve o'clock in a few hours.

Not long ago, someone sent dinner to the base.

"Well, I just drank some porridge."

Xu Yun tilted his head towards a certain direction outside the tent. At this time, he could vaguely see several sideline team members busy delivering dinner.

However, tonight's "standard meals" are not high-standard, most of them are corn-bread potatoes with vegetable leaf soup with elm leaves.

Wotou bitter teeth, elm leaves bitter.

Xu Yun's ability to drink polished rice porridge is mainly related to his status as a patient, and he needs recuperation during the recovery period.

Then Xu Yun put his eyes on Ye Duzheng's calculation paper again, and took a few serious glances:

"Huh? Director Ye, is this a variation of the Stokes equations?"

Ye Duzheng was slightly taken aback, and seemed a little surprised that Xu Yun could recognize the content of the equation.

But he quickly remembered Xu Yun's identity, and nodded slightly:

"Yes, it is the N-S equation system, with a little change on the basis of vorticity."

According to Lao Guo's previous introduction.

Xu Yun is a graduate of the Department of Mathematics at Cambridge University. It is normal to recognize the N-S equation system. After all, this equation is a major problem in the field of mathematics.

Or put it another way.

In terms of Xu Yun's ability to come up with the meteorological Doppler radar theory, it's no wonder he can't recognize the N-S equations.

Xu Yun then turned his head to look at the crackling scene full of abacus, and casually asked Ye Duzheng:

"Director Ye, how is your progress now?"

"schedule?"

Ye Duzheng raised his eyes and looked at Xu Yun for a second, then shook his head, with a wry smile on his lips:

"How can there be progress? Comrade Han Li, what you see now is all - I don't know how to deduce it later."

Ye Duzheng said it.

He also pinched the front half of the ballpoint pen with his fingers to make a small lever, and slapped the end of the pen on the calculation paper twice, and he seemed a little bored.

The calculation of weather data is not a secret, so Ye Duzheng didn't want to hide anything.

After all, people have a desire to talk.

Then Ye Duzheng sighed and shook his head, ready to honestly change his mind - since the variant he considered was not feasible, he could only calculate according to the plan given by Mr. Zhu.

even if

There are likely to be some problems with that idea.

And just as Ye Duzheng was picking up his pen to write, Xu Yun's weak voice suddenly came from his ear:

"Director Ye, I have an idea. Do you think it is feasible to add a Bernoulli function after this variant?"

Ye Duzheng's pen tip stopped after writing a few letters.

After a while.

Ye Duzheng raised his head full of surprise, and looked at Xu Yun with a mummy-like expression on his face:

"Comrade Han Li, what did Ni (fourth tone↓) say?"

Under the emotion.

Ye Duzheng even had the accent of his hometown, Jinmen.

And opposite him.

Looking at Ye Duzheng with wide-eyed eyes, Xu Yun was also a little surprised in his heart—he thought that the concept of localized distribution of vorticity was relatively complete now.

But soon, he reacted quickly.

Too.

The key figure in the convection-diffusion equation is Suhas Patankar, who is only in his early twenties in terms of age.

Although Xu Yunji doesn't know exactly when he proposed the SIMPLE improved algorithm, Suhas Patankar is not a genius who became famous at a young age.

He wanted SIMPLE to improve the algorithm, and proposed that it would be more than ten years later anyway.

It is not an exaggeration to say.

These years, the research on the Navier-Stokes equation in the entire mathematics and physics circles is still in a very primitive state.

Even the original version of the SIMPLE algorithm, a semi-implicit method for solving coupled pressure equations, was not proposed until 1972.

Think here.

Xu Yun then decided to help Ye Duzheng a little - although he really had no intention of doing so before.

But this kind of thing that can make the rabbit catch up with or even overtake the first echelon, he is naturally very happy to do it.

Anyway, no money, just try a little bit.

Then Xu Yun paused, quickly organized some thoughts in his mind, and said to Ye Duzheng:

"Director Ye, what I mean is to add a Bernoulli function after this variant, and then take a curl. Do you think it is feasible?"

"This is what I heard from a senior when I was at Cambridge University. At that time, the situation they derived happened to be the same variant"

Swish——

As a result, Xu Yun didn't finish his sentence.

Ye Duzheng lowered his head and wrote down a function on the paper:

C=p/ρ+u/2.

This function comes from the equation (u/2)=(u)u+u×ω, which is the Bernoulli function.

Then Ye Duzheng took a curl according to what Xu Yun said, and obtained a new formula:

ω/t=×[u×ω]+vω.

Don't look at this formula that looks like kaomoji, it seems to be (￣▽￣)~*(￣▽￣)/(ω)[]~(￣▽￣)~* again.

For Ye Duzheng.

The moment he saw it, his heart skipped a beat!

This is

The evolution equation of ω!

At the same time, because ×(u×ω)=(ω)u(u)ω, this evolution equation can also be rewritten in the form of convective derivatives:

Dω/Dt=(ω)u+vω.

write here.

Ye Duzheng paused again, turned his head to look at Xu Yun again, and asked impatiently:

"Comrade Han Li, what's next? What's the idea behind?"

This moment.

Ye Duzheng seemed to have returned to the days when he was studying in Chicago.

At that time, he was chasing a mystery novel serialized in the Chicago Daily, and every time he finished a chapter, he couldn't wait to update it crazily.

If it is not for the fear of losing the valuable qualifications to study abroad.

Ye Duzheng even considered whether to tie the author to a small black room to update - he must update 50,000 words a day, otherwise he would not be able to eat that day!

And opposite him.

Xu Yun signaled Qiao Caihong to move his wheelchair closer to Ye Duzheng.

Then he took the paper and pen from Ye Duzheng, and explained while writing:

"Director Ye, if you want to continue deriving this equation, you must first understand the physical meaning of this variation."

"Let's introduce another angular momentum equation here for comparison. You see, the physical meaning should be obvious, right?"

Ye Duzheng watched it carefully for half a minute, and quickly said:

"Oh, I get it."

"The description on the right is due to the elongation of the fluid element, the change of the moment of inertia of the voxel, and the viscous moment acting on the voxel, right?"

Xu Yun nodded.

The physical meaning of this variant can almost be regarded as an entry-level concept of vorticity in later generations.

That is, the vorticity of the fluid block may change due to its elongation, causing a change in the moment of inertia, or acceleration or deceleration due to viscous stress.

Immediately afterwards.

Xu Yun wrote another Peclet number.

That is, Pe=ud/α, and a circle is changed on the top, bringing back the original formula.

See here.

Ye Duzheng suddenly heard an unexpected nasal sound from his nostrils, and raised his brows suddenly.

He discovered a problem he hadn't realized before:

According to variants.

Vorticity in a two-dimensional flow is convective and diffuses like heat, so the analogy for the Peclet number is

Re=u/v.

This means that vorticity, like heat, cannot be created or destroyed in a two-dimensional flow.

And it can move from one place to another by convection.

But on the other hand.

∫ωdV is conserved for all localized vorticity clusters.

That is to say

The vortices are convected by the velocity field and propagated by diffusion, but the total vorticity within each vortex remains constant.

In other words.

Boundaries are where the vorticity comes from!

This is a concept that Ye Duzheng has never thought about, which means that many of his previous ideas were wrong, and he really underestimated the depth of the boundary.

But it also means

A NEW MODEL POSSIBLE!

To be precise it should be.

The first truly workable new model in meteorology!

To know.

Although the Norwegian School has made great contributions to numerical weather prediction, even now, the entire meteorological industry still does not have a real model.

In fact.

Follow normal historical development.

Meteorology It wasn't until 1971 that Rasul developed the first climate model.

And Rasul's model predicts not local weather, but climate models related to global warming.

And now.

A new road appeared in front of Ye Duzheng.

A new path that no one has ever explored.

Looking at the shocked Ye Duzheng, Xu Yun looked very calm.

The concepts he mentioned are not based on his personal ability, but come from the relatively complete knowledge system of later generations, which is nothing to be proud of.

After all, it is different from the current period.

Although later generations are still in the cracking stage of the N-S equation, the analytical solution of the general form is still far away-because it is stuck on the nonlinear advection term.

But on the other hand.

It still has analytical solutions in various extreme cases, such as non-rotation, non-viscous and other scenarios.

Later generations can even solve complex fluid flows as long as enough computing resources are invested in DNS.

These are the results of Xu Yun's strong formulas before he traveled, so that people like Xu Yun who are not in the field of meteorology can easily use them to explain.

Of course.

Due to professional barriers, Xu Yun's understanding of vorticity is almost over here.

As for the advanced concepts of equivalent potential temperature, pseudo equivalent potential temperature, latent heat, sensible heat, and radiation.

It's okay for you to ask Xu Yun to explain their meanings, but it would be pure wishful thinking to deduce them further.

But that's okay.

At this point, Ye Duzheng has obviously entered the state of 'enlightenment'.

As far as the ability of the main founder of China's modern meteorology is concerned, even if he doesn't need Xu Yun's help, he can probably handle the rest of the process by himself.

Not to mention that Tao Shiyan, a top weather dynamics expert, exists beside him.

So soon.

Ye Duzheng began to deduce the next steps by himself.

"The governing equation for temperature is DT/Dt=αT"

"Then the equation of the temperature field is naturally DT/Dt=T/t+uT/x=αT"

"According to hydrostatic equilibrium and temperature lapse rate."

"Brother Shiyan, what do you think of changing the turning point pressure of the segmented function here?"

"Just what I want."

Twenty minutes later.

Ye Du was writing down another formula on the paper:

D/Dt(ω/2)=ωiωjSijv(×ω)+v[ω×(×ω)].

And when I saw this formula.

Xu Yun's expression under the bandage also loosened.

call.

His task is considered complete.

Presumably smart classmates have also seen it.

That's right!

The formula that Ye Duzheng wrote at this time is exactly the vorticity quasi-energy equation.

It comes from the scalar product of the convective derivative above and ω, which is the vorticity for the localized distribution.

Among them, the rightmost divergence term usually integrates to zero, which is not necessary like the brain.

The remaining two items on the right correspond to the vorticity quasi-energy produced by vortex line elongation, and the eddy quasi-energy due to viscous loss.

From this formula, it can be seen intuitively that the vortex quasi-energy can be dissipated by friction, just like mechanical energy.

This formula will be mentioned repeatedly when discussing turbulence in later generations, and it can be regarded as an iconic formula.

more importantly.

well known.

Atmospheric diffusion belongs to turbulent diffusion, and there are currently three widely applied theories:

Gradient Transport Theory,

Turbulent Statistical Theory,

similarity theory.

And this formula is the important core of the statistical theory of turbulent flow. On this basis, a model called WRF was born in later generations.

That's right.

WRF.

This is the most common model for meteorological numerical simulation forecasting in later generations, and many minkes also use this thing to run numerical values ​​at home.

Of course.

Civil science in the field of meteorology is far more intelligent than civil science in the fields of physics and mathematics, and there are obvious differences between the two.

Civil science in the field of meteorology is not so much a 'civil science'.

Rather, it is more like those astronomy enthusiasts who drive a telescope to see the stars, and rarely make too many outrageous remarks.

At least it doesn’t mean that I invented the perpetual motion machine, and then I look at the drawing and it’s a Taiji diagram

Minke in the field of meteorology likes to run the local weather model silently at home, and then look at the sky to see if his results are accurate. Overall, he is quite Buddhist.

all in all.

WRF is a very important model even in 2023, let alone this period.

even if

What appeared at this time was only a prototype.

Afterwards, Ye Duzheng extended the formula to the field of isobaric surface and isodensity surface, and carried out related calculations of circulation.

During the period, the girl Qiao Caihong also stepped forward to watch with great interest for two minutes. When she returned to Xu Yun's side, her expression became like this: @v @after an hour.

Ye Duzheng and Tao Shiyan jointly deduced the complete eddy field and fitted a special mathematical model.

From Xu Yun's point of view.

This model is still quite different from the WRF of later generations - after all, there is no computing power of later generations these days, but the core logic is still similar.

To put it simply, the cylindrical tangent space and horizontal mapping are used first, the local space is constructed and its neighbors are mapped, and the isometric mapping is constructed.

Then, the conditional local convolution kernel is redesigned to meet the convolution characteristics tailored to local conditions. Adjacent convolution kernels with similar local features and different geographical characteristics share three conditions.

As for the mathematical mechanism of the model is the Fourier transform, Ye Duzheng constructed the mixing operation as a continuous global convolution, which can be effectively realized through FFT in the Fourier domain, and the complexity of space mixing is reduced to the lowest.

The model even took into account accumulated liquid and frozen water, using total rainfall particles as a diagnostic variable, and the number of data sets reached 20. (Inspired by this paper arxiv.org/abs/2101.01000)

It can be said like this.

Today, when computer models have not yet come out, this model can be said to be the pinnacle of human reach.

In addition, I don't know if it is Xu Yun's illusion.

He always felt that Ye Duzheng's model seemed to faintly touch the Fourier neural operator.

Of course.

just feel.

After all, he is really not good at learning in this area, so he can't draw a specific conclusion for a while.

It may be an illusion, or it may be real.

It's okay if it's just a misjudgment.

But if it's true.

Then on the current timeline of this dungeon, the fun in the future will be great.

After all, this thing has long gone beyond the scope of fluid mechanics, and involves AI.

Then another ten minutes passed.

Tao Shiyan gathered the data of each group to the front of the stage, and Ye Duzheng introduced his model ideas to everyone.

Considering that everyone's understanding ability is different, Ye Duzheng mainly focused on calculation.

That is, it focuses on telling everyone how to calculate, and ignores the specific principles first—because what they need now is a direct calculation model and tool, and they don't need to know how the tool is derived.

Fifteen minutes later.

groups started

final calculation.

soon.

Crackling——

The sound of the abacus and the operation of a few hand-cranked computers sounded again inside the tent.

That's right, hand-cranked computers.

This thing can be regarded as a standard old antique equipment, which is almost extinct in later generations, and has strong and strong characteristics of the times.

how to say

In terms of age, it is somewhat similar to the DVD and PHS of later generations, which are products of a specific period.

Invented in 1878, the hand-operated computer mostly uses a pin-wheel structure. Generally, it can only do four arithmetic operations, such as square number, cube number, square root, and cube root.

If you need to input trigonometric functions and logarithms, you need to look up the table.

Nowadays, the hand-operated computers used in China are all "Flying Fish" brand, one of the few domestically produced mechanical equipment that is better than imported during this period.

The first batch of "Flying Fish" hand-operated computers produced 500 units, most of which were given to the Second Ministry of Machinery and the Fifth Academy, and some were given to the 156 project of that year.

The Fifth Academy used this hand-operated computer to calculate a trajectory from the missile’s take-off points to its shutdown, and it took almost two months in terms of time—this is still a missile without the ability to change orbit.

In addition, the "Flying Fish" hand-cranked computer is much more sophisticated than the one imported from Germany, so it looks petite like a girl.

Therefore, it was also given a nickname by the Second Ministry of Machinery that sounded very uncomfortable to the author:

fish girl.

all in all.

At this point, there is nothing wrong with Xu Yun at all - if we talk about written and mental arithmetic skills, he is probably not as good as many seniors of this era.

So he waited for the result alone, while Qiao Caihong and several sideline team members helped drive away the mosquitoes.

Half an hour passed.

After staying for a while in the morning, Lao Guo, who continued to research the project, got off work and hurried to the site with Cai Shaohui from the research group.

I don't know if it was Xu Yun's illusion.

He always felt that Lao Guo coughed much more frequently than before

after an hour.

A final report was handed over to Ye Duzheng.

However, Ye Duzheng was not in a hurry to report to Lao Guo, but he and Tao Shiyan randomly checked a few links for verification.

After verification is correct.

Just now Ye Duzheng came to Lao Guo with the report.

"Guo Gong, Cheng Gong."

Ye Duzheng first greeted Lao Guo, then glanced at Cheng Kaijia who had been staying beside Lao Guo, and said with a serious expression:

"Fortunately, a new batch of weather forecast results have been released."

"This result has been retested by me and Comrade Tao Shiyan, and there are no mistakes or omissions in mathematics."

Lao Guo's face remained unchanged, but his left hand holding the briefcase still gained some strength.

It can be seen that his heart is not peaceful:

"Director Ye, what did the higher-ups deduce?"

Hearing this, Ye Duzheng took a deep breath, opened the manuscript in his hand, and introduced:

"Guo Gong, Cheng Gong, first of all I want to emphasize one thing."

"That is, our weather data collection started 12 hours ago, but due to efficiency issues, the results were not available until just now."

"That is to say. The result we derived actually includes the weather forecast for the past twelve hours."

Old Guo heard the words and nodded.

This sentence is not difficult to understand.

According to their prior arrangements.

The meteorological Doppler radar collects data every 20 minutes. The data is filtered and sent to the Capital Computer Institute, and then processed by the computer into a parameter field and sent back to the base for further calculation by Ye Duzheng and the others.

So many times, the process lasted for more than ten hours, which is close to half a day.

Although due to the problem of computational efficiency, these data cannot be obtained instantaneously or in a short time.

But this situation does not affect the objective existence of weather forecast results in the past dozen hours-it's just that they have lost their timeliness.

But from a reference point of view.

The weather conditions in the past 12 hours can verify the derivation results to a certain extent.

It's like someone sent a letter guessing the situation in the next six months, and it has been a year since it was delivered to the recipient due to various reasons.

Although this letter loses the meaning of conveying information, it can be used to verify whether the writer's judgment and vision of the current situation are correct.

Think here.

Lao Guo could not help but look at Ye Duzheng, thought for a moment, and asked him:

"Director Ye, what's the report's forecast for the past 12 hours?"

Ye Duzheng turned the file over to him, revealing the contents above, and introduced:

"Guo Gong, look."

"According to the forecast results, there was less Doppler feedback of rain particles in the past 12 hours, so there will be no rain on the entire Jinyintan Grassland."

"However, the vertical sand emission efficiency is higher, the long vertical vector of aerosol presents a regional distribution, and the vertical discriminant variable is very obvious."

"So based on the data fitting, we judge that there may be a northwesterly wind with a small intensity of sand and dust between 11:00 and 13:00 noon."

After listening to Ye Duzheng's introduction quietly, Lao Guo immediately looked at Zhou Cai at the side, and asked him:

"Assistant Zhou, what is the actual situation in the grassland today?"

As the assistant to the factory director of the base, Zhou Cai's weather conditions on that day belonged to the data he had to follow up and summarize every day.

In the current period when data communication has not yet appeared, he got the overall weather situation even earlier than Ye Duzheng and Tao Shiyan.

Hearing Lao Guo's question.

Zhou Cai immediately took out a small notebook, flipped through a few pages, and said quickly:

"In the past 12 hours, there was indeed no rainfall record on the grassland. To be precise, there is no rainfall record in the whole Haiyan County. Instead, there was a light rain in the nearby Huangyuan County, which lasted for about 40 minutes."

"As for the dust. Oh, there is indeed a record of dust, which was reported by comrades from the animal husbandry sideline team."

"The starting point of the sand and dust is near the No. 6 branch factory. The time is around 1:30 in the afternoon. The direction...is indeed northwest wind."

I heard this.

The atmosphere at the scene suddenly became a little subtle.

It didn't rain, and there was dust again

Forecast for the previous 12 hours

Is it right?

After a while.

Cheng Kaijia, who had been silent all this time, spoke, his face still kept a very restrained calm:

"The information is all right, but a few comrades, I think there is a certain chance of this situation, at least these results alone can't explain too many things."

"Firstly, it is not uncommon for the grassland to not rain for half a day. Secondly, if I remember correctly, the sand and dust on Jinyintan Beach in this season should basically be northwest wind."

"So to determine whether the results of the deduction are accurate, I think a new round of evaluation will continue."

I heard this.

Several people at the scene nodded in agreement.

Students who have studied geography should know it.

In summer.

When the southwest monsoon reaches the Bay of Bengal and then advances northward, it hits the Qinghai-Tibet Plateau and is divided into two branches: east and west:

One turned easterly along the Himalayas and blew westward.

The other branch flows along the direction of the mountains to the southwestern region of my country, intensifying the effect of water vapor channels, increasing precipitation at the edge of the plateau, and intensifying the drought inside the plateau due to the effect of rain shadow.

So in the place of Xihai.

The northwest wind accounts for more than 80% in winter and summer, and the southeast wind appears only occasionally.

Therefore, the description of the absence of rain for half a day and the small-scale Northwest dust does not really prove much.

If you want to prove that the derivation result is accurate enough, you have to go through a bigger test.

Think here.

Lao Guo looked at Ye Duzheng again, and asked him:

"Director Ye, how does the derivation result predict the next weather? — For example, is there any forecast for rainy weather?"

"It's raining"

When Ye Duzheng heard this, a subtle expression appeared on his face:

"Of course there is, and the time is very close to now."

Lao Guo's heart trembled, and he asked:

"Oh? When?"

clatter——

Ye Duzheng turned another page of the report, looked at the results and said to Lao Guo:

"In three hours, between 11:00 p.m. and 1:00 a.m., there should be a half-hour protest"

"Thunderstorm."

Note:

Yesterday, in order to change the biological clock, I woke up very late at night and coded all night, so I updated it in the early morning.

As I said before, this kind of situation will be very common when the update is released, and the amount will not be small, but the time may not be fixed, so please don’t rush, if I really don’t update that day, I will ask for leave in advance.