The books once interested me

coolboy

The addition and subtraction of two vectors are straightforward and easy to understand. However, when it gets to product and division, it gets more complicated. It turns out that there is no division in vector operation and there are two different kinds of product operation: inner product and exterior product. One time when I was in college, I read a book in library that briefly introduced the exterior product along with the concept of differential forms, indicating that the differential form was a higher level of calculus that was more beautiful. Later, I came across the following book that contained not only“Differential Forms” but also the other two interesting topics and, thus, I bought the book right away:

Lovelock D., and H. Rund, 1989: Tensors, Differential Forms, and Variational Principles. Dover Pub., Inc., New York, 366 pp.

coolboy

The topic of “variational principles” is not only interesting but also considered to be beautiful. The beauty of variational principles/method is often described in the field of classic mechanics where the Newton’s second law of motion can also be alternatively described by the so-called “principle of least action”. The beauty of such an alternative expression is as follows: the Newton’s second law of motion is an experimental law. It is not supposed to be derivable from something other than many experimental data. On the other hand,  the “principle of least action” says that this law also has some physical rationale behind it! The similar idea has also been applied to many other fields such as the quantum mechanics. In fluid mechanics, I first learnt the beauty or the power of variational method in the following book:

Morel, P. (Editor), 1973: Dynamic Meteorology. D. Reidel Publishing Company, Boston, 622 pp.

The book contained a set of lecture notes delivered by then six world renowned atmospheric dynamists. One of those was by J. G. Charney:

Charney, J. G., 1973: Planetary Fluid Dynamics. In: “Dynamic Meteorology,” P. Morel (Ed.), pp. 97-352. D. Reidel Publishing Company, Boston.

in which the author derived stability/instability criterions for a circular vortex by the variational method.

coolboy

In Charney’s lecture notes, he cited an important work by T.D.Lee (李政道) in fluid mechanics. I suspected most people overlooked or forgot Lee’s this work long time ago so I mentioned it specifically in sciencenet once the opportunity appeared:

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coolboy [2009-7-20]:

武际可老师介绍了几位大物理学家的力学贡献。[Ref. 1] 我再来补充一下。

海森堡（W.Heisenberg）和李政道（T.D.Lee）在流体力学湍流理论中也有贡献。其中李政道关于二维湍流中能量不能无限制地从大尺度向小尺度传递的推断是原创性很大的贡献。

湍流中最有名的Kolmogorov理论的核心就认为湍流运动的实质是流体运动能量不断地从大尺度向小尺度传递，直至分子尺度的热耗散为止。包括海森堡和李政道等的很多很多人对能量具体如何传递的细节（能谱方程）的描述都有贡献。但李政道在后来的一篇论文中说，哈！搞了半天这二维湍流中的能量其实还并不是从大尺度向小尺度传递的呢！！所以我认为这一贡献是原创性很大的贡献。

Reference:
[1] 几位大物理学家的力学贡献 [武际可]
http://blog.sciencenet.cn/blog-39472-244419.html
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coolboy

Variational method was fully utilized in the following monograph to study fluid stability problems, especially the global stability based on fluid total energy:

Joseph, D. D., 1976: Stability of Fluid Motions. I. Springer-Verlag, New York, 282.
Joseph, D. D., 1976: Stability of Fluid Motions. II. Springer-Verlag, New York, 274.

I found the following descriptions on uniqueness by the author especially inspiring:

Solutions of the Navier-Stokes problem (1.1) have two fundamental properties of uniqueness:
(1) There is only one solution of (1.1) which starts from an assigned initial field;
(2) When [nu] is large all solutions of (1.1) tend to a single basic flow.
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What is the final destiny of all these uniquely determined solutions of the Navier-Stokes equations? For small values of the viscosity the final set of flows which evolve from a given set of initial fields is generally “turbulent”, and the resulting flows can perhaps be usually characterized only in a statistical sense. But when [nu]>[nu]_e, the energy stability theorem guarantees that all solution tend to a single limiting solution which is uniquely determined by the data {U_S(x,t),F(x,t),V(t)} after the effect of initial conditions has disappeared.

{U_S(x,t),F(x,t),V(t)} = {boundary condition, external force, total fluid volume}

coolboy

Talking about T.D.Lee (李政道), I have one book authored by him on my bookshelves:

Lee, T. D.(李政道), 1981: Particle Physics and Introduction to Field Theory. 粒子物理和场论简引. Harwood Academic Pub., New York, 865 pp.

One reason that the book interested me was that there was also a Chinese title printed on the cover in parallel with its English title. Near the end of the book, the author also showed a Chinese idiom describing the nature of the physical laws:

道可道，非常道。名可名，非常名。
The principle that can be stated
Cannot be the absolute principle.
The name that can be given
Cannot be the permanent name.
* Laotse, Dao De Jing (~550 B.C.)

I recalled one interesting experience on attending a public lecture by Lee about particle physics in early 1980s. In the beginning of that lecture, he wrote five Chinese characters 水、木、金、土、火 on the blackboard in circular positions and also slowly read them in both Chinese and English, saying that ancient Chinese developed 五行 theory to study the fundamental particles. Therefore, the particle physics is a fundamental science problem that human being has been constantly seeking the answers.

At the end of that lecture, there was a question-and-answer session. There was one person from the audience who looked like a graduate student from physics department asking a very long question. It appeared that he wrote the long question on a piece of paper and read the long question from the audience. The question appeared to be general but full of technical details, asking exactly how some particles were interacted with each other, etc. Since it was a public lecture in a big hall with a large audience, Lee gave the following brief answer: You need to take a particle physics course to get the answers to these questions; if University of ***** dose not offer a good course, you are welcome to come to Columbia University. The audience smiled or laughed after his answer.

coolboy

T. D. Lee (李政道) belongs to a category of the so-called celebrity scientists. Many lectures given by celebrity scientists are often not on discussing or solving specific science problems but on some general science or research principles described by specific or personal stories. I once described another example of this kind of lectures given by Chang-Lin Tien (田长霖) in early 1990s to students majoring in civil engineering:

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Coolboy wrote and submitted his first paper
http://bbs.lasg.ac.cn/bbs/thread-35262-2-5.html
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In addition to learning how the four-stroke engine worked, we also learnt how iron was processed into steel in middle school. That included the knowledge of various types of furnaces to make the steel and also some basic knowledge of how different kinds of little amount of metals mixed with iron to form different types of steel. The reason I mention this now is that it relates to another interesting story of how later professor Chang-Lin Tien made 1,000 US dollars in one day. 1,000 US dollars do not worth much in these days but it worthed a lot in 1960s when the story happened. As a result, Chang-Lin Tien was very proud of himself while telling this story. One of Chang-Lin Tien’s friends was a manager in a steel company and, one day, he invited Chang-Lin Tien to pay a visit to the company because he heard people saying that this professor was a smart scientist. Chang-Lin Tien’s friend would pay him 1,000 US dollars if professor Tien was able to visit and stay in the factory for one day, to be accompanied by factory technicians and look around the factory, and possibly to make some suggestions at the end of the visit. After receiving the check for 1,000 US dollars, Chang-Lin Tien made the following two suggestions to save energy that were all adopted later by the factory:

(1) To replace the existing wires/cables with thicker ones [that would reduce the heat dissipation of those wires];
(2) To install iron meshes in the furnace chimneys [to raise the furnace temperature].

He did not mention the reasons for his suggestions and I added those in the above brackets. The first suggestion indicates that those were electric furnaces and thicker wires would reduce the electric resistance of those wires when the electric power was supplied to the furnaces. I got this figured out long after his speech because my thought kept dwelling on his second suggestion at the time. I said to him: your idea of iron meshes in chimneys was the atmospheric greenhouse effect, right? He said to me: you are exactly right!

Here was my thought: processing iron into steel requires high furnace temperature to let impurities within iron to be exhausted and evaporated, AND we also need chimneys to allow the hot air with impurities to escape from the furnace. At the same time, a lot of heat is also escaped from those chimneys through two processes: (i) convection and (ii) radiation. The installed iron meshes still allow the hot air with impurities to pass but will absorb the higher radiance from the furnace, re-emit part of the absorbed energy back to the furnace, and thus raise the furnace temperature, which is exactly the same as CO2 in the atmosphere raising the surface temperature.

Chang-Lin Tien (田长霖), who also specialized in radiation, was known to many Chinese scientists:
http://www.berkeley.edu/news/media/releases/2002/10/tien.html

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coolboy

I also remembered a few other things in that lecture. Tien said that in his final PhD defense presentation there was one professor in committee who was notorious to ask students hard questions. He asked Tien three questions: (i) What is non-local thermodynamic equilibrium? (ii) What is ......? (iii) What is ......? The first question was the only one I caught from his lecture and still remember it now. To each and every question, Tien’s answers were honest and all the same: “I don’t know.” The professor said to Tien: I will let you pass your defense though you do not know the answers to these questions. However, these are all important questions and you need to remember these questions even if you do not know the answers to these questions now.

Later, when Chang-Lin Tien became a professor, he would always first propose a very hard problem to his new graduate student and let him/her think for three months to see whether the student would be able to come up some strange ideas to solve the hard problem. Often and always, the student would come back after a few weeks and ask for an easier problem. Professor Tien then will ask the student to remember the hard problem and give an easier and solvable problem to student to work on it.

coolboy

I introduced two books on wave dynamics in the following post while describing the physical significance/meanings of characteristics of first-order partial differential equations:

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[讨论]伯努利方程是能量方程还是动量方程？[301楼]
http://www.cfluid.com/thread-114265-21-1.html

......推荐一下流体波动两本比较好的经典参考书：

Lighthill, M. J., 1978: Waves in Fluids. Cambridge University Press, London and New York, 504 pp.
Whitham, G. B., 1974: Linear and Nonlinear Waves. Wiley (Interscience), New York, 636 pp.

Whitham的书对可压缩流体的介绍要更详细一点。
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G. B. Whitham was also well known for his important contributions to applying the variational method to dispersive and nonlinear waves. Naturally, in the above monograph, he also systematically introduced the variational approach to study dispersive and nonlinear waves.

coolboy

I recently bought the following two books and they arrived at my office around the same time last week:

Buhler O., 2014: Waves and Mean Flows. Second Edition. Cambridge Univ. Press, Cambridge, 360 pp.

Rino, C. L., 2011: The Theory of Scintillation with Applications in Remote Sensing. Wiley & Sons, Inc., Pub., 230 pp.

Although the theory of “scintillation” often belongs to the field of electric engineering, it is closely related to the fluid mechanics through turbulence. I highly recommended the monograph by Monin and Yaglom on turbulence several times on this forum, for example:
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为什么非定常湍流流场也可以采用时间平均法或非均匀流场 [28楼]
http://www.cfluid.com/thread-118732-2-3.html

关于湍流经典（而非近代CFD湍流）理论的世界名著应该是：

Monin, A. S. and A. M. Yaglom, 1971: Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 1. MIT Press, Cambridge, Massachusetts, 769 pp.

Monin, A. S. and A. M. Yaglom, 1975: Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 2. MIT Press, Cambridge, Massachusetts, 874 pp.

我在下一帖子的[15楼]也提到了这一专著，转载如下：
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[讨论]量子力学和流体力学有多大联系？
http://www.cfluid.com/thread-45337-1-5.html

下一本书的最后一章(Chapter 10)讨论到了这个问题：Monin, A. S. and A. M. Yaglom, 1975: Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 2. MIT Press, Cambridge, Massachusetts, 874 pp.

湍流就是不完全确定的流动，故我们要用概率或随机过程来描述研究它。我们不可能、不必要获得随机过程概率的分布函数这一终极（完整）解。我们通过研究各随机物理量（或分量）之间的相关函数（二阶、三阶矩）来了解研究湍流。引入了平稳均匀等假定之后，那些相关函数的计算及和实验比较就变得非常非常简单（如许多分量是零，仅仅是距离的函数而与位置无关等）。当然，对于简化了的相关函数（或含有相关函数的方程）再进行傅立叶变换也会变得简单些。

若知道了某一随机过程的分布函数，则也就知道了该随机过程的所有特性。此外，若知道了某一随机过程的特征函数，则也就知道了它的分布函数(这是因为特征函数是分布密度函数的傅立叶变换)。在一定条件下，这描述湍流随机过程的特征函数的方程刚好与量子力学中的薛定谔方程(表示)相类似。
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Monin和Yaglom的专著是由John L. Lumley组织从俄文翻译编辑成英文的。Lumley则又是下一本非常热门的关于湍流基础理论及应用的教科书的作者之一：

Tennekes, H. and J. L. Lumley, 1972: A First Course in Turbulence. The MIT Press, Cambridge, Massachusetts, 300 pp.

这本书中的雷诺方程是在经典的时间平均下推出来的。也正是因为如此，这本书从头至尾所讲的也都是定态湍流问题，时间导数项就一直（几乎）没出现过。
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I mentioned above that Chapter 10 of Monin and Yaglom’s monograph showed certain connection between turbulence and quantum mechanics. Furthermore, Chpater 9 of the book has the following title: “Wave Propagation Through Turbulence”. This chapter introduced the basic theory of scintillation.

周华

今天刚好在读JLL和Yaglom写的A Century of Turbulence，这两人全景式地回顾了湍流在20世纪的发展，对湍流研究感兴趣的朋友可以阅读一下。

coolboy

周华 发表于 2015-3-2 13:17
今天刚好在读JLL和Yaglom写的A Century of Turbulence，这两人全景式地回顾了湍流在20世纪的发展，对湍流研 ...

Thank 周华 for the introduction. It was an interesting review article. The complete reference of the paper is:

Lumley, J. L., and A. M. Yaglom, 2001: A century of turbulence. Flow, Turbulence and Combustion, 66, 241–286.

It is interesting to note that Chou, Pei-Yuan’s (周培源) work on turbulence remained to be referenced in this review article and, furthermore, it was placed at a historical position similar to those by Boussinesq, Taylor, Prandtl and von Karman.

周华

coolboy 发表于 2015-3-3 10:24
Thank 周华 for the introduction. It was an interesting review article. The complete reference of t ...

是的，这篇文章保留了周培源作为湍流模式理论开创者的地位，其它文献中一般讲到这里就直接讲K41理论了。

coolboy

周华 发表于 2015-3-3 14:23
是的，这篇文章保留了周培源作为湍流模式理论开创者的地位，其它文献中一般讲到这里就直接讲K41理论了。
...

What is “湍流模式理论”? It should be a theory that is able to solve the notorious closure problem of turbulence. In Monin and Yaglom’s monograph, Chou, Pei-Yuan’s (周培源) works were referenced in the following contexts:

In Volume 1, the authors wrote: Following Kolmogorov, Nevzglyado (1945a, b, etc) proposed a number of different hypotheses for the closure of the system of equations (6.5) and (6.8). Similar investigations were carried out in the 1940’s by Chou (1945a, b, 1947). Chou, in particular, was the first to attempt to use, in addition to Eqs. (6.5) and (6.8), the equations of the third-order moments [u’_i*u’_j*u’_k]; the fourth-order moments [u’_i*u’_j*u’_k*u’_l] which then arise are eliminated with the aid of the hypothesis about the vanishing of the fourth-order velocity cumulants, or some related hypothesis.


In Volume 2, the authors wrote: We note that, just before Millionshchikov’s work, Chou Pei Yuan (1940) suggested that the fourth-order velocity moment could be approximated with good accuracy by the sum of four terms of products of second order velocity moments as shown in Eq. (18.1).


Reference:

Chou, P.-Y., 1940: On an extension of Reynolds’ method of finding apparent stress and the nature of turbulence. Chinese J. Phys. 4, 1–33.

coolboy

By the way, I believe many Chinese academicians (院士) who were supposed to be experts in turbulence never read or seriously read Monin and Yaglom’s monograph. The Russian edition of the monograph was published in 1965. Volume 1 and Volume 2 of the English edition were published in 1971 and 1975, respectively. That period corresponded to the vacuum or the chaos period of Chinese culture and science due to the Great Culture Revolution. After the end of the chaos period, scientists who started investigating turbulence most likely focused on many other thinner books on turbulence in order to obtain quick knowledge and results.

coolboy

In addition to the above mentioned monograph on turbulence, the following book by Monin also has certian historical significance on the academic research and style of the former Soviet Union:

Monin, A. S., 1990: Theoretical Geophysical Fluid Dynamics. Kluwer Academic Publishers, Boston, 399 pp.

The book was highly condensed and very difficult to read and understand though the author said in the preface that the book grew out of the lecture notes delivered to the students at the Moscow Institute of Physics and Technology. This is probably the most difficult book in the field of geophysical fluid mechanics. The very unique feature of the book is that it contains Hamiltonian formalisms for three types of fundamental waves in the geophysical fluid: surface gravity waves, internal gravity waves, and Rossby waves. The hardest part of studying wave-wave interactions by Hamiltonian formalism is to find the canonical variables of the fluid motions described by partial differential equations. The first and the most famous one was the Zakharov equations for surface gravity waves. The extension to other types of waves was NOT straightforward at all. For example, the extension to internal gravity waves requires the so-called Clebsch’s transformation buried in Lamb’s old monograph of “Hydrodynamics”. However, V.E. Zakharov and scientists (especially the plasma physicists, Rossby waves were also called drift waves in plasma physics) in the former Soviet Union were absolutely dominant in this field.

Apparently, the Russian edition of the book did not have a reference section. The translator filled in some references but he clearly was not aware of any work on Hamiltonian formalisms of wave dynamics for there was not a single reference on the subject.