The books once interested me

coolboy

Variational method generally leads to sufficient conditions for stability or necessary conditions for instability. This might be part of the reason that variational method was not as popular as the alternative eigenvalue analysis to investigate the linear instability in fluid mechanics for the latter generally leads to both the necessary and sufficient conditions for instability. Another interesting and significant progress after Fjortoft's 1950 paper was the one by V. I. Arnold:
Arnold, V. I., 1965: Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid. Doklady Mat. Nauk., 162, 773-777.

Arnold was already a famous mathematician at the time so his 1965 paper was immediately well received in the science community. Arnold's (1965) approach was mathematically more general and formal in terms of functional variation whereas Fjortoft approach appeared being rooted in the traditional stability analysis based on parcel displacement. More importantly, Arnold claimed that his method dealt with “nonlinear stability” or stability of flow “with respect to finite perturbations”.

After carefully reading and digesting Arnold's paper (1965), several serious researchers understood that Arnold's (1965) variational method only led to the same conclusion of a linear stability (with respect to infinitesimal perturbations) as the one by Fjortoft (1950). Some of the researchers tried (but was still considered to fail) to extend Arnold's conclusion into a nonlinear one by introducing “mean value theorem” in the derivations. In early 1980s, there was a well-known fluid mechanist, calling him “Professor X”, who thought he found a way to truly extend Arnold's linear stability criterion into a nonlinear one. While preparing his draft, he was told that Arnold derived nonlinear stability criterion already. He checked a few other papers by Arnold and still could not convince himself that Arnold solved the problem already. However, there was yet another short paper by Arnold that was not easy to find in most libraries:
Arnold, V. I., 1966: On an a priori estimate in the theory of hydrodynamical stability. Izv. Vyssh. Uchebn. Zaved. Matematika, 54, no. 5, 3-5. (English Transl: Am. Math. Soc. Transl., 79 (1969), 267-269.)

Note that the above paper not only was short (3 pages) but also was translated into English three years after its publication in Russian. That was mostly because the journal was not well known to Western science community at the time. “Professor X” finally got this 3-page paper and discovered the most important contributions made by V. I. Arnold to the field of fluid mechanics. “Professor X” made significant contributions to the science community in popularizing Arnold's nonlinear stability theorems. The contents of Arnold's (1966) paper were also included in his 1978 textbook (Russian edition published in 1974):

Arnold, V. I., 1978: Mathematical Methods of Classical Mechanics. Springer-Verlag, New York, 462 pp.

coolboy

The following three books happened to be on my desk not long time ago when I made serious recommendations to someone about good reading materials on gasdynamics, especially on its numerical modeling:

Chapman, C. J., 2000, High Speed Flow. Cambridge Univ. Press, Cambridge, 258 pp.
Laney, C. B., 1998: Computational Gasdynamics. Cambridge Univ. Press, Cambridge, 613 pp.
LeVeque, R. J., 1992: Numerical Methods for Conservation Laws. Second Edition. Birkhauser Verlag, Berlin, 214 pp.

coolboy

I believe the oldest and a classic monograph on the high speed flow was the one by Courant and Friedrichs:

Courant, R., and K. O. Friedrichs, 1948: Supersonic Flow and Shock Waves. Interscience Publishers, Inc., New York, 464 pp.

Naturally, many terminologies introduced in the book were also adopted later in the fields. One important concept in high speed flow or hyperbolic partial differential equations in general is ‘characteristic curves’. In Courant and Friedrichs (1948), it was introduced as “... two separate ordinary differential equations of the first order which define two one-parametric families of ‘characteristic curves’ or simply ‘characteristics’, C+ and C- in the (x,y)-plane, belong to the solution u(x,y),v(x,y).” The simplified version of ‘characteristics’ for the meaning of ‘characteristic curves’ was frequently used in the later part of the book.

However, later, in a classic book on partial differential equations (by the same lead author), the authors only used its formal version of 'characteristic curves' and the simplified version was hardly used:

Courant, R., and D. Hilbert, 1962: Methods of Mathematical Physics. Vol. 2. Wiley-Interscience, New York, 831 pp.

The term ‘characteristic curves’ was translated into Chinese as ‘特征线’. When I was a student in China many years ago, I recalled that ‘特征线’ was the only term used in professors’ lectures and in all the Chinese professional literature. However, when I attended the classes in USA later, I noted that professors mostly only used its simplified version of ‘characteristics’ in lectures. Gradually, some of the English textbooks replaced the formal term of ‘characteristic curves’ by its simplified version of ‘characteristics’. For example, in the following textbook, the term ‘characteristic curves’ seems never appeared:

Chorin, A. J., and J. E. Marsden, 1992: A Mathematical Introduction to Fluid Mechanics. Third Edition. Spring-Verlag, New York, 169 pp.

A related question is: should we also (与时俱进地) replace the Chinese term ‘特征线’ by its simplified English version of ‘特征’? I think we should not do so. The Chinese term ‘特征’ does not simplify much in its writing but cause great confusion in its mathematical meaning. In other words, a correct translation of ‘characteristics’ into Chinese should be ‘特征线’ when the mathematical meaning of ‘characteristics’ is actually ‘characteristic curves’, which, of course, can only be done by professionals.

coolboy

On this forum, I once introduced the concept or the term ‘特征线’:
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[讨论]伯努利方程是能量方程还是动量方程？ [6#]
http://www.cfluid.com/thread-114265-1-1.html

“...这三个方程的左端项刚好对应于流体速度场的三个分量。流体块在沿着由此速度场确定的轨迹流动时，其所对应的（原偏微分方程中的）u是一个常数。此流体轨迹在数学上也称为'特征线’，在伯努利方程推导中常称“沿流线积分”就是“沿特征线积分”。所谓“沿流线积分”其实也就是求解上述的5个常微分方程组。”
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Here, the term ‘特征线’ happens to match the term ‘流线’, which makes the above description quite natural and easy to understand. On the other hand, if we adopted a simplified term ‘特征’, we would have an uneasy description:
“...这三个方程的左端项刚好对应于流体速度场的三个分量。流体块在沿着由此速度场确定的轨迹流动时，其所对应的（原偏微分方程中的）u是一个常数。此流体轨迹在数学上也称为'特征’，在伯努利方程推导中常称“沿流线积分”就是“沿特征积分”。所谓“沿流线积分”其实也就是求解上述的5个常微分方程组。”

coolboy

Various analytic or asymptotic methods for solving wave equations are introduced in the following book:

Bleistein, N., 1984: Mathematical Methods for Wave Phenomena. Academic Press, New York, 341 pp.

coolboy

The following two books bridge the common gaps between basic knowledge of physics a good physicist generally possesses and a special background of atmospheric radiative transfer a good atmospheric physicist will acquire in many years of his/her training:

McCartney, E. J., 1976: Optics of the Atmosphere. Scattering by Molecules and Particles. John Wiley & Sons, New York, 408 pp.
McCartney, E. J., 1983: Absorption and Emission by Atmospheric Gases: The Physical Processes. John Wiley & Sons, New York, 320 pp.

coolboy

Two classic books on light scattering processes on my bookshelves are

van de Hulst, H. C., 1957: Light Scattering by Small Particles. John Wiley & Sons, Inc., New York, 470 pp, (Reprinted by Dover).
Bohren, C. F. and D. R. Huffman, 1983: Absorption and Scattering of Light by Small Particles. John Wiley & Sons, Inc., 530 pp.

The style of the book by van de Hulst was more like a review or summary to the field at the time though the book also contained introductory materials. On the other hand, the book by Bohren and Huffman was in a textbook style for which natural procedures of solving Maxwell equations to clearly defined problems were comprehensively presented.

coolboy

Bohren and Huffman’s 1983 textbook on absorption and scattering is well known to the field of atmospheric physics for its clarity and broad coverage. I think the book is even better known to a larger field of material science though the lead author is a meteorologist or an atmospheric physicist. The lead author C. F. Bohren is probably best known as an atmospheric physicist due to his following two books on popular science:

Bohren, C. F., 1987: Clouds in a Glass of Beer: Simple Experiments in Atmospheric Physics. John Wiley & Sons, Inc., New York, 195 pp.
Bohren, C. F., 1991: What Light Through Yonder Window Breaks? More Experiments in Atmospheric Physics. John Wiley & Sons, Inc., New York, 190 pp.

I myself first bought his 1987 book right after its publication and bought the 1983 book much later while exploring the field in great details.

coolboy

Given the micro radiation parameters of a medium such as scattering cross sections of individual particles as derived, for example, from the scattering theory described in van de Hulst (1957), the macro radiation fields can be derived by solving the radiative transfer equation. When the scattering processes are emphasized, the best reference that provided a complete and comprehensive coverage of various methods in astrophysics and atmospheric sciences was

van de Hulst, H. C., 1980: Multiple Light Scattering: Tables, Formulas and Applications, Volumes I and II. Academic Press, New York, 739 pp.


A classic book in this field before the computer age was:

Chandrasekhar, S., 1950: Radiative Transfer. Oxford Univ. Press, 393 pp. (Reprinted by Dover.)

coolboy

S. Chandrasekhar was a Nobel Prize laureate in physics who wrote many monographs in different fields. His following monograph was known to many people in the field of fluid mechanics:

Chandrasekhar, S., 1961: Hydrodynamic and Hydro_m_a_g_n_e_t_i_c Stability. Oxford Univ. Press, 652 pp. (Reprinted by Dover.)

The third book by S. Chandrasekhar on my bookshelves was a collection of his seven public lectures:

Chandrasekhar, S., 1987: Truth and Beauty – Aesthetics and Motivations in Science. The University of Chicago Press, Chicago and London, 170 pp.

coolboy

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NASA将向太阳发射探测器  (2017-6-1)
http://www.cfluid.com/article-28107-1.html

据英国《每日邮报》报道，NASA近日在芝加哥大学举行的一次电视直播节目中宣布将于2018年夏季向太阳发射一颗探测器，用于探测太阳外层大气的气象活动。这颗探测器原名“太阳探测器加（SPP, Solar Probe Plus）”，后来决定更名为“帕克太阳探测器（PSP，Parker Solar Probe）”，用于表彰芝加哥大学的帕克教授（Prof. Parker）在1958年首次提出太阳风概念。NASA还在直播中将一个PSP探测器模型赠送给帕克教授作为纪念。
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The above news report mentioned a name (帕克), E. N. Parker, who was somewhat related to S. Chandrasekhar mentioned in the previous two posts through the following interesting street story or anecdote.

It was said that E. N. Parker submitted his paper on solar wind to “Astrophysical Journal” but the paper was strongly criticized and rejected by the reviewers who were not only experts but also well established in the field at the time. Parker's explanation to the solar wind was based on fluid mechanics and was essentially based on the simple Bernoulli equation. The following monograph also described Parker's theory:

Parker, E. N., 1963: Interplanetary Dynamical Processes. Interscience Publishers, New York, 272 pp.

Bernoulli equation has also been discussed in the following post on this forum:
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[讨论]伯努利方程是能量方程还是动量方程？
http://www.cfluid.com/thread-114265-1-1.html
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The criticisms essentially said that Parker's assumption of considering the interplanetary gases as continuum or fluid was too naive and incorrect. Learning his paper being rejected, Parker directly went to Chandrasekhar's office, explained his theory face-to-face to Chandrasekhar who was an editor of “Astrophysical Journal”, and complained being suppressed by well-established peers in the field. At the time, Chandrasekhar sympathized with Parker's experience because Chandrasekhar himself once was also strongly criticized and ridiculed by a well-established peer (Arthur Eddington) when he was young. As a result, Chandrasekhar (as an editor) made a personal/final decision to accept the publication of Parker's paper right in his office. Parker and his theory on solar wind also became famous and were gradually accepted by more and more people in the field.

I was never able to find out for sure who might be the reviewers who rejected and ridiculed Parker's 1958 paper. However, based on the science background, the research styles and the works they did around the time, I suspected J. W. Chamberlain and S. Chapman could be potential candidates to the event I described above. I have following books by these two authors:

Chamberlain, J. W., 1961: Physics of the Aurora and Airglow. Academic Press, New York, 704 pp.
Chamberlain, J. W., 1978: Theory of Planetary Atmospheres: An Introduction to Their Physics and Chemistry. Academic Press, 330 pp.
Chamberlain, J. W., and D. M. Hunten, 1987: Theory of Planetary Atmospheres: An Introduction to Their Physics and Chemistry. Second Edition. Academic Press, 481 pp.
Chapman, S., and T. G. Cowling, 1970: The Mathematical Theory of Non-uniform Gases. Third Edition. Cambridge University Press, Cambridge, 422 pp.
Chapman, S., and R. S. Lindzen, 1970: Atmospheric Tides. D. Reidel Publ., Dordrecht, Holland, 200 pp.

coolboy

It appeared that S. Chandrasekhar had a good scientific judgement while inserted his personal influence on a science issue not so closely related to his home field. However, this is not always the case. There were also some smart and famous scientists making stupid mistakes or reinventing wheels in the fields other than the ones of their expertise. I once mentioned an example showing that a Nobel Prize recipient published scientifically wrong and ridiculous papers in the field who knew little, mainly because he was an editor of the journal:

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庆承瑞：全球变暖与反变暖之争和病态科学 [102楼]
http://www.cfluid.com/thread-84936-7-1.html
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Coolboy:
上世纪三十年代及六十年代初，就有知名学者根据温室效应模式及金星大气主要成分是二氧化碳而预测金星表面的温度会很高，预测会有600K。六十年代初又根据金星微波辐射的观测而证实金星表面的高温。六十年代中后期美苏两国又通过宇宙飞船开始对金星大气及地面进行实地观测。但就在晚至1968年，也还有不承认或不懂温室效应的一些科学家（也可称非主流科学家）在《Science》上互发论文争辩这金星地表的极地冰盖到底是只延伸到高纬的60度呢还是一直延伸到中纬的45度？可笑吧？
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通流:
《Science》还让这些争论发表，是不是那杂志也很可笑？
我们国家还还以那个杂志作为科研水平高低的一个尺度，是不是更？
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今天有点时间就简单地给出一个谜底吧！
就这个例子，我认为荒唐、可笑的论文能在高质量杂志上发表的（主要）原因（之一）是由于对大气物理这一领域而言是“非主流科学家”的作者其实是一位获得过诺贝尔奖的知名（化学）科学家，当时也还是《Science》杂志的主编或副主编。
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The person mentioned in the story was Willard F. Libby who was awarded the Nobel Prize in Chemistry in 1960. The relevant papers on Venus ice caps versus ice sheets were:

Libby, W. F., 1968: Ice caps on Venus? Science, 159, 1097-1098.
Libby, W. F., 1968: Venus: Ice sheets. Science, 160, 1474.

coolboy

先插一个趣闻，也算是为下一个故事做一个铺垫。

上面帖子提到 S. Chandrasekhar 认为 Arthur Eddington 打压、嘲笑自己，并为此一段时间内耿耿于怀。Eddington是谁呢？他是公认的天体物理学当时的权威、创始人。他对爱因斯坦广义相对论的验证和及时推广起到了尤其重要的作用。这种人自然也会比较自信、甚至自负。那么 Eddington 自己又最佩服谁呢？ Eddington 最佩服的是曾经在大学时教过他课的一个老师。那人就是 Horace Lamb。他是当时著名的流体力学家。在此论坛及这个帖子中多次提到他的下一本经典书：

Lamb, H., 1932: Hydrodynamics, 6th edition. Dover, New York, NY, 738 pp.

大家知道学术界流传一个关于兔子、狼虎、狮子的寓言。说是兔子写了一篇不怎么样的论文就敢挑战狼虎之辈，并把它们都给灭了。原因就是在兔子的背后其实还有着一只狮子给兔子撑腰。当 Eddington 成名之后人们也认为他是学术界的狮子的时候，他曾说过这样的话：“While I know what it is to be treated something like a lion, I would rather like to become something of a Lamb.”。句子中的 Lamb 是双关语，其实是指 Horace Lamb.

coolboy

Another more interesting example of a famous scientist working in the fields other than his expertise was Luis W. Alvarez. Luis W. Alvarez was awarded the Nobel Prize in Physics in 1968. However, he was better known or was more famous, especially to the general public, in the field of paleontology (古生物学). In 1980, Alvarez hypothesized that an asteroid approximately 10 km in size struck the earth some 65 million years ago, creating a huge explosion, lofting a cloud of debris and dust into the atmosphere, and severely blocking sunlight that suppressed photosynthesis and drastically lowered the global surface temperature. As a result, dinosaurs and many other species became extinct. Alvarez's hypothesis or theory created a shock in the field of paleontology because, if it were correct, it would have solved the biggest puzzle in paleontology. At the time, paleontology was considered to be a well-established science field with a sound theoretical foundation of Darwin's theory of evolution. There existed many different hypotheses and a few well established theories that solved the biggest problem of dinosaur extinction within the field of paleontology. On the other hand, Alvarez was considered as an outsider. At the time, it was really unthinkable that an outsider suddenly came to the field and gave the solution to a long-standing difficult problem in the field of paleontology. As a result, Alvarez immediately received many criticisms from other paleontologists. However, it turned out that Alvarez's hypothesis can explain all the major aspects of the dinosaur extinction. Most importantly, the theory contains a predictive clue of an anomalously rich iridium layer in the earth's crust that can be tested and verified. Alvarez's theory of explaining the extinction of dinosaurs 65 million years ago after more than 100 million years of domination on the earth is now well accepted by the science community.

Since we have discussed the topic of global warming extensively on this forum, let me also mention here one old hypothesis (before Alvarez's hypothesis) on the extinction of dinosaurs that was related to the global warming. Geological evidence indicated that the earth's surface temperature rose significantly toward the end of the Cretaceous period (白垩纪). It was also known in biological studies that mammals' testicle (睾丸) functioned normally only in a narrow range of temperature. Because of a large ratio of body weight to body surface of the dinosaurs, which makes the dissipation of body heat extremely slow, a worldwide rise in temperature at the end of the Cretaceous period (about 65 million years ago) caused the testicle of dinosaurs to stop functioning and led to their extinction by sterilization of male dinosaurs. The major difficulty or the key logical hole of this hypothesis was that it failed to explain the extinction and the patterns of the extinction of many other species across a wide range of habitats, from terrestrial to marine, which happened simultaneously with the dinosaur extinction. There was no such difficulty in Alvarez's theory.

Below was the paper that proposed the catastrophic hypothesis of the dinosaur extinction:

Alvarez, L. W., Alvarez, W., F. Asaro, and H. V. Michel, 1980: Extraterrestrial cause for the Cretaceous-Tertiary Extinction. Science, 208, 1095-1108.

The second author Walter Alvarez, a geologist, was the son of Luis Alvarez. Hence, this work was also considered a good example of father-son team work in science community.

Alvarez's theory on dinosaur extinction also had a significant impact on the field of atmospheric sciences. Since 1950s, various environmental effects on weather and climate changes following nuclear explosions, including the one caused by a significant reduction of solar radiation due to the debris clouds from the explosions, were investigated by the atmospheric science community. Alvarez's work injected new insights into the field, reinvigorated the research by focusing on a full nuclear exchange corresponding to an all-out atomic war, and alerted the general public on a severe consequence of a "nuclear winter" that would have the same effect as the one that caused the dinosaur extinction.

It was possible that the close connection between "dinosaur extinction" and "nuclear winter", which were both popular science topics in early 1980s, inspired Alvarez to devote more or most of his energy to the field of atmospheric sciences. His focused deliberation in the Earth's atmosphere led him to propose a new hypothesis on a fundamental issue in the field of atmospheric sciences or, more specifically, in the field of atmospheric dynamics. Will he be successful again, shock the science community, and become famous in the field of atmospheric sciences or instead he will meet his Waterloo this time?

(To be continued)

coolboy

As a physicist in training, L. Alvarez was thinking the atmospheric motion in terms of conservation of mass, energy and angular momentum. If the hot air rises at the equator and the cold air sinks at the high latitude regions, one would expect an eastward jet stream at the high altitude, as one often sees it from the weather maps on TV weather analysis shows. This eastward jet stream can be easily understood by the conservation of the angular momentum as the high altitude air parcels move from equator to mid- and high latitudes. This is similar to the situation of a figure skater rotating faster as she concentrates her body weight toward her body center. However, it appeared that nobody paid any attention to the air flow direction near the surface as the air parcels move from high latitudes toward the equator to fill the gaps left from the hot rising air parcels. Furthermore, Alvarez realized that the majority of the areas in the low latitude regions were covered by oceans where the topographic and frictional effects were minimal. Therefore, based on the conservation of angular momentum, L. Alvarez hypothesized that there should exist a steady and systematic air flow near the oceanic surface in the low latitude region that always moves westward and toward the equator. This time, he submitted a science proposal to National Science Foundation (NSF) and proposed to lead an expedition team to actually measure the equatorial surface air flow to confirm his hypothesis.

L. Alvarez's proposal to NSF was declined and he was advised that the air flow he described in the proposal was called "trade winds" and was part of the so-called "Hadley cell" explained based on the conservation of angular momentum more than 250 years ago by George Hadley, which was already well known in the atmospheric science community:

Hadley, G., 1735: Concerning the cause of the general trade winds. Phil. Trans., 29, 58-62.

The observational characters and physical mechanism of the "Hadley cell" were discussed in almost every monograph or textbook in the field of atmospheric dynamics, for example,

Lorenz, E. N., 1967: The Nature and Theory of the General Circulation of the Atmosphere. World Meteo. Org., Geneva, 161 pp.
Lindzen, R. S., 1990: Dynamics in Atmospheric Physics. Cambridge Univ. Press, Cambridge, UK, 310 pp.

An easy and interesting location to observe the steady trade winds is at the Big Island of Hawaii where the steady northeast trade winds coupled with the mountain on the island form two distinctively different regional climates on the two sides of the mountain. On the windward side of the mountain, it is tropical rain-forest whereas on the leeward side, it has a desert climate.

When I heard Alvarez's story on his proposal to NSF, I first laughed at the occurrence of such an event (of a Nobel Prize recipient submitting a proposal to verify the Hadley cell). While trying to understand how he arrived at this idea, I learned and understood his contribution to solving the dinosaur extinction puzzle and realized the importance of bringing fresh ideas from outside to the field. [他山之石 可以攻玉。] Later, much later, one of my own science works happened to be closely related to Alvarez's work on dinosaur extinction. The close connection was immediately realized and firmly established as a result of my awareness of Alvarez's work on dinosaur extinction. My efforts in understanding how Alvarez might develop the idea of Hadley cell in his NSF proposal got paid off.