National Academy of Engineering Memorial Tributes: National Academy of Engineering, Volume 10
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Memorial Tributes: National Academy of Engineering, Volume 10

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             CHIA-SHUN YIH                                            265
                               CHIA-SHUN YIH
                                BY YUAN-CHENG FUNG
                CHIA-SHUN YIH was a humane, humorous, and poetic fluid dynamicist.
            He invented elegant mathematical transformations that simplify the differential
            equations and boundary conditions of the flow of nonhomogeneous fluids. He
            devised efficient methods of calculations. He discovered many exact or closed
            form solutions of waves and instabilities in fluid flow, and of course also many
            approximate solutions. He devised efficient calculations and pertinent
            experiments. He developed the field of stratified flow for its beauty and
            applications to atmospheric, oceanic, and other flows of scientific,
            environmental, and industrial interest. In his memory, his friends organized an
            international symposium at the U.S. National Congress of Applied Mechanics in
            June 1998, and dedicated a book, Fluid Dynamicsat the Interfaces (Cambridge
            University Press, 1999), to him.
                Chia-Shun Yih was born on July 25, 1918, in Kweiyang City, Kweizhou
            Province, which lies in the southern midwest part of China. Kweizhou is a
            beautiful mountainous country. Chia-Shun was born into a scholarly family, the
            son of Yih Ding-Jan and Hsiao Wan-Lan. His father was a specialist on silk and
            silkworm culture. His father’s profession was fortunate for me, because it made
            his father come to work in Kiangsu Province, which lies on the east coast of
            China, where I was born, where every family raised silkworms in the spring.
            Chia-Shun attended junior middle school (grades 7 to 9) in Zhengkiang, the
            provincial capital of
             CHIA-SHUN YIH                                            266
             Kiangsu. Then he and I both passed the entrance exam of the Soozhou Senior
             Middle School (grades 10 to 12) and entered in 1934. Soozhou has a long
             history. It was the capital of the Kingdom of Woo (585 B.C. to 490 B.C.). Our
             school ground was old and beautiful. The oldest hall of the school, where we
             often took examinations, was called the Purple Sun Hall, in honor of Master Zhu
             Hsi (1130 to 1200 AD). The walls of the hall were lined with plaques of black
             stone on which Zhu Hsi’s poems and lectures were carved. The halo of tradition
             was real.
                While we were in high school, the storm of war was gathering in China.
             Japan had occupied Manchuria in 1931 and invaded Shanghai in 1932. Full-scale
             war between China and Japan finally broke out on July 7, 1937, soon after our
             graduation from high school. We managed to take the entrance examination of
             the National Central University and got accepted. The university was located
             originally in Nanjing, the capital of China at that time. Before we could enter,
             however, it was moved to Chongqing, in Sichuan Province in the central midwest
             of China.
                At our university, Chia-Shun studied, among other things, mathematics and
             the theory and design of bridges. Our college years were spent in makeshift
             classrooms and laboratories, classes at the crack of dawn to avoid air raids, long
             hours in the dugouts, military training, and an endless stream of exciting or sad
             news. One wintry day, Japanese planes came and bombed out our simple shower
             hut, and for weeks afterward some of us had to bathe in the emerald water of the
             nearby Chia-Ling River, beautiful but cold.
                After graduation, Chia-Shun worked first in the National Hydraulics
             Laboratory in Guanshien, Sichuan. There he studied the work of Li Bing, who
             more than 2,300 years ago, invented a system of constructing and reconstructing
             control dikes every year, which works to this day. Li Bing’s design made
             Chengdu plain one of the richest areas in China for 2,300 years. Then Chia-Shun
             worked for the Chinese Bridge Company in Kweiyang, his hometown, designing
             highway bridges. In 1944 he taught at Kweizhou University. Then he married
             Loh Hung-Kwei, who gave birth to their first son, Yiu Yo Yih. The marriage
             lasted only a few years.
             CHIA-SHUN YIH                                            267
                Then a group of American professors visited China and upon their return
            raised forty-some graduate scholarships from various American universities and
            offered them to the Chinese Ministry of Education. By nationwide examinations,
            the Ministry of Education chose forty-two students to study in the United States.
            We were among the forty-two, and in 1945 we came to the United States via
                After a brief stay at Purdue University, Chia-Shun went to the University of
            Iowa to study fluid mechanics with Hunter Rouse and John McNown, with whom
            he maintained a warm friendship throughout his life. He signed up also for
            courses in music appreciation and French conversation. The young instructor of
            French conversation was Shirley Ashman from Maine. Chia-Shun and Shirley
            fell in love and were married in 1949.
                In the summer of 1947, Chia-Shun went to Brown University and listened to
            C.C.Lin’s lectures on fluid dynamics and was inspired. On returning to Iowa, he
            told me that he was concentrating his study on the smoke from a lighted
            cigarette. The smoke rises, curls up, becomes turbulent, and disperses. He was
            fascinated. His mentor, Hunter Rouse, encouraged him to pursue the subject in
            depth. It became a part of his Ph.D. dissertation. From that little seed a whole
            field grew up in his mind. In the following years, Chia-Shun developed the
            general theory of the dynamics of nonhomogeneous fluid with broad
            applications. This beginning of a big endeavor with a small subject is a trait of his
            research career, consistent with his love of poetry. A poet sees the arrival of
            spring in a single flower bud. The cigarette smoke contains the same truth and
            same beauty as the larger subjects.
                Chia-Shun got his Ph.D. in 1948. From 1948 to 1955, Chia-Shun taught and
            conducted research at the University of Wisconsin, the University of British
            Columbia, Colorado A&M University, the University of Nancy in France, and the
            University of Iowa. He finally settled down at the University of Michigan in Ann
            Arbor. For sabbatical leave he went to Europe. He spent a year (1959 to 1960) at
            Cambridge University, England, a year (1964) in Geneva, another year (1970 to
            1971) in the Universities of Paris and Grenoble in France, and a year (1977 to
             CHIA-SHUN YIH                                            268
             at Chatoux Lab in Paris and the Technische Hochschule Karlsruhe, in Germany.
             After he retired in 1988, he served as a graduate research professor at the
             University of Florida in Gainesville for three years.
                Honors followed Chia-Shun’s achievements. In 1968 the University of
            Michigan celebrated its sesquicentennial and chose to give special honors to a few
            outstanding professors among its faculty. Chia-Shun was given the title of
            Stephen P.Timoshenko Distinguished University Professor of Fluid Mechanics.
            In 1970 he was elected a member of Academia Sinica. In 1980 he was elected a
            member of the U.S. National Academy of Engineering. He was honored by the
            Chinese Institute of Engineers with the 1968 Achievement Award and by the
            Chinese Engineers and Scientists Association of Southern California with the
            1973 Achievement Award. In 1974 he was the University of Michigan’s Henry
            Russel Lecturer. In 1981 he was given the Theodore von Kármán Medal by the
            American Society of Civil Engineers. The American Physical Society gave him
            the Fluid-Dynamics Prize in 1985 and the Otto Laporte Award in 1989. In 1992
            he had the honor to present the Sir Geoffrey Taylor Lecture at the University of
            Florida. Chia-Shun was a great admirer of Sir Geoffrey. Earlier, in 1976, Chia-
            Shun had dedicated to Sir Geoffrey a volume of Advances in Applied Mechanics
            that he edited. In the preface, Chia-Shun said of G.I.Taylor, “His work was
            always marked by an originality of thought and a freshness of approach that
            continue to delight his readers, and a characteristic welding of analysis to
            experiments that is rarely attempted, let alone attained, by others.” My feeling is
            that this describes Chia-Shun himself very well.
                In daily life the Yih family is warm, relaxed, and somewhat idealistic. Son
            Yiu Yo is a computer expert, son David is a Ph.D. musician, and daughter
            Katherine is an ecological biologist working on public health. Chia-Shun played
            flute and painted with oils in the style of the French impressionists. He was
            gregarious and a wonderful storyteller. He loved to eat and often cooked for
            friends. He was a true gardener and could name many plants by their Latin
            names. He took long walks in the countryside everyday whenever weather
            permitted. He loved students and
             CHIA-SHUN YIH                                            269
             treated them as family members. Inspiration could come to him at any time, in
             any place. During the garden wedding ceremony of his daughter, he whispered to
             me that he had suddenly found the solution of a solitary wave.
                Chia-Shun enjoyed good health all his life. Two days before his death, he
             planted five young flowering trees in his garden. Friends watching him digging
             the holes asked him, why he must dig the holes so big and so deep? He answered,
             “At my age, I want to make sure that every sapling gets its full share of
             endowment! None should be shortchanged.” On April 24, 1997, Chia-Shun died
             while on a commercial airline flight from Detroit to Taipei to participate in the
             Conference on Mechanics and Modern Science at the Academia Sinica. When a
             stewardess tried to wake him up for a stop at Tokyo, she found him unconscious.
             The passenger sitting next to Chia-Shun said he did not notice Chia-Shun had any
             signs of discomfort. Chia-Shun was sent to a hospital immediately after landing,
             but he never woke up. That was April 25th in Tokyo, the 24th in Detroit.
                Chia-Shun’s lighted cigarette study found more formal presentations in his
            Ph.D. dissertation and in his first two papers: one in the Journal of Applied
            Mechanics (1950) under the title of “Temperature Distribution in a Steady,
            Laminar, Preheated Air Jet,” and another in the Proceedings of the First U.S.
            National Congress of Applied Mechanics (1950) under the title of “Free
            Convection Due to a Point Source of Heat.” His formulation of the problem and
            his solutions were really elegant. The laminar flow solution was exact, and it was
            accompanied by a systematic experimental investigation on the transition from
            laminar to turbulent flow. These studies were followed by a series of papers
            dealing with atmospheric diffusion, gravitational convection from a boundary
            source, turbulent buoyant plumes, buoyant plumes in a transverse wind, etc. His
            characteristic approach was to find exact solutions as far as possible, and to check
            with experimental results. From his first paper to the one hundred thirtieth, the
            spirit was the same.
                Chia-Shun’s scientific papers published between 1950 and the early part of
            1990 have been collected in a two-volume set called Selected Papers by Chia-
            Shun Yih, published by World Scien
             CHIA-SHUN YIH 270
             CHIA-SHUN YIH                                            271
             gives rise to a variety of interesting natural phenomena. Yih solved problems on
             the hydraulic jump of layered fluid, atmospheric phenomena, flow in porous
             media, prevention of stagnation zones in flows of a stratified or rotating fluid,
             edge waves, vortex rings, internal waves in pipes, similarity of stratified flows,
             instability driven by viscosity stratification, subharmonic instabilities in
             modulated viscous flows, long wave analysis of free-surface instabilities,
             surface-tension modulated waves, etc.
                The second category of Yih’s papers on the theory of hydrodynamic stability
             consists of a series of fundamental papers on two-dimensional parallel flow for
             three-dimensional disturbances, the stability of unsteady flows or configurations,
             eigen-value bounds for the Orr-Sommerfeld equation, electrically conducting
             fluids, non-Newtonian fluids, viscosity stratification, and thermal conductivity
             stratification. This series of basic papers includes his solutions of a number of
             aeronautical, civil, and manufacturing engineering problems. Examples include
             the flow down an inclined plane, the waves in the deicing liquid sprayed on an
             airplane wing to deice the plane in cold winter weather, and waves in the sheet of
             paper pulp spread on a rotating cylinder in the process of paper making.
                The third category of Yih’s work is gravity waves. He gave solutions to
             water waves in basins of variable depth, waves in channels of various cross
             sections, waves in meandering rivers, edge waves created by a long-shore current
             and a ridge in the seabed, nonlinear wave groups, and ship waves.
                Papers in the fourth category on jets, plumes, and diffusion are especially
             relevant to environmental concerns. Lighted cigarettes, chimneys, and polluting
             cities have a lot in common.
                Finally, a large number of Yih papers collectively classified as the general
             category exhibit the breadth of his interest, from pure mathematics to
             magnetohydrodynamics and biomechanics. Altogether, the Selected Papers by
             Chia-Shun Yih preserves a good record of his journal articles.
                In addition, Yih published two books on stratified flows and one on the
             whole field of fluid mechanics. His Dynamics ofNonhomogeneous Fluids was
             published by Macmillan in 1965. The second edition of this book, which contains a
             great deal of new
             CHIA-SHUN YIH                                            272
             material, was given a new title, Stratified Flows (Academic Press, 1980). The Yih
            style of fresh and concise writing shines through. This style is particularly
            evident in his third book, Fluid Mechanics, A Concise Introduction to the Theory
            (McGraw Hill, 1969). When this book went out of print in 1979, Chia-Shun
            issued an improved edition through the West River Press in order to reduce its
            price for the benefit of students.
                Chia-Shun was interested in biomechanics also. In 1968 he and I published a
            paper together, entitled “Peristaltic Transport” (Journal of Applied Mechanics,
            1968, pages 669–675). We were aiming to understand a disease called
            hydroureter, in which the ureter becomes enlarged, the peristaltic transport
            becomes ineffective, and the kidney injured.
                Chia-Shun did not work much further on biological problems. But he laid
            out a plan to study the blood flow in large arteries by means of the Orr-
            Sommerfeld equation. When he solved the colliding soliton problem in 1993, we
            discussed extensively to aim further research on the arterial blood flow problem.
            There is no doubt that solitons can exist in arteries because of the nonlinear
            characteristics of the elasticity of the blood vessel wall, which stiffens as the
            strain increases. But the arterial tree is characterized by its branching pattern,
            each branch is not very long, and the flow is characterized by the forward and
            reflected waves. Hence his colliding solitons theory is relevant. Unfortunately, he
            died too soon.
                Chia-Shun’s last manuscript was entitled “Tornado-like Flows.” One day,
            after a long drive from Gainesville, Florida, to Ann Arbor, Michigan, he called
            me to tell me that he and Shirley had arrived home safely; and that while Shirley
            was driving, he found a mathematical model of a tornado. He added to a swirling
            horizontal flow of a fluid a core of another fluid of different density and
            temperature, and a model of a tornado is obtained. In his head, he worked out the
            mathematical facets of how a core can lead the weather condition at a high
            altitude to the ground, how the horizontal swirling will generate the maximum
            speed at the surface of the core at the ground level, how the cyclonic action would
            cause the tornado to spin counterclockwise looking down toward the earth in the
            northern hemisphere,
             CHIA-SHUN YIH                                            273
             but clockwise in the southern hemisphere, and how sometimes a  shaped tornado
             can be formed. He explains why the debris of a tornado is always thrown to the
             left in the northern hemisphere. It remained only to check the literature, ask the
             experts about the facts, do some numerical calculations, and write it up. I have a
             rough draft of the paper, but I have not succeeded in tracking down its
                The Selected Papers by Chia-Shun Yih includes only his mathematical and
             physical articles. His other writings were omitted. I am glad that his
             “Remembrance of G.I.Taylor” remained in the Selected Papers (pages 1005–
             1009). But I wish you could read his literary piece, “Old China Remembered,”
            published in TheOhio Review 18 (1977), pages 67–77, (Bibliography No. 84,
            Selected Papers, page 1020). It consists of five short stories, entitled “The Slate
            Court,” “Crepuschule,” “Mulberries,” “Silk from Wild Cocoons,” and “Winter-
            Sweet.” Through them we would really understand the life and imaginations of
            young Chia-Shun. Donald Hall, the poet, in his introduction to this article, said,
            “When I think of Chia-Shun now in his absence, he smiles with a wild
            enthusiasm—and it may be enthusiasm over a poem a thousand years old, or over a
            problem he is solving, or over the petal of a flower in front of us. He delights in
            the…but unlike most humans—scientist or poet or salesman or factory worker—
            his world moves far outside the borders of his work; it is wide with things to be
            loved and cherished.”
                An illustration of Chia-Shun’s seeing poetry in fluid mechanics and fluid
            mechanics in poetry can be found in the frontispieces of his books. He chose a
            1946 photograph of a wheat field in western Kansas to illustrate the dynamics of
            nonhomogeneous fluids and a thirteenth century Chinese painting of a tidal bore
            to illustrate fluid mechanics, and he quoted the poems of La Fontaine, Li Chong
            Chu, and Fung Yen Ci to introduce various topics in fluid mechanics. Such a
            poetic mind was his!
                A list of Yih’s papers published before 1990 is given in SelectedPapers by
            Chia-Shun Yih. Those published from 1990 to 1997 are presented below.
             CHIA-SHUN YIH                                            274
             Yih, C.S.1990. “Wave Formation on a Liquid Layer for Deicing Airplane
             Wings.”Journal of Fluid Mechanics,212: 41–53.
            Yih, C.S.1990. “Infinitely Many Superposable Solutions of the Navier-Stokes
            Equations: Damped Beltrami Flows.” In Of Fluid Mechanics and Related Matters,
            proceedings of a symposium honoring John Miles on his 70th birthday, December
            Yih, C.S.1993. “General Solution for Interaction of Solitary Waves Including
            Head-on Collisions.”Acta Mech. Sinica9:97–101, Science Press, Beijing.
             Yih, C.S.1993. “Solitary Waves in Stratified Fluids and Their Interaction.”Acta
             Mech. Sinica9:193–209, Science Press, Beijing.
             Yih, C.S.1994. “Solitary Waves in Poiseuille Flow of a Rotating Fluid.”Quarterly
             of Applied Mathematics,52:739–752.
             Yih, C.S.1994. “Intermodal Interaction of Internal Solitary Waves.”Quarterly of
             Applied Mathematics,52:753–758.
             Yih, C.S.1995. “Kinetic-Energy Mass, Momentum Mass, and Drift Mass in
             Steady Irrotational Subsonic Flows.”Journalof Fluid Mechanics,297:29–36.
             Yih, C.S. and Wu, T.Y-T.1995. “General Solution for Interaction of Solitary
             Waves Including Head-On Collisions.”Acta Mech. Sinica11:193–199.
             Yih, C.S. and Zhu, S.1996. “Selective Withdrawal from Stratified
             Streams.”Journal of the Australian MathematicalSociety, Series B38:26–40.
             CHIA-SHUN YIH                                            275
             Yih, C.S.1996. “Added Mass.”Chinese Journal of Mechanics,12:9–14.
             Yih, C.S.1997. “The Role of Drift Mass in the Kinetic Energy and Momentum of
             Periodic Water Waves and Sound Waves.”Journal of Fluid Mechanics,331:429–
             Yih, C.S.1997. “Evolution of Darwinian Drift.”Journal ofFluid
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