Wu T.Y.

(Division of Engineering & Applied Science, California Institute of Technology, Pasadena, CA 91125, U.S.A.)

    The news I learned from Professor Zheng Zhemin on the forth­coming observation of the Ninetieth Anniversary of Professor Guo Yonghuai has been well received at California Institute of Technol­ogy, the Caltech and the Alma Mater of Professor Guo. It is with great honor and pleasure I am taking this privileged opportunity of writing a commemorative ode to convey a token of our esteem and affections for Professor Guo.

    I first met Professor Guo in the golden autumn of 1953 when he returned to his Alma Mater on a sabbatical leave from Cornell University with his family, Lipei laushi? and the cute little princess, Guo Qin. I was then in my unwittingly beneficial Research-Fellow years (a term coined by Professor Theodore van Karman, the found­ing father of the Aeronautics school at Caltech, and in fact aero­nautical schools at many other universities in America), so I could roam quite freely around. And I appreciated having the good luck of listening in on inspiring discussions between Professor Guo and our mentor, Professor Qian Xuesen. Their academic discussions led me to realize that Professor Guo was making a significant change from his earlier interest in transonic and supersonic aerodynamics to a new one in asymptotic perturbation mathematics.

    On this note, I recall an anecdote relating to a highly spir­ited yet exceedingly profound dispute on how to take asymptotic perturbation approach to resolving certain physical problems, as viewed by some giants working in the field. It was about one round of stimulating discussion on the paper delivered by Herbert Wagner on his famous theory of a plate planing on water surface at high Froude number, supposedly at the Fourth International Congress for Applied Mechanics held in July 1934 at Cambridge, England. Since the gravity effect is negligible relative to the inertial effects, the former was completely ignored by Wagner. When the paper was opened for discussion, von Karman allegedly queried how can one determine the draft of the plate (i.e. the depth of submergence of the plate trailing edge below the unperturbed water surface far upstream). The answer is of course “it is impossible” because the lift acting on the two-dimensional planing surface makes the water surface react, in accordance with the momentum theorem, to fall off to downward infinity at large distances as there is no Ieveled water surface in this idealized gravity-free world. At this question. Wagner qualified that the water surface falls off only logarithmi­cally, a rate which is rather mild. At this tolerance, von Karman tossed back a questioning smile, said, “A logarithmic infinity is nonetheless aninfinity!”

    In a revisit to this tale afterwards, Professor Guo pointed out to me the deeper significance of the issue of the planing plate’s draft, for, as he saw it, that is the issue that deprives the theory of any hope for making a comparative experimental study. The point of thelesson we learned is crisp clear. While the gravity effect can be neglected near the body, it will regain its importance as the inertial effect keeps falling off with increasing distance away from the body, where the original assumption becomes invalid. Such a clear physical concept is naturally the guiding principle grasped by Professor Guo in developing his intricate mathematical theory.

    At that time. I was working on a cavity flow problem that a submerged hydrofoil may encounter. A hydrofoil deeply submerged (at depth more than a few chord lengths) under a water surface will experience the same lift as an airfoil held at the same incidence an­gle, but would lose about half of this lift if brought up to be planing on the water surface, according to the Wagner-type theory. If the planing plate is forced again to submerge, now bringing with it an air cavity attached to its upper side, the cavitating plate would have only one quarter of the airfoil lift. How can these operating modes be connected, smoothly from one to another seemed most challenging, leave alone the stability problem for the hydrofoil if commissioned to support a vehicle. I cannot recall when or how long I brought this puzzle for discussion with Professor Guo. But the issue of the plate draft again came to bright light. If the draft of the plate is varied, under control, from the water surface down­ward, the spray sheet formed at the leading edge of the planing plate would swing from the upstream direction over to going upward and then fall downstream. This physical picture thus reveals all the nonlinear effects  that require deft handling by applying asymptotic perturbation mathematics Professor Guo pioneered in developing. I was pleased to have the opportunity of telling my German audi­ence and friends these gratifying results from further development of Wagner’s theory at the 8 May 1984 Herbert Wagner Commemo­rative Symposium held at the Deutsche Museum, Munich. This is but one single case that exemplifies the great benefit my students and myself, among innumerable other researchers, have been able to derive from Professor Guo’s invaluable contributions.