Allan is my most influential mentor and set my research style after my stay with him in 1983(Oct)-1984(June), as a visiting associate. On the day of my arrival, he said that I might go to Santa Monica beach everyday if I wished, but if not I might work on a topic of rotordynamics. I knew that this interesting problem was studied also by Prof. Ohashi of University of Tokyo and, to tell the truth, I did not want to be his competitor. By comparing their treatments, I found that more fundamental approach was used at Caltech and I decided to extend it for realistic cases. After developing fundamental equations, I proposed Allan to carry out calculations after returning to Japan and spent the latter half of the stay studying cavitation under Allan’s guidance.
Although the results of calculation could simulate the experimental results qualitatively (convenient word!!), the magnitude was smaller than the experimental results. Instead of being disappointed, Allan kindly built and tested a 2D impeller which is assumed in the theoretical model and showed that the theory can simulate the magnitude as well!! It was eventually found that the elementary flow fields developed for the rotordynamic problem could be conveniently used also for the analyses of rotating stalls in centrifugal impeller, vaned and vaneless diffusers.
Just after my return to Japan, Allan visited Japan to attend the first Cavitation Symposium at Sendai. Although I was not involved in cavitation at that time, he advised me to attend the symposium since I would be involved in the field. Before the Symposium he visited many universities and institutes and reported me about his impression. Perhaps on another visit to Japan, he was interested in visiting Matsue, on the other side of Hiroshima, which is not very familiar to foreign tourists. We drove there from Osaka and visited many marinas and small fishing villages as well. On the trip and other occasions with him, I learned from Allan about important attitudes for a researcher such as “make problems as simple as possible”, “nothing is more practical than a simple theory (said by someone else?)”, ”keep good balance between theory and experiment”. I tried to get closer to them throughout my life.
Allan developed a linear partial cavity model on a flat hydrofoil  and has shown that the cavity length is a function of a parameter (cavitation number)/(incidence angle). It was found that this parameter is important also for the occurrence of various types of cavitation instabilities. He also made the first detailed experimental study of cavitating inducer . He reported about cavitation instabilities such as cavitation surge, alternate blade cavitation, and rotating cavitation. They are found also in modern turbopump inducers and extensive efforts are being made to avoid them.
Although my stay was only 10 months, he introduced me to many students who graduated before and after my stay, on my later visits. I feel very relaxed whenever I find Acosta family member in in various meetings all over the world. It is interesting that the stay with Allan gave me opportunities of getting familiar with Japanese important people, who are very busy and would have no time to talk with me in Japan. The first is Prof. Ohashi. He gave me his rotordanamic test facility on his retirement!! This is still working at Osaka University. The second is Dr. Kamijo, Dr. Yamada, and Dr. Shimura from National Space Laboratory, who introduced me to the interesting field of cavitation instabilities in turbopumps for rocket engines. In solving the problem, Allan’s theoretical and experimental works including those mentioned in the last section were very helpful. So, they invited Allan many times to obtain his suggestions. We collaborated with Dr. Furuya, a student of Allan, for the fundamental study of unsteady cavity response to disturbances.
Thus, I actually got deeply involved in cavitation as Allan predicted at the first Cavitation Symposium.
I am always asking myself how Allan would think, whenever I encounter new problems. I am now wearing the T-shirts and listening to the music both from Allan. So, Allan is always with me and I wish his quick recovery.
 A. J. Acosta, (1955) “A Note on Partial Cavitation of Flat Plate Hydrofoils”, California Institute of Technology Hydrodynamic Laboratory Report No. E-19.9.
 Acosta, A.J., (1958). An Experimental Study of Cavitating Inducers. Second Symposium on Naval Hydrodynamics, Hydrodynamoc Noise, Cavity Flow. August 25-29, Washington D.C., ACR-38, 533-557.
Yoshi Tsujimoto, August, 2019