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Image solution for vertical motion of a point source towards a free surface

Published online by Cambridge University Press:  28 March 2006

John P. Moran
John P. Moran
Affiliation:
Therm Advanced Research, Ithaca, New York
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Abstract

The vertical constant-speed motion of a constant-strength point source towards a horizontal free boundary is analysed. A procedure based on expansions in even powers of the Froude number is employed. The asymptotic expansion of the potential is found to satisfy a simple differential equation, which, when integrated, yields an image-type solution valid for all Froude numbers. Froude-number effects are contained in a distribution of sources along the vertical line from the image of the submerged source with respect to the undisturbed free surface upward to infinity. The solution is valid for arbitrary values of the density ratio across the free surface.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 18 , Issue 2 , February 1964 , pp. 315 - 320
Copyright
© 1964 Cambridge University Press

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References

Brard, R. 1948 Introduction à l'étude théorique du tangage en marche. Bull. Assoc. Tech. Mar. Aero. 47, 455.Google Scholar
Erdelyi, A. 1956 Asymptotic Expansions. New York: Dover.
Finkelstein, A. B. 1957 The initial value problem for transient water waves. Comm. Pure Appl. Math. 10, 511.Google Scholar
Haskind, M. D. 1946 The oscillation of a ship in still water. Izv. Akad. Nauk SSSR. Otd. Tekhn. Nauk 1946, 23. English translation in Tech. & Res. Bull. Soc. Nav. Arch. Mar. Engrs, no. 1–12 (1953).Google Scholar
Havelock, T. H. 1927 The method of images in some problems of surface waves. Proc. Roy. Soc. A, 115, 268.Google Scholar
Sakai, T., Husimi, Y. & Hatoyama, M. 1933 On the resistance experienced by a body moving in an incompressible perfect fluid towards its free surface. Proc. Phys. Math. Soc. Japan, 15 (3rd series), 4.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. Encyclopaedia of Physics (Ed. S. Flügge & C. Truesdell), IX, 446. Berlin: Springer-Verlag.