A note on the cylindrical wave-maker problem in the presence of surface tension
The cylindrical wave-maker problem in deep water under the influence of surface tension considered by \textit{P. F. Rhodes-Robinson} [Proc. Camp. Phil. Soc. 70, 323-337 (1971; Zbl 0235.76006)] is reinvestigated by employing the Weber integral transform in the radial coordinate as used e.g.: by the first author and \textit{K. Kundu} [Int. J. Eng. Sci. 27, No.4, 393-398 (1989; Zbl 0687.76013)] and suitably exploiting a regularity condition of the transform. The solution depends on a parameter \(\lambda\) in the edge condition that is regarded as known. There are now several methods that have been used to obtain the solution of this problem, originally considered by \textit{T. H. Havelock} in Philosophic. Mag. 8, 560 ff. (1929) in the absence of surface tension and by the first author and \textit{A. Chakrabarti} [Appl. Math. Lett. 1, No.3, 225-258 (1988; Zbl 0661.76014)] in the presence of the same. This particular one is interesting as an application of a well-known transform method, which saves on some work and also the outgoing waves are obtained separately from a suitable exploitation of the regularity condition of the integral transform.
scientific article; zbMATH DE number 4199813