A note on the cylindrical wave-maker problem in the presence of surface tension
type: Item
instance of: scholarly article
title: A note on the cylindrical wave-maker problem in the presence of surface tension
zbMATH Open document ID: 0726.76020
DOI: 10.1016/0093-6413(91)90071-4
published in: Mechanics Research Communications
publication date: 1991-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 4199813
zbMATH Keywords: cylindrical wave-maker problem
zbMATH Keywords: deep water
zbMATH Keywords: surface tension
zbMATH Keywords: Weber integral transform
zbMATH Keywords: regularity condition
author: B. N. Mandal
author: Naba Kumar Ghosh
MaRDI profile type: Publication
full work available at URL: 0093-6413(91)90071-4
OpenAlex ID: W2043407874
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description: scientific article; zbMATH DE number 4199813