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Title: Sloshing frequencies of longitudinal modes for a liquid contained in a trough
Authors: McIver, P.
McIver, M.
Issue Date: 1993
Publisher: © Cambridge University Press
Citation: MCIVER, P. and MCIVER, M., 1993. Sloshing frequencies of longitudinal modes for a liquid contained in a trough. Journal of Fluid Mechanics Digital Archive, 252, pp. 525 - 541
Abstract: The sloshing under gravity is considered for a liquid contained in a horizontal cylinder of uniform cross-section and symmetric about a vertical plane parallel to its generators. Much of the published work on this problem has been concerned with twodimensional, transverse oscillations of the fluid. Here, attention is paid to longitudinal modes with variation of the fluid motion along the cylinder. There are two known exact solutions for all modes ; these are for cylinders whose cross-sections are either rectangular or triangular with a vertex semi-angle of in. Numerical solutions are possible for an arbitrary geometry but few calculations are reported in the open literature. In the present work, some general aspects of the solutions for arbitrary geometries are investigated including the behaviour at low and high frequency of longitudinal modes. Further, simple methods are described for obtaining upper and lower bounds to the frequencies of both the lowest symmetric and lowest antisymmetric modes. Comparisons are made with numerical calculations from a boundary element method.
Description: This article was published in the Journal of Fluid Mechanics Digital Archive [© Cambridge University Press]. The definitive version is available at: http://journals.cambridge.org
Version: Published
DOI: 10.1017/S0022112093003866
URI: https://dspace.lboro.ac.uk/2134/4289
ISSN: 0022-1120
Appears in Collections:Published Articles (Maths)

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