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The Quarterly Journal of Mechanics and Applied Mathematics 1993 46(1):71-87; doi:10.1093/qjmam/46.1.71
© 1993 by Oxford University Press
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SLOSHING FREQUENCIES

D. V. EVANS and C. M. LINTON

( School of Mathematics, University of Bristol, University Walk Bristol BS8 1TW )

The normal frequencies of oscillation of fluid inside certain containers are calculated by expressing the velocity potential as a linear combination of harmonic functions each of which satisfies the free-surface boundary condition. The unknown coefficients are then determined by the application of the bottom boundary condition. This is done for three different geometries; a two-dimensional cylinder with semicircular cross-section, a cylinder with semicircular cross-section of finite length and a hemisphere. The method is also used to solve the interior Dirichlet problem, the solutions of which correspond to the ‘irregular frequencies’ that occur when solving the exterior forcing problem using a source distribution to represent the velocity potential. The method provides accurate results for the lower frequencies by truncation of simple homogeneous infinite systems of equations.


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