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Analytically approximate natural sloshing modes for a spherical tank shape

Published online by Cambridge University Press:  12 June 2012

Odd M. Faltinsen  and
Alexander N. Timokha
Odd M. Faltinsen*
Affiliation:
Centre for Ships and Ocean Structures & Department of Marine Technology, Norwegian University of Science and Technology, NO-7091, Trondheim, Norway
Alexander N. Timokha
Affiliation:
Centre for Ships and Ocean Structures & Department of Marine Technology, Norwegian University of Science and Technology, NO-7091, Trondheim, Norway
*
†Email address for correspondence: [email protected]
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Abstract

The multimodal method requires analytical (exact or approximate) natural sloshing modes that exactly satisfy the Laplace equation and boundary condition on the wetted tank surface. When dealing with the nonlinear sloshing problem, the modes should also allow for an analytical continuation throughout the mean free surface. Appropriate analytically approximate modes were constructed by Faltinsen & Timokha (J. Fluid Mech., vol. 695, 2012, pp. 467–477) for the two-dimensional circular tank. The present paper extends this result to the three-dimensional, spherical tank shape and, based on that, establishes specific properties of the linear liquid sloshing.

JFM classification

Mathematical Foundations: Computational methods Mathematical Foundations: Variational methods
Type
Papers
Information
Journal of Fluid Mechanics , Volume 703 , 25 July 2012 , pp. 391 - 401
Copyright
Copyright © Cambridge University Press 2012

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