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On natural modes in moonpools and gaps in finite depth

Published online by Cambridge University Press:  14 February 2018

B. Molin Open the ORCID record for B. Molin [Opens in a new window] ,
X. Zhang ,
H. Huang  and
F. Remy
B. Molin*
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, IRPHE, 13013 Marseille, France Bureau Veritas Marine and Offshore SAS, CS 50101, 92937 Paris La Défense CEDEX, France Department of Marine Technology, Norwegian University of Science and Technology NTNU, 7491 Trondheim, Norway
X. Zhang
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
H. Huang
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
F. Remy
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, IRPHE, 13013 Marseille, France
*
†Email address for correspondence: bernard.molin@centrale-marseille.fr
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Abstract

In this paper an extension of the theoretical model of Molin (J. Fluid Mech., vol. 430, 2001, pp. 27–50) is proposed, where the assumptions of infinite depth and infinite horizontal extent of the support are released. The fluid domain is decomposed into two subdomains: the moonpool (or the gap) and a lower subdomain bounded by the seafloor and by an outer cylinder where the linearized velocity potential is assumed to be nil. Eigenfunction expansions are used to describe the velocity potential in both subdomains. Garrett’s method is then applied to match the velocity potentials at the common boundary and an eigenvalue problem is formulated and solved, yielding the natural frequencies and associated modal shapes of the free surface. Applications are made, first in the case of a circular moonpool, then in the rectangular gap and moonpool cases. Based on so-called single-mode approximations, simple formulas are proposed that give the resonant frequencies.

JFM classification

Waves/Free-surface Flows: Waves/Free-surface Flows Waves/Free-surface Flows: Wave-structure interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 840 , 10 April 2018 , pp. 530 - 554
Copyright
© 2018 Cambridge University Press 

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