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Hydroelastic waves propagating in an ice-covered channel

Published online by Cambridge University Press:  14 January 2020

K. Ren ,
G. X. Wu Open the ORCID record for G. X. Wu [Opens in a new window]  and
Z. F. Li
K. Ren
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, LondonWC1E 7JE, UK
G. X. Wu*
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, LondonWC1E 7JE, UK
Z. F. Li
Affiliation:
School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang212003, China
*
†Email address for correspondence: [email protected]
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Abstract

The hydroelastic waves in a channel covered by an ice sheet, without or with crack and subject to various edge constraints at channel banks, are investigated based on the linearized velocity potential theory for the fluid domain and the thin-plate elastic theory for the ice sheet. An effective analytical solution procedure is developed through expanding the velocity potential and the fourth derivative of the ice deflection to a series of cosine functions with unknown coefficients. The latter are integrated to obtain the expression for the deflection, which involves four constants. The procedure is then extended to the case with a longitudinal crack in the ice sheet by using the Dirac delta function and its derivatives at the crack in the dynamic equation, with unknown jumps of deflection and slope at the crack. Conditions at the edges and crack are then imposed, from which a system of linear equations for the unknowns is established. From this, the dispersion relation between the wave frequency and wavenumber is found, as well as the natural frequency of the channel. Extensive results are then provided for wave celerity, wave profiles and strain in the ice sheet. In-depth discussions are made on the effects of the edge condition, and the crack.

JFM classification

Geophysical and Geological Flows: Ice sheets Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A18
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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