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Wave diffraction by a circular crack in an ice sheet floating on water of finite depth

Li, ZF; Wu, GX; Shi, YY; (2018) Wave diffraction by a circular crack in an ice sheet floating on water of finite depth. Physics of Fluids , 30 (11) , Article 117103. 10.1063/1.5053563.

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Abstract

The problem of wave diffraction by a circular crack in an ice sheet floating on water of finite depth is considered. The fluid flow is described by the linear velocity potential theory, while the infinitely extended ice sheet is modeled as a thin elastic plate with uniform properties. At the crack, zero bending moment and shear force conditions are enforced. The solution starts from the Green function for ice sheet without the crack. This is then used to obtain an integral equation, in which the jumps of the displacement and slope across the crack are the unknowns. For a circular crack, the unknowns are expanded into the Fourier series in the circumferential direction. Through imposing the boundary conditions at the crack, a matrix equation is obtained for the unknowns, which is then truncated and solved. Convergence study is undertaken with respect to the truncation, and it has been found that the series converges fast. A far field identity is used to verify the solution procedure and is found to be satisfied very accurately. Extensive results are provided, and their physical implications are discussed. These include the jumps of the displacement and slope across the crack, resonant motion, far field diffracted wave amplitude, and the deflection of the ice sheet.

Type: Article
Title: Wave diffraction by a circular crack in an ice sheet floating on water of finite depth
DOI: 10.1063/1.5053563
Publisher version: https://doi.org/10.1063/1.5053563
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Flexural waves, Integral equations, Gravity wave, Potential theory
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Mechanical Engineering
URI: http://discovery.ucl.ac.uk/id/eprint/10063584
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