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Scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking

Published online by Cambridge University Press:  06 April 2021

S.C. Barman Open the ORCID record for S.C. Barman [Opens in a new window] ,
S. Das Open the ORCID record for S. Das [Opens in a new window] ,
T. Sahoo Open the ORCID record for T. Sahoo [Opens in a new window]  and
M.H. Meylan Open the ORCID record for M.H. Meylan [Opens in a new window]
S.C. Barman
Affiliation:
Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology Kharagpur, Kharagpur721302, India
S. Das*
Affiliation:
Mathematical and Computational Sciences Division, Institute of Advanced Study in Science and Technology, Guwahati781035, India
T. Sahoo
Affiliation:
Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology Kharagpur, Kharagpur721302, India
M.H. Meylan
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, NSW2308, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The scattering of flexural-gravity waves in a thin floating plate is investigated in the presence of compression. In this case, wave blocking occurs, which is associated with both a zero in the group velocity and coalition of two or more roots of the related dispersion relation. There exists a region in the frequency space in which there are three real roots of the dispersion equation and hence three propagating modes. This multiplicity leads to mode conversion when scattering occurs. In one of these modes, the energy propagation direction is opposite to the wavenumber, making enforcement of the Sommerfeld radiation condition challenging. The focus here is on a canonical problem in flexural-gravity wave scattering, the scattering of waves by a crack. Formulae are developed that apply uniformly at all frequencies, including through the blocking frequencies. This solution is developed by tracking the movement of the dispersion relation roots carefully in the complex plane. The mode conversion is verified by the scattering matrix of the process and through an energy identity. This energy identity for the case of more than one progressive modes is established using Green's theorem and later applied in the scattering matrix to identify the incident and transmitted waves in the scattering process and derive the radiation condition. Appropriate scaling of the reflection and transmission coefficients are provided with the energy identity. The solution method is illustrated with numerical examples.

JFM classification

Waves/Free-surface Flows: Wave scattering Geophysical and Geological Flows: Ice sheets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A11
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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