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

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 regio...

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Bibliographic Details
Published in:Journal of fluid mechanics 2021-04, Vol.916, Article A11
Main Authors: Barman, S.C., Das, S., Sahoo, T., Meylan, M.H.
Format: Article
Language:English
Subjects:
Boundary value problems
Coefficients
Compression
Conversion
Dispersion
Energy
Enforcement
Floating ice
Floating structures
Glaciation
Gravity waves
Group velocity
Ice sheets
JFM Papers
Longitudinal waves
Mathematical problems
Modes
Propagation modes
Radiation
S matrix theory
Scaling
Velocity
Wave propagation
Wave scattering
Wavelengths
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2021.200