Analytical study of wave diffraction by an irregular surface located on a flexible base in an ice-covered fluid

Abstract

The reflection and transmission of surface waves propagating over an irregular surface located on a flexible base in an ice-covered fluid are analyzed within the context of linearized water wave theory. The ice-floe and flexible bed surface are assumed as narrow elastic sheets with different compositions. Under such circumstances, there are two types of proliferating waves that exist for any specific frequency. The proliferating waves having smaller wavenumber spread at just beneath the ice-floe (ice cover mode) and the other spreads over the flexible bottom of the fluid (flexural base mode). An elementary perturbation theory is used for reforming the governing boundary value problem (bvp) to a first-order bvp which is solved by utilizing the Green’s function technique. The first-order correction of the reflection and transmission coefficients are calculated in the form of integrals comprising of a function which represents the base deformation. A particular example of base deformation is taken to evaluate all these coefficients and the results are depicted graphically. The major strength of the recent study is that the results for the values of reflection and transmission coefficients for both the wavenumbers are established to meet the energy relation almost exactly.

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Acknowledgements

The authors are very much indebted to the three learned reviewers for their suggestions and constructive comments, which enabled the authors in carrying out the desired revision of the manuscript. The authors are also grateful to the Associate Editor for his valuable suggestions and for allowing a revision to be carried out.

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Correspondence to Smrutiranjan Mohapatra.

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This work is partly funded by Science and Engineering Research Board (DST), India through a research project to S. Mohapatra (No: SB/FTP/MS003/2013).

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Khuntia, S., Mohapatra, S. & Bora, S.N. Analytical study of wave diffraction by an irregular surface located on a flexible base in an ice-covered fluid. Meccanica 56, 335–350 (2021). https://doi.org/10.1007/s11012-020-01287-y

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Keywords

  • Irregular surface
  • Flexible base surface
  • Ice-floe
  • Green’s function method
  • Reflection and transmission coefficients
  • Energy relation