Abstract
The problem of wave scattering by a finite rigid dock floating in water with variable bottom topography is investigated here. Assuming the variation of the bottom topography to be in the form of small undulations, a simplified perturbation analysis is employed to solve the problem approximately. The first-order corrections to reflection and transmission coefficients are obtained in terms of integrals involving the shape function describing the bottom topography. Two types of shape functions describing a patch of sinusoidal ripples and a Gauss-type curve are considered. For a sinusoidal patch of ripples at the bottom, first-order correction to the reflection coefficient shows a resonating behavior when the wavelength of sinusoidal bottom is half the wavelength of the incident field. It is also observed that when the dock totally shadows the sinusoidal undulations, resonance does not occur.
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Acknowledgments
This work is supported by CSIR, New Delhi, DST research project no. SR/SY/MS:521/08 and DST PURSE scheme and UGC (UPE II) through Jadavpur University. The authors are thankful to Prof. B. N. Mandal for his useful suggestions.
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Dhillon, H., Banerjea, S. (2015). Effect of Variable Bottom Topography on Water Wave Incident on a Finite Dock. In: Mohapatra, R., Chowdhury, D., Giri, D. (eds) Mathematics and Computing. Springer Proceedings in Mathematics & Statistics, vol 139. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2452-5_28
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DOI: https://doi.org/10.1007/978-81-322-2452-5_28
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