Scattering of Gravity Waves by a Rectangular Floating Flexible Porous Plate

Uma Vinod Kumar; Deepika T; Sunanda Saha; Swaroop Nandan Bora

Uma Vinod Kumar Research Scholar, Department of Mathematics, Dayananda Sagar University, Bangalore, Karnataka, India.
Deepika T Research Scholar, Department of Mathematics, Dayananda Sagar University, Bangalore, Karnataka, India.
Sunanda Saha Assistant Professor, Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India.
Swaroop Nandan Bora 4Professor, Department of Mathematics, Indian Institute of Technology, Guwahati, Guwahati, Assam, India.

Abstract

Scattering of oblique surface gravity waves by a finite, floating porous-elastic plate is investigated, with assumptions of linear water wave theory and plate response. A boundary value problem is set up, wherein the thin plate equation together with a porosity parameter is used to formulate the condition on the floating plate. A matched eigenfunction approach is adopted for the solution of this problem, with roots of the dispersion relation being located with the aid of contour plots, and various hydrodynamic scattering quantities are computed. Energy dissipation due to plate porosity is seen to have a significant impact on both reflection and transmission of waves, while flexibility of plate only alters the extent of wave reflection by porous elastic plates. An oscillatory trend is shown by reflection coefficient for smaller values of relative plate width, and there is no variation in reflection or transmission coefficients when the plate width is increased beyond a certain cut-off value. Comparison of scattering properties of four different types of plates highlights the effects of porosity and flexibility and establishes the superiority of a flexible porous plate as a wave attenuating device, with moderate reflection, high energy dissipation and low transmission.

How to cite this article: Kumar UV, Deepika T, Saha S et al. Scattering of Gravity Waves by a Rectangular Floating Flexible Porous Plate. J Adv Res Appl Math Stat 2021; 6(1&2): 4-11.

DOI: https://doi.org/10.24321/2455.7021.202102

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