Semi-analytical approach to study wave interaction with a pair of obliquely submerged heterogeneous flexible structures

ABSTRACT

Analyzing inclined flexible plates of varying thickness is crucial for optimising and attaining precise control over wave reflection and transmission. This is particularly significant in the context of breakwater construction. In contrast to horizontal breakwaters, inclined barriers can penetrate multiple layers of fluid with varying particle velocities, facilitating interactions and causing wave breaking, which results in the dissipation of wave energy. Moreover, compared to vertical structures, inclined ones demonstrate more effective wave attenuation. In the context of the present study, we investigate the interaction of water waves with a pair of obliquely submerged flexible thin plates characterised by non-uniform thickness. In order to model this complex physical scenario, we employ the principles of linear water wave theory in conjunction with Kirchhoff's thin plate theory. By employing repeated integration and Green's integral theorem, we reduce the boundary value problem to a system of coupled integral equations. Through appropriate approximations, we solve this system and obtain numerical values for various hydrodynamic quantities. This model provides comprehensive results for both horizontal and vertical plates, making it highly versatile. We examine the impact of varying thickness and the inclination of the two flexible plates to understand their roles in the wave scattering process and the associated physical parameters. The results obtained from this study shed light on the intricate dynamics involved in wave-structure interactions and can inform the design and optimisation of breakwater systems.

KEYWORDS:

• Linear water wave
• dual flexible plates
• obliquely submerged
• thickness variation
• breakwaters
• integral equations

Acknowledgments

M. S. is thankful to PMRF, an initiative of the Government of India, for providing support to her as a PhD student in the present research work. Also, the author would like to extend her sincere thanks to her supervisor Dr. R. Gayen for reviewing the present manuscript. Further, the author would like to thank the reviewers for their thoughtful comments and efforts towards the improvement of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

No data was used for the research described in the article.