Ocean Engineering 206 (2020) 107374 Available online 18 April 2020 0029-8018/© 2020 Elsevier Ltd. All rights reserved. Contents lists available at ScienceDirect Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng Wave energy dissipation by a floating circular flexible porous membrane in single and two-layer fluids Siluvai Antony Selvan, Harekrushna Behera ∗ Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India ARTICLE INFO Keywords: Floating flexible membrane Circular porous structures Eigenfunction expansion method Membrane deflection Flow distribution Energy dissipation ABSTRACT In this study, the impact of gravity wave on a circular elastic floating permeable membrane is investigated using linear water wave theory in both homogeneous and two-layer fluids. The matched eigenfunction expansion technique is employed to obtain an analytic solution of the boundary value problem. Further, the plane wave integral representation of Bessel and Hankel functions are applied to study the influence of porous structure in damping the far-field wave energy. In order to examine the effect of various physical parameters, heave force exerted on the membrane, deflection of the membrane, reflected and transmitted wave amplitudes, flow distribution around the structure and far-field energy dissipation are computed and analyzed for three different edge conditions such as (i) free edge, (ii) moored edge and (iii) clamped edge. The study reveals that the surface wave amplitude on the lee side of the structure decreases significantly in the presence of floating porous elastic membrane. Moreover, the membrane having clamped edge dissipates more wave energy as compared to that for moored and free edge conditions. 1. Introduction In the last two decades, an increasing number of porous structures have been proposed as breakwaters and constructed in offshore areas to protect the coastline from wave action or to extract wave energy from oceans. The main benefit of these porous structures is that it signif- icantly decrease the disturbances in marine environment. Apart from vertical porous structure, there is a significant interest in submerged horizontal porous structure as these structures are less dependent on water depth and sea bed condition. Many theoretical and experimental studies have been developed regarding the diffraction of water waves by submerged horizontal structures. The role of porosity on scattered wave height and excitation force on a submerged porous disk was studied by Chwang and Wu (1994). The effect of a submerged and essentially horizontal plate for offshore wave control was reviewed by Yu (2002). By employing eigenfunction expansion method, Hu and Wang (2005) analyzed the model consists of vertical permeable wall and a submerged horizontal plate. They observed that a large amount of wave energy can be reduced by the system. Liu et al. (2007) modeled a breakwater which consists a submerged horizontal porous plate placed between the permeable front and rigid back wall. Further, they found that the porosity damps wave force on both horizontal plate and rigid back wall. Liu et al. (2008) developed another model by considering the submerged horizontal plates between the upper porous and lower ∗ Corresponding author. E-mail addresses: antony.selvan22@gmail.com (S.A. Selvan), hkb.math@gmail.com (H. Behera). rigid plate. In general, for solving the physical problem of wave forc- ing on the submerged permeable structures, the solution of complex dispersion relation is required. However, the new method developed by Liu and Li (2011) help to avoid complex dispersion relation in the case of wave action on horizontal submerged permeable plate. Later, using the method of Liu and Li (2011) and Liu et al. (2011) studied the wave action on a submerged horizontal porous disk. Using the explicit relation for reflection coefficient, Evans and Peter (2011) modeled the singularity at edge of submerged porous plate that occurs in velocity continuity. Using the matched eigenfunction expansion, Cho and Kim (2013) investigated the oblique wave action on a horizontal porous structure and the theoretical results are compared against their experimental results. On the other hand, for effective usage of ocean space and protection against ocean waves of high amplitude, the floating rigid/flexible circu- lar structures are preferred. Garrett (1971) investigated the scattering of surface gravity waves by a circular dock to determine the torque, surge and heave forces acting on the dock. Norris and Vemula (1995) derived the flux conservation relation for arbitrary motion for wave interaction with thin plates. Using linear hydro-elastic theory, Cho and Kim (1998) studied the diffraction of surface gravity waves by a horizontal flexible membrane. Using the method of Zilman and Miloh (2000), Peter et al. (2004) extended the same physical problem to the https://doi.org/10.1016/j.oceaneng.2020.107374 Received 9 September 2019; Received in revised form 1 March 2020; Accepted 9 April 2020