481 Interaction between surface gravity wave and submerged horizontal flexible structures * Sarat Chandra Mohapatra 1 , Trilochan Sahoo 2 , C. Guedes Soares 1 1. Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal 2. Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology, Kharagpur, India (Received March 2, 2017, Accepted July 2, 2017) ©China Ship Scientific Research Center 2018 Abstract: Interactions between surface gravity wave and submerged horizontal flexible structures are studied under the assumption of small amplitude water wave theory and structural response. The generalized dispersion relation associated with surface gravity wave interaction with submerged horizontal flexible plate is analyzed to understand the characteristics of the two propagating modes due to the presence of the free surface and submerged horizontal plate. The phase and group velocities are studied in order to analyze the effect of submerged flexible plate on gravity wave motion. The expansion formulae based on Green’s function technique and eigenfunction expansion method using Fourier transform with appropriate orthogonal mode-coupling relation associated with surface gravity wavemaker problems are derived and compared in both the cases of water of finite and infinite depths. The usefulness of the expansion formulae is demonstrated by deriving the solution for surface gravity wave interaction with submerged articulated flexible plate in water of finite depth. Several numerical results on reflection and transmission coefficients related to submerged flexible plate are presented in order to understand the effect of submerged flexible structure on surface wave motion in different cases. Key words: Submerged flexible structures, Greenʼs function, expansion formulae, articulated submerged plate, reflection and transmission coefficients Introduction With the increasing demand of multi-purpose use of coastal and offshore zones, there has been signifi- cant interest to use floating flexible breakwaters, which are light weight, cost effective and environ- mental friendly substitute for the conventional break- waters [1-3] . These types of flexible floating structures are easy to carry, reusable, and rapidly deployable. For infinite water depths, these breakwaters are more economical and can be fabricated on land and easier to transport and handle. Often these structures are made of synthetic fiber, rubber or polymeric materials. The multi-mode motions of these types of flexible struc- tures can be explored to widen the effective frequency range for wave attenuation, especially in irregular waves. Oil booms and silt curtains are practical * Biography: Sarat Chandra Mohapatra (1979-), Male, Ph. D., Post-Doctoral Researcher, E-mail: sarat.mohapatra@centec.tecnico.ulisboa.pt Corresponding author: C. Guedes Soares, E-mail: c.guedes.soares@centec.tecnico.ulisboa.pt examples of membrane structures which are used for specific purposes in sea [4] . There have been many theoretical and experi- mental studies with regards to the performance of vertical flexible wave barriers [5] . The major problems associated with the use of vertical flexible breakwaters are the wave loading and possible blockage of current by the structure. On the other hand, horizontal flexible barriers can reduce the wave amplitude effectively by suppressing the vertical motion of water oscillation. Although, floating flexible barriers are more suitable for deep water uses where wave energy concentration is more on the free surface, the submerged horizontal flexible structures as breakwaters do not hamper seascape and also allow the passage of ships and currents. This kind of structures can be moored despite unfavorable seabed soil conditions. These structures allow for free movement of fish and free passage of seawater and sediment transport beneath, thus friendly to the environment. Since the horizontal structures do not directly block incoming waves, the diffracted and radiated waves including various elastic modes have to be properly tuned for its use as an Available online at https://link.springer.com http://www.jhydrod.com/ 2018,30(3):481-498 https://doi.org/10.1007/s42241-018-0053-2