Wave Control by Flexible Underwater Mound
Authors: Tanaka M. , Ohyama T. , Kiyokawa T. , Uda T. , Ornata A. 
Published: October 2008

ABSTRACT
A flexible submerged breakwater called "Flexible Mound" has been developed for wave control in shallow water as an alternative to the conventional rigid submerged design. The flexible mound is made of an elastic membrane bag attached to the sea floor, and utilizes the complex interaction of incident waves and radiation waves emanating from the membrane. Experimental studies were conducted to compare the performance of flexible and rigid models and to identify the significant parameters affecting the efficiency of the flexible type. Numerical studies based on the boundary integral equation were also carried out to investigate the wave absorption mechanism of the flexible mound. The flexible underwater mound is found to be an effective alternative to the conventional rigid type for shallow water wave control.

INTRODUCTION
With more than 30,000 km of coastlines surrounded by rough seas, detached breakwaters are commonplace in the coastal scenery of Japan. Although these structures serve the intended purpose of shore protection, their undesirable effects on the scenic value of shoreline landscape have been questioned recently. For development of marine recreational zones, there is a particularly strong demand for invisible yet safe and effective wave control. Conventional submerged rigid dikes could partially meet this need if made massive; however, they would raise concerns for marine safety. In response to this demand, and as an alternative to rigid submerged design, the writers have devised a submerged flexible breakwater called "Flexible Mound," made of an elastic bag filled with water. An earlier study by the writers has shown that the flexible design is effective even when the mound height is less than a half of the water depth1. In a subsequent analytical study, Kiyokawa, et al., found that the interaction of radiation waves (generated by the motion of the flexible structure) with the incident waves is responsible for wave dissipation. 2The objective of the present study is to investigate the basic wave transmission characteristics of the flexible mound by physical and numerical model analyses. The experimentaland numerical results generally agree, and several significant design parameters are identified.

NUMERICAL ANALYSIS

Modeling Approach
Consider a regular train of small amplitude waves with angular frequency,? as, propagating onto the flexible mound installed in water of constant depth, h, as shown in Fig.1 In this modeling approach, the elastic membrane is discretized into small elements using the lumped-mass method. Figure 2 shows the forces acting on j-th nodalpoint; where Fj is the hydrodynamic force caused by the pressure difference between the interior and the exterior of the membrane, fj' fj-l are the tensions acting on j-th and j- I-thspring, and fo is the net weight of the mass in the water. The equations of motion for j-th nodal point in the x- and z direction may be written as (Available In Full Paper)
In addition to the assumptions inherent in the velocity potential formulation, the motion of both the fluid and the flexible membrane are assumed to be sufficiently small, so that the linear theory can be applied.