## 1 Introduction  
Oceans and seas cover about 70% of the earth's surface and naturally become an ideal solar energy collector and storage place. These renewable energies are available in different forms such as surface waves, tidal currents or thermal gradients [1; 2; 3; 4; 5; 6]. However, these energy resources are extremely difficult to extract from the open waters both technically and economically. Currently, there is no viable scheme to utilize these energies for large-scale production, although several significant improvements have been demonstrated in the past decade [7; 8]. The overall performance of a sea wave energy conversion (SWEC) device depends on many technical factors such as energy-converting efficiency and transport loss. Most studies on SWEC devices focus on refining the wave converter and energy transport while treating the incoming waves passively. At present, the wave power generation is still in the research frontline and mostly under testing phases, which mostly put emphasis on the energy-conversion efficiency of the back-end electric power generator sets. Sea wave energy is inherently stochastic and the conversion of energy is extremely complex due to the highly varying energy flux and wide time scales. A successful deployment requires a full evaluation of favorable coastal environments, device durability, and energy sustainability, that is truly based on a well-coordinated interdisciplinary effort. The bottleneck encountered is that the engineering conditions of utilizing the energy are limited to specific areas of ocean, often with high average wave energy density for economic consideration, where only small-scale power generation could be carried out. On the other hand, there is relatively less research to control the wave amplitude, which belongs to the front-end wave gathering techniques in reducing the technical threshold [3; 9; 10; 11]. It has been known for some time that sea bottom topography can significantly influence the surface wave amplitude and phases [12; 13]. Since the sea wave potential energy is proportional to the square of the wave amplitude (height), it is proposed here to study the possibility of enhancing the wave amplitude using under-sea periodic arrays of cylinders. These cylinder structures can be used to concentrate water-wave energy, and thus increase the conversion efficiency. For example, if the wave period is fixed, the energy-conversion efficiency depends mainly on the significant wave height, which is roughly proportional to the wave amplitude if other parameters are invariant [14]. Therefore, doubling the wave amplitude using the under-sea structure would yield a quadruple increment of the efficiency. Recently, there have been proposals to utilize periodic structures to concentrate light waves, sound waves and water waves [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. In our previous studies, we have pointed out that by optimizing the constraints of periodic arrangement, surface waves can be enhanced when propagating over periodic structures [26]. Therefore, in this paper we systematically discuss the influence of the energy enhancement factor by searching for the optimal geometrical parameters (the ratio of cylinder radius to the lattice constant and the ratio of the water depth to free water level) and the lattice configurations. Considering the actual seashore requirements, we choose a specific set of parameters and perform a reduced-scale water tank experiment. Both simulation and experimental results are reported and our results show clear physical evidence for the wave amplitude enhancement, which give a very promising opportunity for a successful real-scale nearshore deployment and test. The rest of this paper is arranged in the following way. In Section 2, the two-dimensional shallow water wave equations are derived and solved numerically. In Section 3, the simulation results are presented and discussed. Using the Froude scaling scheme, we design and conduct a reduced-scale water tank experiment.