Numerical Study of Metamaterial-Inspired Water Wave Control Technologies

Abstract

Ocean waves serve as both a coastal hazard and a renewable energy resource. On one hand, they drive erosion and flooding, posing significant risks to coastal communities. On the other, they offer a vast but largely untapped source of sustainable energy. Addressing these challenges requires innovative solutions that integrate coastal protection with wave energy development. The application of electromagnetic metamaterial concepts to water wave control technologies presents a promising approach, enabling wave redirection, concentration, cloaking, and sheltering. This study presents a numerical investigation using advanced computational fluid dynamics (CFD) methods to evaluate the hydrodynamic performance of three metamaterial-inspired structures: a shallow-water waveguide, an annular water wave concentrator, and a cylindrical water wave superscatterer. The concept of an effective refractive index for water waves is proposed through an analogy with electromagnetic waves, based on which the wave-controlling mechanism is explained. The interactions between free surface waves and these structures are simulated using a three-dimensional Navier-Stokes solver, based on the finite volume method and volume of fluid method. Following validation against experimental data, systematic parametric studies are conducted to examine the effects of structural design and wave conditions, including baffle configuration, wave frequency, water depth, and wave nonlinearity, on their wave-controlling performance. The results demonstrate the wave energy redistribution capabilities of the three structures. The shallow-water waveguide effectively redistribute wave energy through refraction and reflection, with wave amplitude increasing up to 2.3 times over the platform while decreasing by over 70% in the gap region. The annular water wave concentrator achieves significant energy focusing, amplifying wave height to over two times at the centre, with guiding baffles channelling the flow through gaps and enabling an invisibility effect across the domain. The cylindrical superscatterer modifies local water depth and flow direction, enhancing wave energy concentration and sheltering, increasing wave height up to 3.6 times within the structure while reducing it to 0.2 times in the wave shadow zone. Parametric studies reveal that water depth, wave frequency, and wave nonlinearity significantly influence the structures' performance. While wave amplification remains effective across a broad frequency range, depth variations can alter key wave processes, affecting refraction, diffraction, and reflection. Wave nonlinearity enhances wave amplification in the annular concentrator, increasing crest-to-trough asymmetry. However, in the shallow-water waveguide and superscatterer, this amplification effect slightly diminishes due to less pronounced refraction and additional energy dissipation mechanisms such as wave breaking. Furthermore, an increase in incident wave height weakens the invisibility effect in the concentrator and contracts the wave shadow zone of the superscatterer. These findings highlight the potential of metamaterial-inspired structures for enhancing wave energy exploitation and providing innovative coastal protection solutions. By strategically positioning wave energy converters in energy-focusing zones, wave energy harvesting can be made more efficient and cost-effective. Meanwhile, these structures offer compact, efficient alternatives to conventional breakwaters, mitigating wave impact forces through energy redistribution.