Concentrators for Water Waves

By introducing concepts from transformation optics to the manipulation of water waves, we design and experimentally demonstrate two annular devices for concentrating waves, which employ gradient depth profiles based on Fabry-Pérot resonances. Our measurements and numerical simulations confirm the concentrating effect of the annular devices and show that they are effectively invisible to the water waves. We show that transformation optics is thus an effective framework for designing devices to improve the efficiency of wave energy collection, and we expect potential applications in coastline ocean engineering.

Figure 1

The schematic diagram and the two devices. (a) The top view and cross section of the schematic diagram of concentrator with a gradient depth profile. The small and large concentrators are shown in (b) and (c), respectively.

Figure 2

The wave amplitudes of experimental measurements and simulation results for the small concentrator. For $m=2$, (a) is the experimental measurement with a background wavelength of 50 mm, (b) is the simulation result with the linear dispersion and a background wavelength of 52.5 mm, (c) is the simulation result with the transcendental dispersion and a background wavelength of 48.5 mm. For $m=3$, (d) is the experimental measurement with a background wavelength of 31 mm, (e) is the simulation result with the linear dispersion and a background wavelength of 35 mm, (f) is the simulation result with the transcendental dispersion and a background wavelength of 29.7 mm.

Figure 3

(a) The experimental amplitude magnification factors of the concentrator with and without baffles from 1.1 to 1.75 Hz for incident amplitude of 1.2 mm. (b) The simulated amplitude magnification factors of a single point. (c) The simulated averaged amplitude magnification factors for the inner part. (d) The amplitude magnification factors of the inner part from 1.1 to 1.75 Hz for incident amplitude of 1.2 (black), 1.7 (red), and 2 mm (blue) for the big-size concentrator, respectively. (e) The simulated amplitude profiles of concentrator with baffles at the frequency of 1.5 Hz. (f) The simulated amplitude profiles of concentrator without baffles at the frequency of 1.5 Hz.

Figure 4

Screenshots from experimental videos. (a) The boat with the incident wave amplitude of 2 mm. The boat in the inner part of the concentrator at the frequency of (b) 1.1, (c) 1.2, (d) 1.3, (e) 1.5, (f) 1.6, and (g) 1.7 Hz.