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Metamaterials helped to collect more energy from ocean waves

Chunyang Li et al. / Phys. Rev. Lett.

Chinese physicists have developed and built a device that concentrates the energy of ocean waves through their interference. The constructed prototypes strengthened the amplitude of water surface oscillations up to three times and practically did not create reflected waves. The prototype for the concentrator was a “lens” made of metamaterial, developed by scientists two years ago. The article is published in  Physical Review Letters , it is briefly reported by Physics .

Ocean waves generated by the wind, contain a large amount of energy that could be collected and used. The average thickness of ocean waves reaches15 kilowatts per meter, which exceeds the specific power of tides, wind and solar radiation. Unfortunately, at present scientists do not know how to effectively collect the energy of ocean waves – for example, the wave power plant Pelamis Wave Energy Converter, installed near the coast of Portugal in 2008, has a capacity of about 750 kilowatts and converts about one percent of the energy of excitement into electricity. The main obstacle that prevents the use of wave energy is the “smearing” of their energy over a large area. Because of this, it is required to use a variety of energy converters, each of which loses some of the energy during conversion.

The Chenyang group led by Huanyang Chen figured out how to solve this problem by developing and building a device that concentrates the energy of ocean waves. To do this, scientists used their experience from  transformational optics  – a science that controls the properties of electromagnetic waves using metamaterials. Metamaterials Are materials that consist of a large number of metaatoms, devices that change the characteristics of a wave (for example, frequency or direction) at a given point. To calculate how a large number of meta atoms will act together, more computing power is needed, and therefore transformational optics was born only in the late 1990s, when computers reached the desired level of development. At the present time, transformational optics is actively developing; more about the latest developments of scientists from this field can be read in the materials “Anatomy of an Invisible Cap” and  “Games with Light . ”

The prototype for the ocean wave concentrator was the device developed by Chen’s group in 2015. This device of the cylindrical form consisted of thin radially divergent metal plates directing electromagnetic waves to the center of the device. The space between the plates was filled with a medium with a variable refractive index , as a result of which the rays with a given frequency were not only directed to the center of the instrument, but fell into resonance and amplified. Because of the requirement for the continuity of the refractive index, it was difficult to build this device, but scientists were able to produce a prototype and focus with its help the energy of microwave radiation.

On the other hand, it is much easier to produce a similar device for concentrating the energy of ocean waves (which are sometimes called gravitational waves ). The shallow water equations that describe the propagation of ocean waves near the shore look almost the same as the equations of two-dimensional electrodynamics, so it is not necessary to change the design of the device. At the same time, the depth of the water layer serves as an analogue of the refractive index in hydrodynamics, on the surface of which waves propagate. More precisely, its root: the dispersion relation for the waves looks like ω = nk = k √ ( gh ), where ω is the wave frequency, k  is its wave number,g – acceleration of free fall, h  – depth of layer, and  n  – effective “index of refraction”. Constructing a pad with continuously changing depth is quite simple. If we choose the radii and the depth of each of the sections in such a way that the resonance condition is satisfied , after reaching the device, the waves will not be reflected, and all their energy will be concentrated in the central region.

To test how the proposed scheme will work in practice, physicists have fabricated two prototype devices. In the first prototype, a smaller size, the radius of the outer edge was 70 millimeters, the radius of the inner region was 35 millimeters, and the depth of water smoothly changed from 8 millimeters (outer area) to 2 millimeters (inner area). Thus, the effective “index of refraction” changed twofold. The thickness of 50 plates printed on a 3D printer and installed between the inner and outer parts was approximately 1.1 millimeters. The second prototype was much larger: the radii of its outer and inner rings were 42.9 and 24.8 centimeters respectively, the walls were 0.5 centimeters thick and the water depth varied from 10 to 3.3 centimeters (which corresponds to a change in the “refractive index” in 1.7 times).Then the scientists calculated on what wavelengths the constructed concentrators will work most effectively. They took into account that the approximation of shallow water, which was used in the preliminary design of devices (ω = k √ ( gh )), works well only if the wavelength is at least 20 times greater than the depth of the liquid layer. Otherwise, we need to use a more accurate transcendental relation that relates the frequency of the wave to the wave vector, takes into account the nonlinearities of the equations and the capillary effects.

As a result, the researchers found that the first prototype (smaller) amplifies waves with a resonant frequency of about two times. More precisely, at a resonant frequency of about 4.95 hertz, at which one wavelength is laid in the gap between the outer and inner rings, the amplitude of the waves in the central part was 2.21 times greater than in the outer part, and at a frequency of 7.05 hertz (one and a half wavelengths) – in 1.94 times. In this case, reflected waves did not arise. For the second prototype it was possible to achieve even greater amplification – the amplitude of the waves in the central part was more than 3 times greater than the amplitude of the incident waves with a frequency of about 1.5 hertz.

To visually demonstrate the amplification of waves, scientists placed a toy boat in the center of the hub and recorded its fluctuations on the video.

In the future, the authors of the article plan to build full-size devices that can concentrate the energy of real ocean waves. Scientists hope that their development will help to more effectively process the energy of ocean waves into electricity, and also protect the banks from destruction.Physicists often use metamaterials to control the behavior of sound, gravitational or electromagnetic waves. For example, with the help of metamaterials scientists managed to increase 160 times the energy of sound waves passing through the surface of water and air, “hide” the underwater object from acoustic detectors, “turn off” traces of the object floating on the water and even get electromagnetic “flying donuts”.

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