Wavelength manipulation in shallow water via space transformation method

Abstract

Wavelength is an important component of water waves. Realizing the active control of wavelength is of great significance for the protection of offshore structures and the development of wave energy. In this study, a circular wavelength modulator is proposed based on the space transformation method, which can reduce or amplify the wavelength arbitrary. The transformed spaces of a wavelength reducer and a wavelength amplifier are designed. According to the form invariance of the water-wave governing equation, the anisotropic medium parameters including water depth and gravity acceleration in the modulation fields are obtained, which means the wave control can be realized in ordinary spaces instead of in the deformed transformed spaces. The wave distributions in the modulation fields are calculated by solving the Helmholtz equation to validate the proposed wavelength modulator. It is found that the wavelength can be manipulated as expected with the anisotropic medium. In addition, the results show that the wavelength is controlled due to the scattering of the anisotropic medium. Moreover, the proposed wavelength modulator is frequency independent and omnidirectional.