Modeling of airborne ultrasound reflection from water surface waves

Abstract

Airborne ultrasound reflection from water surface waves is modelled to advance uses of acoustic signals to measure water surface waves and apply the measurements to explore interactions of water waves with rigid structures in a laboratory setting. When the ultrasound is incident on a moving periodic water surface wave, the reflected signal can be treated as diffraction from a moving corrugated reflection grating. Under the condition that the amplitude of the water surface waves is much less than the incident acoustic wavelength, diffraction theory leads to analytical formulas for the spectra of the acoustic signal relating to the water wave amplitudes and frequencies. Complementary modeling based on ray theory and wave superposition illustrates the diffraction and validates formulas of water wave reflection from a surface-piercing barrier structure, where two counter-propagating water waves are involved.