Dynamic imaging of a capillary-gravity wave in shallow water using amplitude variations of eigenbeams

Dynamic acoustic imaging of a surface wave propagating at an air-water interface is a complex task that is investigated here at the laboratory scale through an ultrasonic experiment in a shallow water waveguide. Using a double beamforming algorithm between two source-receiver arrays, the authors isolate and identify each multi-reverberated eigenbeam that interacts with the air-water and bottom interfaces. The waveguide transfer matrix is recorded 100 times per second while a low-amplitude gravity wave is generated by laser-induced breakdown at the middle of the waveguide, just above the water surface. The controlled, and therefore repeatable, breakdown results in a blast wave that interacts with the air-water interface, which creates ripples at the surface that propagate in both directions. The amplitude perturbations of each ultrasonic eigenbeam are measured during the propagation of the gravity-capillary wave. Inversion of the surface deformation is performed from the amplitude variations of the eigenbeams using a diffraction-based sensitivity kernel approach. The accurate ultrasonic imaging of the displacement of the air-water interface is compared to simultaneous measurements with an optical camera, which provides independent validation.