Models of the Formation of Doppler Spectrum of Surface Reverberation for Sound Waves of the Meter Range

Abstract—Narrowband spectra of sound scattered on the surface wave in the frequency range from 500 to 3000 Hz have been analyzed. Experimental results and theoretical models are reviewed. Previously published work by the authors is reviewed and new results are presented. The first characteristic case considered is forward scattering, where the sound transmitter and receiver are substantially separated from each other in space, and a continuous emission of a sinusoidal signal is produced. For this case, it is shown that the modulation spectrum of the scattered signal repeats the frequency spectrum of the surface wave with a certain coefficient and small corrections. The second considered characteristic case is a monostatic location, where the receiver and transmitter are combined and tone-pulse signals are emitted. Previously, for this case, it was implicitly expected that the reverberation spectrum would be generated by Bragg scattering on surface waves corresponding to half of the sound wavelength, and hence the spectrum of the scattered signal would be discrete. However, the experimental results indicate that the monostatic scattering spectra have a smooth bell-shape. Explaining this requires taking the effects of modulation of short surface waves by the long-wave component into account. Additionally, to explain the experimental phenomenon, the authors include a model of sound scattering on air bubbles, which are located in the near-surface layer of water and make oscillatory movements in the field of orbital currents of surface waves.