High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition. Herein, underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation. And with the principles of grating and constructive interference, the mechanism of this acoustic scattering modulation is explained. The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles, which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field, respectively, which is a high-order Bragg scattering phenomenon. Unlike the conventional Doppler effect, the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency. Therefore, even if a low-frequency underwater acoustic field is incident, it will produce obvious frequency shifts. Moreover, under the action of ideal sinusoidal waves, swells, fully grown wind waves, unsteady wind waves, or mixed waves, different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics. For the swell wave, which tends to be a single harmonic wave, the moving rough sea surface produces more obvious high-order scattering and frequency shifts. The same phenomena are observed on the sea surface under fully grown wind waves, however, the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum. Comparing with the swell and fully-grown wind waves, the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.