Theoretical investigation of sound propagation from a moving directional source in a shallow-water waveguide

Abstract

Doppler phenomena resulting from a moving directional source can be complicated in shallow water environments. This study presents a semi-analytical method to calculate the Doppler-shifted field (DSF) caused by a directional source moving horizontally in a shallow-water waveguide. First, an improved normal-mode (NM) model is developed to comprehensively account for the Doppler-induced changing modal shapes, eigenvalue shifts, and the contribution of the branch cut integral. Next, an analytical, modal expression for the DSF is derived based on the principles of Huygens and Taylor series expansion. The solution is expressed as a sum over propagating eigenmodes, with the modal excitation determined by the source directivity depending upon the grazing angle of each pair of modal plane waves. This modal expression is applicable to any type of radiators moving in a shallow-water environment with an arbitrary sound speed profile. By employing the proposed theoretical model, we analyze the beam Doppler shift produced by a piston-like radiator moving in a two-layer waveguide. The simulation indicates that an apparent asymmetry arises in the DSF when the beam grazing angle sweeps over the critical angle of the seafloor. This finding confirms that the beam Doppler shift acts as the third mechanism causing significant differences between the field generated by a directional moving source and that by the same source at rest, which may have practical applications in underwater acoustic detection for moving sources.