Semi-analytical solution for sound propagation from a moving directional source in a shallow-water waveguide

Understanding the waveguide fields produced by moving directional sources is of crucial importance in underwater acoustic detection. In practice, moving underwater targets often exhibit directionality, especially at high frequencies. Herein, we present a semi -analytical method to calculate the Doppler -shifted field (DSF) from a directional source moving horizontally in a range -independent, shallow -water waveguide. We develop a novel normal -mode model using a modal -projection approach with a perfectly matched layer. This comprehensively accounts for changes in modal shape, eigenvalue shifts, and the branch -integral contribution. We derive an analytical expression for the DSF based on Huygens' principle, and the solution is presented 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 expression is valid for any type of radiator moving in a range -independent environment with a smoothly varying sound -speed profile. We then present a theoretical analysis of the Doppler beam shift produced by a piston -like radiator. This reveals that the observed angular offset of modal plane waves can be attributed to the Doppler beam shift and confirms that this is a new mechanism causing considerable differences between the fields generated by a directional moving source and by the same source at rest. This has potential value in various applications, particularly for underwater acoustic detection of moving targets.