Abstract:

Representation of scattered acoustic field as an integral of Green's function over acoustic sources is a powerful technique. However, the Green's function of a plane three-dimensional waveguide in its common form is an infinite series of the waveguide's normal modes. Due to slow convergence of the series at small horizontal distances between the source and the receiver, the investigation of the near field and its effect on scattering is impractical. Furthermore, the integral representation of the acoustic field is not applicable to the downward propagation of acoustic waves in such a waveguide. The author previously showed, that the Green's function of a three-dimensional fluid layer could be transformed into a sum of a quickly converging series and an asymptotic term. It was demonstrated that the series is convergent at infinitely small distances between the source and the receiver as well as in the case where the receiver is located directly underneath the source. The integral representation of the field, generated by a dipole layer, requires the use of spatial derivatives of Green's function. In the present work, the derivatives of the modified Green's function with respect to the radial and vertical cylindrical coordinates are obtained. Convergence of the derivatives is investigated at small radial distances between the source and the receiver as well as in the case where the receiver is underneath the source. It is shown that the obtained derivatives converge well in these situations in comparison with the derivatives of the Green's function in its common form. As a result, the obtained derivatives are suitable for the modelling of acoustic field near the source and in the region directly underneath the source.