Atmospheric sound propagation using a three-dimensional parabolic equation

A numerical method for solving the three-dimensional parabolic wave equation (3-D PE) is presented to investigate long-range sound propagation in the atmosphere near the ground. An implicit finite-difference scheme based on the alternating directions method is formulated. The pressure field is calculated in cylindrical coordinates for all the azimuth ranges from 0° to 360°, so that only a periodicity condition is required. A hard reflecting ground is considered and a homogeneous boundary condition at the top of the mesh is applied. The validity of the 3-D PE is shown by comparison with measurements carried out in an anechoic chamber. The diffraction of sound behind a thin barrier of finite length is studied. A good agreement with calculations is obtained for the sound-pressure level behind the barrier. In particular, the term involving azimuth derivatives is taken into account in the 3-D PE and enables one to properly calculate the diffraction from both side edges of the screen. Moreover, calculations show that the presence of wind may modify the position of interferences created by the screen. [Work supported by Direction des Recherches Etudes et Techniques.]