Solution of wide-angle parabolic equations for long-range sound propagation in a moving medium
* Presenting author
Narrow-angle parabolic equations, which are widely used for outdoor sound propagation, are suitable for propagation angles up to 15º-20º off the main axis (generally the horizontal direction). Wide-angle parabolic equations (WAPEs) are thus needed to accurately solve long-range problems involving refraction and scattering from elevated layers, such as audible-range propagation in stable nighttime conditions, and infrasound refraction by the stratosphere. However, it is difficult to derive WAPEs that are numerically feasible to solve while properly accounting for motion in the propagation medium (i.e., wind in the atmosphere). As a starting point, we adopt here a recently derived extra-wide-angle parabolic equation (EWAPE) for moving media which accounts for the propagation angles up to 90º with respect to the nominal propagation direction. A WAPE is then derived from the EWAPE using a Padé (2,2) approximation, which is valid for angles up to roughly 55º. The resulting equation is generally suitable for long-range sound propagation applications in a moving atmosphere. We consider here solutions for example problems involving ducting and shadow zones. The solutions are compared to narrow-angle approximations and to wide-angle solutions based on the effective sound-speed approximation.