An analytical model for turbulence scattered rays in the shadow zone for outdoor sound propagation calculation

摘要

In outdoor sound propagation, an inherent problem of the ray tracing method is its inability todetermine the sound pressure level in the shadow zone, where geometrical rays do not penetrate.This is a serious problem in a turbulent atmosphere where significant sound energy will be scatteredinto the shadow. Empirical corrections that are determined from measurements or numericalsimulations are limited to situations within the bounds of the empirical corrections. This paperdescribes a different approach where the ray tracing model is modified analytically into a scatteredray model. Rays are first diffracted from the shadow boundary, which is determined by thegeometrical ray paths. The diffracted rays are then scattered by turbulence in their way to thereceiver. The amount of scatter is determined from turbulence statistics that are determined from aGaussian turbulence model. Most of the statistics are determined analytically except one element,which is determined empirically from numerical simulations. This turbulence scattered ray model isshown to have good accuracy against calculations based on the parabolic equation, and againstpreviously published measurement data. It was found that the agreement is good both with andwithout turbulence, at distance up to 2 km from the shadow boundary.