An extended substitute-sources method for a turbulent atmosphere: Calculations for upward refraction

Journal article, 2003

The substitute-sources method (SSM) was previously implemented for a single noise barrier in a turbulent atmosphere by applying a substitute surface between the barrier and the receiver [1, 2]. Here, the method is extended, aiming to more general applicability to traffic noise propagation in urban environments. In the method, multiple substitute surfaces are used along the propagation path. The atmospheric turbulence causes a transfer of the initially coherent field into a residual, random field along the propagation path. The mean sound level at the receiver position is found from uncorrelated addition of the substitute surfaces' contributions. The calculation of each contribution is based on a mutual coherence function (MCF) for a turbulent atmosphere. The strength of the substitute sources and the Green functions to the received pressure are calculated for a non-turbulent atmosphere, here by using a fast field program (FFP). A special MCF for the residual field is derived. Examples are calculated for a turbulent atmosphere with upward refraction or without refraction. The results are compared with those from a parabolic equation method (PE) for the refractive cases and with an analytical solution otherwise. The results show good agreement, which indicates that the SSM could be useful for predictions of outdoor sound propagation.