A WIDE-ANGLE PARABOLIC EQUATION FOR ACOUSTIC WAVES IN INHOMOGENEOUS MOVING MEDIA: APPLICATIONS TO ATMOSPHERIC SOUND PROPAGATION

Abstract

Two new derivations of "vector" parabolic equations (PE) for use in acoustic propagation have recently been published. In these cases, PEs have been derived from first principles and incorporate velocity fluctuations of the medium as two additional vector terms. In the simpler case, large spatial-scale velocity fluctuations can be accommodated. In the more general case, multi-scale velocity fluctuations can be accommodated. In this paper we report on a series of two-dimensional numerical experiments which compares sound propagation predicted from traditional PEs with sound propagation predicted from these two "vector" PEs. Two types of velocity fields are simulated. One, suitable for approximating an atmospheric boundary layer, is a field in which velocity has only a horizontal component, but whose magnitude can depend on height, i.e., v=v x (z). The other is a field having random spatial fluctuations over a range of length scales and could be suggestive of atmospheric turbulence. In both cases celerity inhomogeneities are also included. Results suggest that at least, in two dimension, the standard PE using an effective index of refraction is not accurate to describe the effects of the mean and turbulent velocity on sound propagation near the ground. We suspect that in three-dimensional problems, the added terms in the "vector" PEs will significantly increase in importance.