A wide-angle parabolic equation for acoustic waves in inhomogeneous movingmedia: Applications to atmospheric sound propagation

Two new derivations of "vector" parabolic equations (PE) for use in acousti c propagation have recently been published. In these cases, PEs have been d erived from first principles and incorporate velocity fluctuations of the m edium as two additional vector terms. In the simpler case, large spatial-sc ale velocity fluctuations can be accommodated. In the more general case, mu lti-scale velocity fluctuations can be accommodated. In this paper we report on a series of two-dimensional numerical experiment s which compares sound propagation predicted from traditional PEs with soun d propagation predicted from these two "vector" PEs. Two types of velocity fields are simulated. One, suitable for approximating an atmospheric bounda ry layer, is a held in which velocity has only a horizontal component, but whose magnitude can depend on height, i.e., nu = ur(nu (x)). 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 inho mogeneities are also included. Results suggest that at least, in two dimension, the standard PE using an e ffective index of refraction is not accurate to describe the effects of the mean and turbulent velocity on sound propagation near the ground. We suspe ct that in three-dimensional problems, the added terms in the "vector" PEs will significantly increase in importance.