Fluctuations of spherical waves in a turbulent atmosphere: effect of the axisymmetric approximation in computational methods

The validity of the axisymmetric parabolic-equation (PE) method for line-of -sight sound propagation in a turbulent atmosphere is investigated. The axi symmetric PE method is a finite-difference method for solving a 2D paraboli c wave equation, which follows from the 3D wave equation by the assumption of axial symmetry around the vertical axis through the source. It is found that this axisymmetric approximation has a considerable spurious effect on the fluctuations of the sound field. This is concluded from analytical expr essions for the log-amplitude and phase variances, derived both for isotrop ic turbulence and for axisymmetric turbulence. The expressions for axisymme tric turbulence are compared with the results of numerical computations wit h the PE method. (C) 2000 Acoustical Society of America. [S0001-4966(00)028 10-1].