A phase screen approach to sound propagation through small-scale turbulence

Abstract

A Green’s function method has recently been used to derive a fast parabolic (PE) method for atmospheric sound propagation over a locally reacting ground surface [K. E. Gilbert, X. Di, and C. You, J. Acoust. Soc. Am. 90, 2307(A) (1991)]. Because the algorithm can take range steps many wavelengths long, it is approximately 100 times faster than existing PE algorithms that use a Crank–Nicolson range step. In applying the fast PE method to propagation in a turbulent atmosphere, however, one must somehow account for inhomogeneities that are considerably smaller than the optimum range step of the PE. To avoid losing the speed of the method by taking short-range steps, the use of ‘‘integrated-turbulence’’ phase screens has been investigated. On a given range step, the phase screen method incorporates the integrated phase change due to turbulence into a random phase factor that is applied at the end of the range step. The objective is to use long range steps and still accurately account for the effects of small-scale turbulence. Results from the phase screen approach are compared to calculations based on a Crank–Nicolson method which accurately accounts for small-scale turbulence by taking very short-range steps. A theoretical and numerical analysis is given for the maximum range step one can use with realistic models for atmospheric turbulence.