Non-Markov character of sound propagation over relatively short ranges in the turbulent atmosphere

Abstract

The Markov approximation is widely used in wave propagation in random media, including sound propagation in the turbulent atmosphere. This approximation, which significantly simplifies formulations for the statistical moments of the propagating field, is valid if the propagation range is greater than the outer length scale of random inhomogeneities. For sound propagation in the turbulent atmosphere, this length scale can be as large as 400–500 m (23% of the height of the atmospheric boundary layer), indicating that the Markov approximation might not be applicable for relatively short ranges. In this paper, the statistical characteristics of a sound field propagating in the turbulent atmosphere, such as the correlation functions of the log-amplitude and phase fluctuations, the mean sound field, and the mutual coherence function are calculated, without using the Markov approximation. The new results are then compared with those obtained in the Markov approximation. The difference between the two formulation...