Non-Markov character of the phase fluctuations for sound propagation over relatively small ranges in the turbulent atmosphere

Abstract

The Markov approximation significantly simplifies formulations for the statistical moments of a wave propagating in a random medium. For the phase fluctuations, the Markov approximation is expected to be valid if the propagation range is much greater than the scale of largest inhomogeneities in a medium. In the atmospheric boundary layer, this scale can be several hundred meters, indicating that the Markov approximation might be inapplicable for relatively small ranges. In this paper, using geometrical acoustics, the correlation function and variance of the phase fluctuations of a plane sound wave are calculated without the Markov approximation and compared to previous results based on this approximation. The mean sound field and the spatial mutual coherence function (MCF) are also analyzed by expressing them in terms of the phase fluctuations. It is shown that for ranges smaller than the scale of largest inhomogeneities, the variance of the phase fluctuations is significantly smaller than that found with the Markov approximation. For large ranges, the relative difference between the two results tends to zero, while the absolute difference remains constant and can be much greater than unity. For the MCF, the Markov approximation is valid for both small and large ranges.