Moment equations and path integrals for wave propagation in random media have been applied to many ocean acoustics problems. Both these techniques make use of the Markov approximation. The expansion parameter, which must be less than one for the Markov approximation to be valid, is the subject of this paper. There is a standard parameter (the Kubo number) which various authors have shown to be sufficient. Fourth moment equations have been successfully used to predict the experimentally measured frequency spectrum of intensity in the mid-ocean acoustic transmission experiment (MATE). Yet, in spite of this success, the Kubo number is greater than 1 for the measured index of refraction variability for MATE, arriving at a contradiction. Here, that contradiction is resolved by showing that the Kubo parameter is far too pessimistic for the ocean case. Using the methodology of van Kampen, another parameter is found which appears to be both necessary and sufficient, and is much smaller than the Kubo number when phase fluctuations are dominated by large scales in the medium. This parameter is shown to be small for the experimental regime of MATE, justifying the applications of the moment equations to that experiment.
Validity of the Markov approximation in ocean acousticsa)
Portions of this work were presented in “Some validity issues in the theory and modeling of WPRM,” by Terry Ewart and Frank Henyey at the 143rd Meeting of the Acoustical Society of America [J. Acoust. Soc. Am. 111, 2351 (2002)].
Frank S. Henyey, Terry E. Ewart; Validity of the Markov approximation in ocean acoustics. J. Acoust. Soc. Am. 1 January 2006; 119 (1): 220–231. https://doi.org/10.1121/1.2130963
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